Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Precalculus
For Exercises 67-84, solve the equation. (See Examples 7-8) w+34w+1=w5wFor Exercises 67-84, solve the equation. (See Examples 7-8) x+26x+1=x7xFor Exercises 67-84, solve the equation. (See Examples 7-8) cc3=3c334For Exercises 67-84, solve the equation. (See Examples 7-8) 7d778=dd7For Exercises 67-84, solve the equation. (See Examples 7-8) 2x51x+5=11x225For Exercises 67-84, solve the equation. (See Examples 7-8) 2c+31c3=10c29For Exercises 67-84, solve the equation. (See Examples 7-8) 14x2x121x4=2x+3For Exercises 67-84, solve the equation. (See Examples 7-8) 2x2+5x+62x+2=1x+3For Exercises 67-84, solve the equation. (See Examples 7-8) 5x2x22x24=4x2+3x+2For Exercises 67-84, solve the equation. (See Examples 7-8) 4x22x81x216=2x2+6x+8For Exercises 67-84, solve the equation. (See Examples 7-8) 3xx+25x4=2x214xx22x8For Exercises 67-84, solve the equation. (See Examples 7-8) 4cc51c+1=3c2+3c24c5For Exercises 67-84, solve the equation. (See Examples 7-8) m2m+1+1=2m3For Exercises 67-84, solve the equation. (See Examples 7-8) 7+20z=3z2For Exercises 67-84, solve the equation. (See Examples 7-8) 18m23m+2=6m3For Exercises 67-84, solve the equation. (See Examples 7-8) 48m24m+3=12m4For Exercises 85-102, solve the equations. (See Examples 9 and 10) a.p=6b.p=0c.p=6For Exercises 85-102, solve the equations. (See Examples 9 and 10) a.w=2b.w=0c.w=2For Exercises 85-102, solve the equations. (See Examples 9 and 10) a.x3=4b.x3=0c.x3=7For Exercises 85-102, solve the equations. (See Examples 9 and 10) a.m+1=5b.m+1=0c.m+1=1For Exercises 85-102, solve the equations. (See Examples 9 and 10) 23x4+7=9For Exercises 85-102, solve the equations. (See Examples 9 and 10) 42t+7+2=22For Exercises 85-102, solve the equations. (See Examples 9 and 10) 3=c7+1For Exercises 85-102, solve the equations. (See Examples 9 and 10) 4=z+83For Exercises 85-102, solve the equations. (See Examples 9 and 10) 2=8+11y+4For Exercises 85-102, solve the equations. (See Examples 9 and 10) 6=7+9z3For Exercises 85-102, solve the equations. (See Examples 9 and 10) 3y+5=y+1For Exercises 85-102, solve the equations. (See Examples 9 and 10) 2a3=a+2For Exercises 85-102, solve the equations. (See Examples 9 and 10) 14w=4wFor Exercises 85-102, solve the equations. (See Examples 9 and 10) 3z=13zFor Exercises 85-102, solve the equations. (See Examples 9 and 10) x+4=x7For Exercises 85-102, solve the equations. (See Examples 9 and 10) k3=k+3For Exercises 85-102, solve the equations. (See Examples 9 and 10) 2p1=12pFor Exercises 85-102, solve the equations. (See Examples 9 and 10) 4d3=34dFor Exercises 103-122, solve the equation. (See Examples 11-13) 1=2+2x+7For Exercises 103-122, solve the equation. (See Examples 11-13) 6=9+53xFor Exercises 103-122, solve the equation. (See Examples 11-13) m+18+2=mFor Exercises 103-122, solve the equation. (See Examples 11-13) 2n+29+3=nFor Exercises 103-122, solve the equation. (See Examples 11-13) 42x53+6=10For Exercises 103-122, solve the equation. (See Examples 11-13) 34x15+2=8For Exercises 103-122, solve the equation. (See Examples 11-13) 8pp+5=1For Exercises 103-122, solve the equation. (See Examples 11-13) d+46+2d=1For Exercises 103-122, solve the equation. (See Examples 11-13) 3y+3=2yFor Exercises 103-122, solve the equation. (See Examples 11-13) k2=2k+32For Exercises 103-122, solve the equation. (See Examples 11-13) 2x+52/3=18For Exercises 103-122, solve the equation. (See Examples 11-13) 3x62/3=48For Exercises 103-122, solve the equation. (See Examples 11-13) 3x+13/2+2=66For Exercises 103-122, solve the equation. (See Examples 11-13) 2x13/23=122For Exercises 103-122, solve the equation. (See Examples 11-13) m3/4=5For Exercises 103-122, solve the equation. (See Examples 11-13) n5/6=3For Exercises 103-122, solve the equation. (See Examples 11-13) 2p4/5=18For Exercises 103-122, solve the equation. (See Examples 11-13) 5t2/3=15For Exercises 103-122, solve the equation. (See Examples 11-13) 2v+71/3v31/3=0For Exercises 103-122, solve the equation. (See Examples 11-13) 5u61/53u+11/5=0For Exercises 123-152, solve for the specified variable. (See Examples 14-15) A=lwforlFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) E=IRforRFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) P=a+b+cforcFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) W=KTforKFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) 7x+2y=8foryFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) 3x+5y=15foryFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) 5x4y=2foryFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) 7x2y=5foryFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) S=n2(a+d)fordFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) S=n2[2a+(n1)d]foraFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) 6=4x+txforxFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) 8=3x+kxforxFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) 6x+ay=bx+5forxFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) 3x+2y=cx+dforxFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) A=r2forr0For Exercises 123-152, solve for the specified variable. (See Examples 14-15) V=r2hforr0For Exercises 123-152, solve for the specified variable. (See Examples 14-15) a2+b2=c2fora0For Exercises 123-152, solve for the specified variable. (See Examples 14-15) a2+b2+c2=d2forc0For Exercises 123-152, solve for the specified variable. (See Examples 14-15) kw2cw=rforwFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) dy2+my=pforyFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) s=v0t+12at2fortFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) S=2rh+r2hforrFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) 1f=1p+1qforpFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) 1R=1R1+1R2+1R3forR3For Exercises 123-152, solve for the specified variable. (See Examples 14-15) 16+x2y2=zforxFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) 4+x2+y2=zforyFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) P1V1T1=P2V2T2forT1For Exercises 123-152, solve for the specified variable. (See Examples 14-15) t1s1v1=t2s2v2forv2For Exercises 123-152, solve for the specified variable. (See Examples 14-15) T=2LgforgFor Exercises 123-152, solve for the specified variable. (See Examples 14-15) t=2sgforsFor Exercises 153-156, solve the equation. 3x2x1x+62=0For Exercises 153-156, solve the equation. 5y3y4y+12=0For Exercises 153-156, solve the equation. 98t349t28t+4=0For Exercises 153-156, solve the equation. 2m3+3m2=92m+3Explain why the value 5 is not a solution xx5+15=5x5 .Explain why the value 2 is not the only solution to the equation 2x+4=2x3+10 .For Exercises 159-160, solve for the indicated variable. x2xy2y2=0forxFor Exercises 159-160, solve for the indicated variable. 3a2+2abb2=0foraFor Exercises 161-166, write an equation with integer coefficients and the variable x that has the given solution set. 4,2For Exercises 161-166, write an equation with integer coefficients and the variable x that has the given solution set. 7,1For Exercises 161-166, write an equation with integer coefficients and the variable x that has the given solution set. 23,14For Exercises 161-166, write an equation with integer coefficients and the variable x that has the given solution set. 35,17For Exercises 161-166, write an equation with integer coefficients and the variable x that has the given solution set. 5,5For Exercises 161-166, write an equation with integer coefficients and the variable x that has the given solution set. 2,2Write each expression in terms of i . a.81b.50c.11Simplify. a.i13b.i103c.i64d.i30Perform the indicated operations. Write the answer in the form a+bi. 83i2+4i+5+7iMultiply. Write the result in the form a+bi . 5+4i3iMultiply. Write the result in the form a+bi. a.47i2b.103i10+3i6SPSolve the equation by applying the square root property. 2c2+80=0.Solve the equation by applying the quadratic formula. 512x212x+14=09SP10SPSolve. 2t2/3=157t1/3The imaginary number i is defined so that i=1andi2=.For a positive real number b, the value b=.Given a complex number a+bi , the value of a is called the part and the value of b is called the part.Given a complex number a+bi , the expression abi is called the complex .The equation m2/3+10m1/3+9=0 is said to be in form, because making the substitution u= results in a new equation that is quadratic.Consider the equation 4x2+12+44x2+1+4=0. if the substitution u= is made, then the equation becomes u2+4u+4=0.For Exercises 7-18, write each expression in terms of i and simplify. (See Example 1) 121For Exercises 7-18, write each expression in terms of i and simplify. (See Example 1) 100For Exercises 7-18, write each expression in terms of i and simplify. (See Example 1) 9810PEFor Exercises 7-18, write each expression in terms of i and simplify. (See Example 1) 49For Exercises 7-18, write each expression in terms of i and simplify. (See Example 1) 136For Exercises 7-18, write each expression in terms of i and simplify. (See Example 1) 105For Exercises 7-18, write each expression in terms of i and simplify. (See Example 1) 615For Exercises 7-18, write each expression in terms of i and simplify. (See Example 1) 982For Exercises 7-18, write each expression in terms of i and simplify. (See Example 1) 455For Exercises 7-18, write each expression in terms of i and simplify. (See Example 1) 63718PEFor Exercises 19-26, simplify each expression and write the result in standard form, a+bi. 8+3i14For Exercises 19-26, simplify each expression and write the result in standard form, a+bi. 4+5i6For Exercises 19-26, simplify each expression and write the result in standard form, a+bi. 46i2For Exercises 19-26, simplify each expression and write the result in standard form, a+bi. 915i3For Exercises 19-26, simplify each expression and write the result in standard form, a+bi. 18+484For Exercises 19-26, simplify each expression and write the result in standard form, a+bi. 20+5010For Exercises 19-26, simplify each expression and write the result in standard form, a+bi. 14987For Exercises 19-26, simplify each expression and write the result in standard form, a+bi. 10+1255For Exercises 27-30, simplify the powers of i. (See Example 2) a.i20b.i29c.i50d.i4128PEFor Exercises 27-30, simplify the powers of i. (See Example 2) a.i37b.i37c.i82d.i82For Exercises 27-30, simplify the powers of i. (See Example 2) a.i103b.i103c.i52d.i52For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi. (See Examples 3-6) 27i+83i32PEFor Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi. (See Examples 3-6) 15+21i1840iFor Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi. (See Examples 3-6) 250+100i80+25iFor Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi. (See Examples 3-6) 2.3+4i8.12.7i+4.66.7i36PEFor Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi. (See Examples 3-6) 2i5+i38PEFor Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi. (See Examples 3-6) 36i10+iFor Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi. (See Examples 3-6) 25i8+2iFor Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi. (See Examples 3-6) 37i2For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi. (See Examples 3-6) 103i2For Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi. (See Examples 3-6) 354+544PEFor Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi. (See Examples 3-6) 2i2+2+i246PEFor Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi. (See Examples 3-6) 104i10+4iFor Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi. (See Examples 3-6) 39i3+9iFor Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi. (See Examples 3-6) 2+3i23iFor Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi. (See Examples 3-6) 5+7i57iFor Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi. (See Examples 3-6) 6+2i3i52PEFor Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi. (See Examples 3-6) 85i13+2iFor Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi. (See Examples 3-6) 103i11+4iFor Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi. (See Examples 3-6) 513iFor Exercises 31-56, perform the indicated operations. Write the answers in standard form, a+bi. (See Examples 3-6) 67iFor Exercises 57-72, solve the equations. (See Examples 7-8) 4u2+64=0For Exercises 57-72, solve the equations. (See Examples 7-8) 8p2+72=0For Exercises 57-72, solve the equations. (See Examples 7-8) t122=174For Exercises 57-72, solve the equations. (See Examples 7-8) a132=479For Exercises 57-72, solve the equations. (See Examples 7-8) t28t=24For Exercises 57-72, solve the equations. (See Examples 7-8) p224p=156For Exercises 57-72, solve the equations. (See Examples 7-8) 4z2+24z=160For Exercises 57-72, solve the equations. (See Examples 7-8) 2m2+20m=70For Exercises 57-72, solve the equations. (See Examples 7-8) y2=4y6For Exercises 57-72, solve the equations. (See Examples 7-8) z2=8z19For Exercises 57-72, solve the equations. (See Examples 7-8) tt6=10For Exercises 57-72, solve the equations. (See Examples 7-8) mm+10=34For Exercises 57-72, solve the equations. (See Examples 7-8) 76c+12=56c2For Exercises 57-72, solve the equations. (See Examples 7-8) 52d+1=3d2For Exercises 57-72, solve the equations. (See Examples 7-8) 9x2+49=0For Exercises 57-72, solve the equations. (See Examples 7-8) 121x2+4=0For Exercises 73-80, (a) evaluate the discriminant and (b) determine the number and type of solutions to each equation. (See Example 9) 3x24x+6=0For Exercises 73-80, (a) evaluate the discriminant and (b) determine the number and type of solutions to each equation. (See Example 9) 5x22x+4=0For Exercises 73-80, (a) evaluate the discriminant and (b) determine the number and type of solutions to each equation. (See Example 9) 2w2+8w=3For Exercises 73-80, (a) evaluate the discriminant and (b) determine the number and type of solutions to each equation. (See Example 9) 6d2+9d=2For Exercises 73-80, (a) evaluate the discriminant and (b) determine the number and type of solutions to each equation. (See Example 9) 3xx4=x4For Exercises 73-80, (a) evaluate the discriminant and (b) determine the number and type of solutions to each equation. (See Example 9) 2xx2=x+3For Exercises 73-80, (a) evaluate the discriminant and (b) determine the number and type of solutions to each equation. (See Example 9) 1.4m+0.1=4.9m2For Exercises 73-80, (a) evaluate the discriminant and (b) determine the number and type of solutions to each equation. (See Example 9) 3.6n+0.4=8.1n2For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11) 2x+5272x+530=0For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11) 3x7263x716=0For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11) x2+2x218x2+2x=45For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11) x2+3x214x2+3x=40For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11) x2+22+x2+242=0For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11) y2329y2352=0For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11) m10m26n10m27=0For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11) x+6x212x+6x+35=0For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11) 2+3t22+3t=12For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11) 5y+32+65y+3=8For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11) 5c2511c15+2=0For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11) 3d23d134=0For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11) y12y146=0For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11) n12+6n1416=0For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11) 9y410y2+1=0For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11) 100x429x2+1=0For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11) 4t25t=0For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11) 9m16m=0For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11) 30k223k1+2=0For Exercises 81-100, make an appropriate substitution and solve the equation. (See Examples 10-11) 3q2+16q1+5=0For Exercises 101-104, verify by substitution that the given values of x are solutions to the given equation. x2+25=0a.x=5ib.x=5iFor Exercises 101-104, verify by substitution that the given values of x are solutions to the given equation. x2+49=0a.x=7ib.x=7iFor Exercises 101-104, verify by substitution that the given values of x are solutions to the given equation. x24x+7=0a.x=2+i3b.x=2i3For Exercises 101-104, verify by substitution that the given values of x are solutions to the given equation. x26x+11=0a.x=3+i2b.x=3i2Prove thata+bic+di=acbd+ad+bci.Prove that a+bi2=a2b2+2abi.For Exercises 107-108, solve the equation in two ways. a. Solve as a radical equation by first isolating the radical. b. Solve by writing the equation in quadratic in quadratic form and using an appropriate substitution. y+4y=21For Exercises 107-108, solve the equation in two ways. a. Solve as a radical equation by first isolating the radical. b. Solve by writing the equation in quadratic in quadratic form and using an appropriate substitution. w3w=10Explain the flaw in the following logic. 94=94=36=6Discuss the difference between the products a+babanda+biabi.Give an example of a complex number that is its own conjugate.Give an example of two complex numbers that are not real numbers, but whose product is a real number.Given a quadratic equation, what is the discriminant and what information does it provide about the given quadratic equation?Explain how to determine if an equation is in quadratic form.For Exercise 115-120, factor the expressions over the set of complex numbers. For assistance, consider these examples. InSectionR.3wesawthatsomeexpressionsfactoroverthesetofintegers.Forexample:x24=x+2x2.Someexpressionsfactoroverthesetofirrationalnumbers.Forexample:x25=x+5x5.Tofactoranexpressionsuchasx2+4,weneedtofactoroverthesetofcomplexnumbers.Forexample,verifythatx2+4=x+2ix2i. a.x29b.x2+9For Exercise 115-120, factor the expressions over the set of complex numbers. For assistance, consider these examples. InSectionR.3wesawthatsomeexpressionsfactoroverthesetofintegers.Forexample:x24=x+2x2.Someexpressionsfactoroverthesetofirrationalnumbers.Forexample:x25=x+5x5.Tofactoranexpressionsuchasx2+4,weneedtofactoroverthesetofcomplexnumbers.Forexample,verifythatx2+4=x+2ix2i. a.x2100b.x2+100For Exercise 115-120, factor the expressions over the set of complex numbers. For assistance, consider these examples. InSectionR.3wesawthatsomeexpressionsfactoroverthesetofintegers.Forexample:x24=x+2x2.Someexpressionsfactoroverthesetofirrationalnumbers.Forexample:x25=x+5x5.Tofactoranexpressionsuchasx2+4,weneedtofactoroverthesetofcomplexnumbers.Forexample,verifythatx2+4=x+2ix2i. a.x264b.x2+64For Exercise 115-120, factor the expressions over the set of complex numbers. For assistance, consider these examples. InSectionR.3wesawthatsomeexpressionsfactoroverthesetofintegers.Forexample:x24=x+2x2.Someexpressionsfactoroverthesetofirrationalnumbers.Forexample:x25=x+5x5.Tofactoranexpressionsuchasx2+4,weneedtofactoroverthesetofcomplexnumbers.Forexample,verifythatx2+4=x+2ix2i. a.x225b.x2+25For Exercise 115-120, factor the expressions over the set of complex numbers. For assistance, consider these examples. InSectionR.3wesawthatsomeexpressionsfactoroverthesetofintegers.Forexample:x24=x+2x2.Someexpressionsfactoroverthesetofirrationalnumbers.Forexample:x25=x+5x5.Tofactoranexpressionsuchasx2+4,weneedtofactoroverthesetofcomplexnumbers.Forexample,verifythatx2+4=x+2ix2i. a.x23b.x2+3For Exercise 115-120, factor the expressions over the set of complex numbers. For assistance, consider these examples. InSectionR.3wesawthatsomeexpressionsfactoroverthesetofintegers.Forexample:x24=x+2x2.Someexpressionsfactoroverthesetofirrationalnumbers.Forexample:x25=x+5x5.Tofactoranexpressionsuchasx2+4,weneedtofactoroverthesetofcomplexnumbers.Forexample,verifythatx2+4=x+2ix2i. a.x211b.x2+11For Exercise 121-124, write an equation with integer coefficients and the variable x that has the given solution set. 2i,2iFor Exercise 121-124, write an equation with integer coefficients and the variable x that has the given solution set. 9i,9iFor Exercise 121-124, write an equation with integer coefficients and the variable x that has the given solution set. 12iFor Exercise 121-124, write an equation with integer coefficients and the variable x that has the given solution set. 29iFranz borrowed a total of $10,000 . Part of the money was borrowed from a lending institution that charged 5.5 simple interest. The rest of the money was borrowed from a friend to whom Franz paid 2.5 simple interest. Franz paid his friend back after 9 months (0.75 yr) and paid the lending institution after 2 yr. If the total amount Franz paid in interest was $735 , how much did he borrow from each source?How much 4 acid solution should be mixed with 200mL of a 12 acid solution to make a 9 acid solution?A fishing boat can travel 60km with a 2.5-km/hr current in 2 hr less time than it can travel 60 km against the current. Determine the speed of the fishing boat in still water.Sheldon and Penny were awarded a contract to paint 16 offices in the new math building at a university. Once all the preparation work is complete, Sheldon can paint an office in 30 min and Penny can paint an office in 45 min. a. How long would it take them to paint one office working together? b. How long would it take them to paint all 16 offices?A sail on a sailboat is in the shape of two adjacent right triangles. The hypotenuse of the lower triangle is 10 ft, and one leg is 2 ft shorter than the other leg. Find the lengths of the legs of the lower triangle.A fireworks mortar is launched straight upward from a pool deck 2 m off the ground at an initial velocity of 40 m/sec. a. Write a model to express the height of the mortar s (in meters) above ground level. b. Find the time(s) at which the mortar is at a height of 60 m. Round to 1 decimal place. c. Find the time(s) at which the rocket is at a height of 100 m.If $6000 is borrowed at 7.5 simple interest for 2 yr, then the amount of interest is.Suppose that 8 of a solution is fertilizer by volume and the remaining 92% is water. How much fertilizer is in a 2-L bucket of solution?If d=rt,thent=If d=rt,thenr=Rocco borrowed a total of $5000 from two student loans. One loan charged 3% simple interest and the other charged 2.5% simple interest, both payable after graduation. If the interest he owed after 1 yr was $132.50 , determine the amount of principle for each loan. (See Example 1)Laura borrowed a total of $22,000 from two different banks to start a business. One bank charged the equivalent of 4 simple interest, and the other charged 5.5 interest. If the total interest after 1 yr was $910 , determine the amount borrowed from each bank.Fernando invest money in a 3-yr CD (certificate of deposit) that returned the equivalent of 4.4% simple interest. He invested $2000 less in an 18-month CD that had a 3% return. If the total amount of interest from these investments was $706.50 , determine how much was invested in each CD.Ebony bought a 5-yr Treasury note that paid the equivalent of 2.8% simple interest. she invested $5000 more in a 10-yr bond earning 3.6% than she did in the Treasury note. If the total amount of interest from these investments was $5300 , determine the amount of principal for each investment.Ethanol fuel mixture have "E" number that indicate the percentage of ethanol in the mixture by volume. For example, E10 is a mixture of 10 ethanol and 90 gasoline. How much E5 should be mixed with 5000 gal of E10 to make an E9 mixture? (See Example 2)A nurse mixes 60 cc of a 50 saline solution with a 10% saline solution to produce a 25% saline solution. How much of the 10% solution should he use?The density and strength of concrete are determined by the ratio of cement and aggregate (aggregate is sand, or crushed stone). Suppose that a contractor has 480 ft3 of dry concentrate mixture that is 70 sand by volume. How much pure sand must be added to form a new mixture that is 75 sand by volume?Antifreeze is a compound added to water to reduce the freezing point of a mixture. In extreme cold (less than 35F ), one car manufacturer recommends that a mixture of 65 antifreeze be used. How much 50 antifreeze solution should be drained from a 4-gal tank and replaced with pure antifreeze to produce a 65 antifreeze mixture?Jesse takes a 3-day kayak trip and travels 72 km south from Everglades City to a camp area in Everglades National Park. The trip to the camp area with a 2-km/hr current takes 9 hr less time than the return trip against the current. Find the speed that Jesse travels in still water. (See Example 3)A plane travels 800 mi from Dallas, Texas, to Atlanta, Georgia, with a prevailing west wind of 40 mph. The return trip against the wind takes 12 hr longer. Find the average speed of the plane in still air.Jean runs 6 mi and then rides 24 mi on her bicycle in a biathlon. She rides 8 mph faster than she runs. If the total time for her to complete the race is 2.25 hr, determine her average speed running and her average speed riding her bicycle.Barbara drives between Miami, Florida, and West Palm Beach, Florida. She drives 50 mi in clear weather and then encounters a thunderstorm for the last 15 mi. She drives 20 mph slower through the thunderstorm than she does in clear weather. If the total time for the trip is 1.5 hr, determine her average speed in nice weather and her average speed driving in the thunderstorm.Two passengers leave the airport at Kansas City, Missouri. One flies to Los Angeles, California, in 3.4 hr and the other flies in the opposite direction to New York City in 2.4 hr. With prevailing westerly winds, the speed of the plane to New York City is 60 mph faster than the speed of the plane to Los Angeles. If the total distance traveled by both planes is 2464 mi, determine the average speed of each plane.Two planes leave from Atlanta Georgia. One makes a 5.2-hr flight to Seattle, Washington, and the other makes a 2.5-hr flight to Boston, Massachusetts. The plane to Boston averages 44 mph slower than the plane to Seattle. If the total distance travelled by both planes is 3124 mi, determine the average speed of each plane.Darren drives to school in rush hour traffic and averages 32 mph. He returns home in mid-afternoon when there is less traffic and averages 48 mph. What is the distance between his home and school if the total traveling time is 1 hr 15 min?Peggy competes in a biathlon by running and bicycling around a large loop through a city. She runs the loop one time and bicycles the loop five times. She can run 8 mph and she can ride 16 mph. If the total time it takes her to complete the race is 1 hr 45 min, determine the distance of the loop.Joel can run around a 14mi track in 66 sec, and Jason can run around the track in 60 sec. If the runners start at the same point on the track and run in opposite directions, how long will it take the runners to cover 14mi ? (See Example 4)Marta can vacuum the house in 40 min. It takes her daughter 1 hr to vacuum the house. How long would it take them if they worked together?One pump can fill a pool in 10 hr. Working with a second slower pump, the two pumps together can fill the pool in 6 hr. How fast can the second pump fill the pool by itself?Brad and Angelina can mow their yard together with two lawn mowers in 30 min. When Brad works alone, it takes him 50 min. How long would it take Angelina to mow the lawn by herself?A patio is configured from a rectangle with two right triangles of equal size attached at the two ends. The length of the rectangle is 20 ft. The base of the right triangle is 3 ft less than the height of the triangle. If the total area of the patio is 348ft2 , determine the base and height of the triangular portions.The front face of a house is in the shape of a rectangle with a Queen post roof truss above. The length of the rectangle region is 3 times the height of the truss. The height of the rectangle is 2 ft more than the height of the truss. If the total area of the front face of the house is 336ft2 , determine the length and width of the rectangular region.A baseball diamond is in the shape of a square with 90-ft sides. How far is it from home plate to second base? Give the extract value and give an approximation to the nearest tenth of a foot.The figure is a cube with 6-in. sides. Find the extract length of the diagonal through the interior of the cube d by following these steps. a. Apply the Pythagorean theorem using the sides on the base of the cube to find the length of diagonal c. b. Apply the Pythagorean theorem using c and the height of the cube as the legs of the right tringle through the interior of the cube.The sail on a sailboat is in the shape of two adjacent right triangles. In the lower triangle, the shorter leg is 2 ft less than the longer leg. The hypotenuse is 2 ft more than the longer leg. (See Example 5) a. Find the length of the sides of the lower tringle. b. Find the total sail area.A portion of a roof truss is given in the figure. The tringle on the left is configured such that the longer leg is 7 ft longer than the shorter leg, and the hypotenuse is 1 ft more than twice the shorter leg. a. Find the lengths of the sides of the tringle on the left. b. Find the lengths of the sides of the tringle on the right.The display area on a cell phone has a 3.5-in. diagonal. a. If the aspect ratio of length to width is 1.5 to 1, determine the length and width of the display area. Round the values to the nearest hundredth of inch. b. If the phone has 326 pixels per inch, approximate the dimension in pixels.The display area on a computer has a 15-in. diagonal. If the aspect ratio of length to width is 1.6 to 1, determine the length and width of the display area. Round the values to the nearest hundredth of an inch.NBA basketball legend Michael Jordan had a 48-in. vertical leap. Suppose that Michael jumped from ground level with an initial velocity of 16 ft/sec. a. Write a model to express Michael's height (in ft) above ground level t seconds after leaving the ground. b. Use the model from part (a) to determine how long it would take Michael to reach his maximum height of 48 in. (4 ft).At the time of this printing, the highest vertical leap on record is 60 in., held by Kadour Ziani. For this record-setting jump, Kadour left the ground with an initial velocity of 85ft/sec. a. Write a model to express Kadour's height (in ft) above ground level t seconds after leaving the ground. b. Use the model from part (a) to determine how long it would take Kadour to reach his maximum height of 60 in. (5 ft). Round to the nearest hundredth of a second.A bad punter on a football team kicks a football approximately straight upward with an initial velocity of 75 ft/sec. a. If the ball leaves his foot from a height of 4 ft, write an equation for the vertical height s (in ft) of the ball t seconds after being kicked. b. Find the time(s) at which the ball is at a height of 80 ft. Round to 1 decimal place.In a classic Seinfeld episode, Jerry tosses a loaf of bread (a marble rye) straight upward to his friend George who is leaning out of a third-story window. a. If the loaf of bread leaves Jerry's hand at a height of 1 m with an initial velocity of 18 m/sec, write an equation for the vertical position of the bread s (in meters) t seconds after release. b. How long will it take the bread to reach George if he catches the bread on the way up at a height of 16 m? Round to the nearest tenth of a second.Suppose that 40 deer are introduced in a protected wilderness area. The population of the herd P can be approximated by P=40+20x1+0.05xr where x is the time in years since introducing the deer. Determine the time required for the deer population to reach 200.Starting from rest, an automobile's velocity v (in ft/sec) is given by v=180t2t+10r , where t is the time in seconds after the car begins forward motion. Determine the time required for the car to reach a speed of 60 ft/sec 41mph.Brianna's SUV gets 22 mpg in the city and 30 mpg on the highway. The amount of gas she uses A (in gal) is given by A=122c+130h , Where c is the number and h is the number of highway miles driven. If Brianna drove 165 mi on the highway and used 7 gal of gas, how many city miles did she drive?Dexter's truck gets 32 mpg on the highway and 24 mpg in the city. The amount of gas he uses A (in gal) is given by A=124C+132h, where c is the number of city miles driven and h is the number of highway miles driven. If Dexter drove 60 mi in the city and used 9 gal of gas, how many highway miles did he drive?At a construction site, cement sand, and gravel are mixed to make concrete. The ratio of cement to sand to gravel is 1 to 2.4 to 3.6. 1f a 150-lb bag of sand is used, how much cement and gravel must be used?The property tax on a $180,000 house is $1296 . At this rate, what is the property tax on a house tax is $240,000 ?In addition to measuring a person's individual HDL and LDL cholesterol levels, doctors also compute the ratio of total cholesterol to HDL cholesterol. Doctors recommend that the ratio of total cholesterol to HDL cholesterol be kept under 4. Suppose that the ratio of a patient's total cholesterol to HDL is 3.4 and her HDL is 60 mg/dL. Determine the patient's LDL level and total cholesterol. (Assume that total cholesterol is the sum of the LDL and HDL levels.)For a recent Congress, there were 10 more Democrats than Republicans in the U.S. Senate. This resulted in a ratio of 11 Democrats to 9 Republicans. How many senators were Democrat and how many were Republican?When studying wildlife populations, biologists sometimes use a technique called "mark-recapture." For example, a researcher captured and tagged 30 deer in a wildlife management area. Several months later, the researcher observed a new sample of 80 deer and determined that 5 were tagged. What is the total number of deer in the population?To estimate the number of bass in a lake, a biologist catches and tags 24 bass. Several weeks later, the biologist catches a new sample of 40 bass and finds that 4 are tagged. How many bass are in the lake?Seismographs can record two types of wave energy (P waves and S waves) that travel through the Earth after an earthquake. Traveling through granite, P waves travel approximately 5 km/sec and S waves travel approximately 3 km/sec. If a geologist working at a seismic station measures a time difference of 40 sec between an earthquake's P waves and S waves, how far from the epicenter of the earthquake is the station?Suppose that a shallow earthquake occurs in which the P waves travel 8 km/sec and the S waves travel 4.8 km/sec. If a seismologist measures a time difference of 20 sec between the arrival of the P waves and the S waves, how far is the seismologist from the epicenter of the earthquake?Henri needs to have a toilet repaired in his house. The cost of the new plumbing fixtures is $110 and labor is $60/hr. a. Write a model that represents the cost of the repair C (in $ ) in terms of the number of hours of labor x. b. After how many hours of labor would the cost of the repair job equal the cost of a new toilet of $350 ?After a hurricane, repairs to a roof will cost $2400 for materials and $80/hr in labor. a. Write a model that represents the cost of the repair C (in $ ) in terms of the number of hours of labor x. b. If an estimate for a new roof is $5520, after how many hours of labor would the cost to repair the roof equal the cost of a new roof?On moving day, Guyton needs to rent a truck. The length of the cargo space is 12 ft and the height is 1 ft less than the width. The brochure indicates that the truck can hold 504ft3 . What are the dimensions of the cargo space? Assume that the cargo space is in the shape of a rectangular solid. (See Example 1)Lorene Plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets of cardboard from which she cuts out 6-in. Squares from each corner. The length of the original piece of cardboard is 12 in. more than the width. If the volume of the box is 1728in.3 , determine the dimensions of the original piece of cardboard.The population P of a culture of Pseudomonas aeruginoso bacteria is given by P=1718t2+82,000t+10,000 , where t is the time in hours since the culture was started. Determine the time(s) at which the population was 600,000. Round to the nearest hour.The distance d (in ft) required to stop a car that was traveling at speed v (in mph) before the brakes were applied depends on the amount of friction between the tires and the road and the driver's reaction time. After an accident, a legal team hired an engineering firm to collect data for the stretch of road where the accident occurred. Based on the data, the stopping distance is given by d=0.05v2+2.2v. a. Determine the distance required to stop a car going 50 mph. b. Up to what speed (to the nearest mph) could a motorist be traveling and still have adequate stopping distance to avoid hitting a deer 330 ft away?Is it possible for the measures of the angles in a tringle to be represented by three consecutive odd integers? Explain.Bob wants to change a $100 bill into an equal number of $20 bills, $10 bills, and $5 bills. Is this possible? Explain.A golden rectangle is a rectangle in which the ratio of its length to its width is equal to the ratio of the sum of its length and width to its length: LW=L+WL (values of L and W that meet this condition are said to be in the golden ratio). a. Suppose that a golden rectangle has a width of 1 unit. Solve the equation to find the exact value for the length. Then give a decimal approximation to 2 decimal places. b. To create a golden rectangle with a width of 9 ft, what should be the length? Round to 1 decimal place.An artist has been commissioned to make a stained glass window in the shape of a regular octagon. The octagon must fit inside an 18-in. square space. Determine the length of each side of the octagon. Round to the nearest hundredth of an inch.A farmer has 160 yd of fencing material and wants to enclose three rectangular pens. Suppose that x represents the length of each pen and y represents the width as shown in the figure. a. Assuming that the farmer uses all 160 yd of fencing, write an expression for y in terms of x. b. Write an expression in terms of x for the area of one individual pen. c. If the farmer wants to design the structure so that each pen encloses 250yd2 , determine the dimensions of each pen.At noon, a ship leaves a harbor and sails south at 10 knots. Two hours later, a second ship leaves the harbor and sails east at 15 knots. When will the ships be 100 nautical miles apart? Round to the nearest minute.Pam is in a canoe on a lake 400 ft from the closest point on a straight shoreline. Her house is 800 ft up the road along the shoreline. She can row 2.5 ft/sec and she can walk 5 ft/sec. If the total time it takes for her to get home is 5 min (300 sec), determine the point along the shoreline at which she landed her canoe.