Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Precalculus
14AYUIn Problems 15-20, find the distance from P 1 to P 2 . P 1 =( 0,0,0 ) and P 2 =( 4,1,2 )In Problems 15-20, find the distance from P 1 to P 2 . P 1 =( 0,0,0 ) and P 2 =( 1,2,3 )In Problems 15-20, find the distance from P 1 to P 2 . P 1 =( 1,2,3 ) and P 2 =( 0,2,1 )In Problems 15-20, find the distance from P 1 to P 2 . P 1 =( 2,2,3 ) and P 2 =( 4,0,3 )In Problems 15-20, find the distance from P 1 to P 2 . P 1 =( 4,2,2 ) and P 2 =( 3,2,1 )In Problems 15-20, find the distance from P 1 to P 2 . P 1 =( 2,3,3 ) and P 2 =( 4,1,1 )In Problems 21-26, opposite vertices of a rectangular box whose edges are parallel to the coordinate axes are given. List the coordinates of the other six vertices of the box. ( 0,0,0 );( 2,1,3 )In Problems 21-26, opposite vertices of a rectangular box whose edges are parallel to the coordinate axes are given. List the coordinates of the other six vertices of the box. ( 0,0,0 );( 4,2,2 )In Problems 21-26, opposite vertices of a rectangular box whose edges are parallel to the coordinate axes are given. List the coordinates of the other six vertices of the box. ( 1,2,3 );( 3,4,5 )In Problems 21-26, opposite vertices of a rectangular box whose edges are parallel to the coordinate axes are given. List the coordinates of the other six vertices of the box. ( 5,6,1 );( 3,8,2 )In Problems 21-26, opposite vertices of a rectangular box whose edges are parallel to the coordinate axes are given. List the coordinates of the other six vertices of the box. ( 1,0,2 );( 4,2,5 )In Problems 21-26, opposite vertices of a rectangular box whose edges are parallel to the coordinate axes are given. List the coordinates of the other six vertices of the box. ( 2,3,0 );( 6,7,1 )In Problems 27-32, the vector v has initial point P and terminal point Q . Write v in the form ai+bj+ck ; that is, find its position vector. P=( 0,0,0 ) ; Q=( 3,4,1 )In Problems 27-32, the vector v s has initial point P and terminal point Q . Write v in the form ai+bj+ck ; that is, find its position vector. P=( 0,0,0 ) ; Q=( 3,5,4 )In Problems 27-32, the vector v has initial point P and terminal point Q . Write v in the form ai+bj+ck ; that is, find its position vector. P=( 3,2,1 ) ; Q=( 5,6,0 )In Problems 27-32, the vector v has initial point P and terminal point Q . Write v in the form ai+bj+ck ; that is, find its position vector. P=( 3,2,0 ) ; Q=( 6,5,1 )In Problems 27-32, the vector v has initial point P and terminal point Q . Write v in the form ai+bj+ck ; that is, find its position vector. P=( 2,1,4 ) ; Q=( 6,2,4 )In Problems 27-32, the vector v has initial point P and terminal point Q . Write v in the form ai+bj+ck ; that is, find its position vector. P=( 1,4,2 ) ; Q=( 6,2,2 )In Problems 33-38, find v . v=3i6j2kIn Problems 33-38, find v . v=6i+12j+4kIn Problems 33-38, find v . v=ij+kIn Problems 33-38, find v . v=ij+kIn Problems 33-38, find v . v=2i+3j3kIn Problems 33-38, find v . v=6i+2j2kIn Problems 39-44, find each quantity if v=3i5j+2k and w=2i+3j2k . 2v+3wIn Problems 39-44, find each quantity if v=3i5j+2k and w=2i+3j2k . 3v2wIn Problems 39-44, find each quantity if v=3i5j+2k and w=2i+3j2k . vwIn Problems 39-44, find each quantity if v=3i5j+2k and w=2i+3j2k . v+wIn Problems 39-44, find each quantity if v=3i5j+2k and w=2i+3j2k . v wIn Problems 39-44, find each quantity if v=3i5j+2k and w=2i+3j2k . v + w45AYUIn Problems 45-50, find the unit vector in the same direction as v . v=3jIn Problems 45-50, find the unit vector in the same direction as v . v=3i6j2kIn Problems 45-50, find the unit vector in the same direction as v . v=6i+12j+4kIn Problems 45-50, find the unit vector in the same direction as v . v=i+j+kIn Problems 45-50, find the unit vector in the same direction as v . v=2ij+k51AYU52AYU53AYU54AYU55AYU56AYU57AYU58AYU59AYU60AYU61AYU62AYU63AYU64AYU65AYU66AYU67AYU68AYU69AYU70AYU71AYU72AYU73AYU74AYU75AYU76AYU77AYU78AYU79AYU1AYUTrue or False For any vector v,vv=0 .3AYUTrue or False uv is a vector that is parallel to both uandv .5AYU6AYUIn Problems 7-14, find the value of each determinant. [ 3 4 1 2 ]In Problems 7-14, find the value of each determinant. [ 2 5 2 3 ]In Problems 7-14, find the value of each determinant. [ 6 5 2 1 ]In Problems 7-14, find the value of each determinant. [ 4 0 5 3 ]In Problems 7-14, find the value of each determinant. [ A B C 2 1 4 1 3 1 ]In Problems 7-14, find the value of each determinant. [ A B C 0 2 4 3 1 3 ]In Problems 7-14, find the value of each determinant. [ A B C 1 3 5 5 0 2 ]In Problems 7-14, find the value of each determinant. [ A B C 1 2 3 0 2 2 ]In Problems 15-22, find (a) vw , (b) wv , (c) ww , and (d) vv . v=2i3j+k w=3i2jkIn Problems 15-22, find (a) vw , (b) wv , (c) ww , and (d) vv . v=i+3j+2k w=3i2jkIn Problems 15-22, find (a) vw , (b) wv , (c) ww , and (d) vv . v=i+j w=2i+j+kIn Problems 15-22, find (a) vw , (b) wv , (c) ww , and (d) vv . v=i4j+2k w=3i+2j+kIn Problems 15-22, find (a) vw , (b) wv , (c) ww , and (d) vv . v=2ij+2k w=jkIn Problems 15-22, find (a) vw , (b) wv , (c) ww , and (d) vv . v=3i+j+3k w=ikIn Problems 15-22, find (a) vw , (b) wv , (c) ww , and (d) vv . v=ijk w=4i3kIn Problems 15-22, find (a) vw , (b) wv , (c) ww , and (d) vv . v=2i3j w=3j2kIn Problems 23-44, use the given vectors u,v,andw to find each expression. u=2i3j+kv=3i+3j+2kw=i+j+3k uvIn Problems 23-44, use the given vectors u,v,andw to find each expression. u=2i3j+kv=3i+3j+2kw=i+j+3k vwIn Problems 23-44, use the given vectors u,v,andw to find each expression. u=2i3j+kv=3i+3j+2kw=i+j+3k vuIn Problems 23-44, use the given vectors u,v,andw to find each expression. u=2i3j+kv=3i+3j+2kw=i+j+3k wvIn Problems 23-44, use the given vectors u,v,andw to find each expression. u=2i3j+kv=3i+3j+2kw=i+j+3k vvIn Problems 23-44, use the given vectors u,v,andw to find each expression. u=2i3j+kv=3i+3j+2kw=i+j+3k wwIn Problems 23-44, use the given vectors u,v,andw to find each expression. u=2i3j+kv=3i+3j+2kw=i+j+3k ( 3u )v30AYU31AYU32AYUIn Problems 23-44, use the given vectors u,v,andw to find each expression. u=2i3j+kv=3i+3j+2kw=i+j+3k u( uv )34AYUIn Problems 23-44, use the given vectors u,v,andw to find each expression. u=2i3j+kv=3i+3j+2kw=i+j+3k u( vw )36AYU37AYU38AYU39AYU40AYU41AYU42AYU43AYU44AYU45AYU46AYU47AYU48AYU49AYU50AYU51AYU52AYUFind a unit vector normal to the plane containing v=i+3j2kandw=2i+j+3kFind a unit vector normal to the plane containing v=2i+3jkandw=2i4j3k .Volume of a Parallelepiped A parallelepiped is a prism whose faces are all parallelograms. Let A,BandC be the vectors that define the parallelepiped shown in the figure. The volume V of the parallelepiped is given by the formula V=| ABC | . Find the volume of a parallelepiped if the defining vectors are A=3i2j+4k,B=2i+j2k,andC=3i6j2k .Volume of a Parallelepiped Refer to Problem 55. Find the volume of a parallelepiped whose defining vectors are A=i+6k,B=2i+3j8k,C=8i5j+6kProve for vectors uandv that uv 2 = u 2 v 2 ( uv ) 2 [Hint: Proceed as in the proof of property (4), computing first the left side and then the right side.]58AYUShow that if uandv are orthogonal unit vectors, then uv is also a unit vector.Prove property (3).Prove property (5).Prove property (9). [Hint: Use the result of Problem 57 and the fact that if the angle between uandv , then uv= u v cos .]63AYU1RE2RE3RE4RE5RE6RE7RE8RE9RE10RE11RE12RE13RE14RE15RE16RE17RE18RE19RE20RE21RE22RE23RE24RE25RE26RE27RE28RE29RE30RE31RE32RE33RE34RE35RE36RE37RE38RE39RE40RE41RE42RE43RE44RE45RE46RE47RE48RE49RE50RE51RE52RE53RE54RE55RE56RE57RE58RE59RE60RE61RE62RE63RE64RE65RE66RE67RE68RE69RE70RE71RE72RE73RE74RE75RE76RE77RE78RE79RE80RE81RE82RE83RE84REIn Problems 13, identify each equation. If it is a parabola, give its vertex, focus, and directrix; if an ellipse, give its center, vertices, and foci; if a hyperbola, give its center, vertices, foci, and asymptotes. (x+1)24y29=1In Problems 13, identify each equation. If it is a parabola, give its vertex, focus, and directrix; if an ellipse, give its center, vertices, and foci; if a hyperbola, give its center, vertices, foci, and asymptotes. 8y=(x1)24In Problems identify each equation. If it is a parabola, give its vertex, focus, and directrix; if an ellipse, give its center, vertices, and foci; if a hyperbola, give its center, vertices, foci, and asymptotes.
In Problems 46, find an equation of the conic described; graph the equation. Parabola: focus (1,4.5), vertex (1,3)In Problems find an equation of the conic described; graph the equation.
Ellipse: center vertex focus
In Problems find an equation of the conic described; graph the equation.
Hyperbola: center vertex contains the point
In Problems 79, identify each conic without completing the square or rotating axes. 2x2+5xy+3y2+3x7=0In Problems 79, identify each conic without completing the square or rotating axes. 3x2xy+2y2+3y+1=0In Problems identify each conic without completing the square or rotating axes.
10CT11CT12CTA parabolic reflector (paraboloid of revolution) is used by TV crews at football games to pick up the referees announcements, quarterback signals, and so on. A microphone is placed at the focus of the parabola. If a certain reflector is 4 feet wide and 1.5 feet deep, where should the microphone be placed ?For find
In the complex number system, solve the equation
For what numbers x is 6xx2 ?4CR5CR6CR7CR8CR9CR10CRSolve the equation where.
Find the rectangle equation of the plane curve x(t)=5tanty(t)=5sec2t2t2The formula for the distance d from P 1 =( x 1 , y 1 ) to P 2 =( x 2 , y 2 ) is d= _______.(p.4)To complete the square of x 2 4x , add_______ .(pp. A28-A29)Use the Square Root Method to find the real solutions of ( x+4 ) 2 =9 .(p.A48)The point that is symmetric with respect to the x-axis to the point is_______. (pp.19-21)To graph y= ( x3 ) 2 +1 , shift the graph of y= x 2 to the right_____units and then ______1 unit.(pp. 106-114) _________ is the collection of all points in a plane that are same distance from a fixed point as they are from a fixed line. The line through the focus and perpendicular to the directrix is called the __________ of the parabola.
7AYU8AYU9AYU10AYUIn Problems 13-20, the graph of a parabola is given. Match each graph to its equation. (A) y 2 =4x (C) y 2 =4x (E) ( y1 ) 2 =4( x1 ) (G) ( y1 ) 2 =4( x1 ) (B) x 2 =4y (D) x 2 =4y (F) ( x+1 ) 2 =4( y+1 ) (H) ( x+1 ) 2 =4( y+1 )In Problems 13-20, the graph of a parabola is given. Match each graph to its equation. (A) y 2 =4x (C) y 2 =4x (E) ( y1 ) 2 =4( x1 ) (G) ( y1 ) 2 =4( x1 ) (B) x 2 =4y (D) x 2 =4y (F) ( x+1 ) 2 =4( y+1 ) (H) ( x+1 ) 2 =4( y+1 )In Problems 13-20, the graph of a parabola is given. Match each graph to its equation. (A) y 2 =4x (C) y 2 =4x (E) ( y1 ) 2 =4( x1 ) (G) ( y1 ) 2 =4( x1 ) (B) x 2 =4y (D) x 2 =4y (F) ( x+1 ) 2 =4( y+1 ) (H) ( x+1 ) 2 =4( y+1 )In Problems 13-20, the graph of a parabola is given. Match each graph to its equation. (A) y 2 =4x (C) y 2 =4x (E) ( y1 ) 2 =4( x1 ) (G) ( y1 ) 2 =4( x1 ) (B) x 2 =4y (D) x 2 =4y (F) ( x+1 ) 2 =4( y+1 ) (H) ( x+1 ) 2 =4( y+1 )In Problems 13-20, the graph of a parabola is given. Match each graph to its equation. (A) y 2 =4x (C) y 2 =4x (E) ( y1 ) 2 =4( x1 ) (G) ( y1 ) 2 =4( x1 ) (B) x 2 =4y (D) x 2 =4y (F) ( x+1 ) 2 =4( y+1 ) (H) ( x+1 ) 2 =4( y+1 )In Problems 13-20, the graph of a parabola is given. Match each graph to its equation. (A) y 2 =4x (C) y 2 =4x (E) ( y1 ) 2 =4( x1 ) (G) ( y1 ) 2 =4( x1 ) (B) x 2 =4y (D) x 2 =4y (F) ( x+1 ) 2 =4( y+1 ) (H) ( x+1 ) 2 =4( y+1 )In Problems 13-20, the graph of a parabola is given. Match each graph to its equation. (A) y 2 =4x (C) y 2 =4x (E) ( y1 ) 2 =4( x1 ) (G) ( y1 ) 2 =4( x1 ) (B) x 2 =4y (D) x 2 =4y (F) ( x+1 ) 2 =4( y+1 ) (H) ( x+1 ) 2 =4( y+1 )In Problems 13-20, the graph of a parabola is given. Match each graph to its equation. (A) y 2 =4x (C) y 2 =4x (E) ( y1 ) 2 =4( x1 ) (G) ( y1 ) 2 =4( x1 ) (B) x 2 =4y (D) x 2 =4y (F) ( x+1 ) 2 =4( y+1 ) (H) ( x+1 ) 2 =4( y+1 )In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand. Focus at ( 4,0 ) ; vertex at ( 0,0 )In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand. Focus at ( 0,2 ) ; vertex at ( 0,0 )In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand. Focus at ( 0,3 ) ; vertex at ( 0,0 )In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand. Focus at ( 4,0 ) ; vertex at ( 0,0 )In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand. Focus at ( 2,0 ) ; directrix the line x=2In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand. Focus at ( 0,1 ) ; directrix the line y=1In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand. Directrix the line y= 1 2 ; vertex at ( 0,0 )In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand. Directrix the line x= 1 2 ; vertex at ( 0,0 )In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand. Vertex at ( 0,0 ) ; axis of symmetry the y-axis ; containing the point ( 2,3 )In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand. Vertex at ( 0,0 ) ; axis of symmetry the x-axis ; containing the point ( 2,3 )In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand. Vertex at ( 2,3 ) ; focus at ( 2,5 )In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand. Vertex at ( 4,2 ) ; focus at ( 6,2 )In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand. Vertex at ( 1,2 ) ; focus at ( 0,2 )In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand. Vertex at ( 3,0 ) ; focus at ( 3,2 )In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand. Vertex at ( 3,4 ) ; directrix the line y=2In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand. Vertex at ( 2,4 ) ; directrix the line x=4In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand. Focus at ( 3,2 ) ; directrix the line x=1In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand. Focus at ( 4,4 ) ; directrix the line y=2In Problems , find the vertex, focus, and directrix of each parabola. Graph the equation.
In Problems 3956, find the vertex, focus, and directrix of each parabola. Graph the equation. y2=8xIn Problems , find the vertex, focus, and directrix of each parabola. Graph the equation.
In Problems 3956, find the vertex, focus, and directrix of each parabola. Graph the equation. x2=4yIn Problems , find the vertex, focus, and directrix of each parabola. Graph the equation.
In Problems , find the vertex, focus, and directrix of each parabola. Graph the equation.
In Problems , find the vertex, focus, and directrix of each parabola. Graph the equation.
In Problems 3956, find the vertex, focus, and directrix of each parabola. Graph the equation. (y+1)2=4(x2)In Problems , find the vertex, focus, and directrix of each parabola. Graph the equation.
In Problems , find the vertex, focus, and directrix of each parabola. Graph the equation.
In Problems , find the vertex, focus, and directrix of each parabola. Graph the equation.
In Problems 3956, find the vertex, focus, and directrix of each parabola. Graph the equation. x2+6x4y+1=0In Problems , find the vertex, focus, and directrix of each parabola. Graph the equation.
In Problems , find the vertex, focus, and directrix of each parabola. Graph the equation.
In Problems , find the vertex, focus, and directrix of each parabola. Graph the equation.
In Problems 3956, find the vertex, focus, and directrix of each parabola. Graph the equation. x24x=2yIn Problems , find the vertex, focus, and directrix of each parabola. Graph the equation.
In Problems , find the vertex, focus, and directrix of each parabola. Graph the equation.
In Problems 57-64, write an equation for each parabola.In Problems 57-64, write an equation for each parabola.In Problems 57-64, write an equation for each parabola.In Problems 57-64, write an equation for each parabola.In Problems 57-64, write an equation for each parabola.In Problems 57-64, write an equation for each parabola.In Problems 57-64, write an equation for each parabola.In Problems 57-64, write an equation for each parabola.