The region is bounded by the curve y = 6x – x² and y = x² – 2x –

Q: A graph of the function g(x) = sin (x) is shown. Use the graphing utility to sketch the graph of the…

A: Graph of the function g(x)=sin(x) is given

Q: Use synthetic division to divide. -4x3+ 23x2- 31x+ 12 4х — 3 -16x2+ 12x+ 16 -4x2- 12x+ 16 -x²+ 5x- 4…

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Q: Find the area bounded by these curves.

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Q: A kite, 120 ft above the ground, is moving horizontally at the rate of 10 ft/sec. At what rate is…

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Q: Write an equation of the plane with normal vector n= (2,8, -4) passing through the point (3,-9,-5)…

A: Vector equation of plane is used.

Q: Select the answer option that corresponds with polar coordinates (1, -). 90° W/2 150° 45 1 7 radians…

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Q: Find the area enclosed by the given parametric curve and the x-axis. x = 2 sin(t),  y = sin(t)…

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Q: Find the slope of the line 3x-4y-10=0 О а. 4/3 O b. 3/4 О с. 3 O d. 4

A: Solve the following

Q: f(x) = x* - 2x? ... Choose the correct graph below. O A. В. C. D. Ay 10- -40

A: Given query is to find the graph is the function.

Q: Find T(t) and N(t) at the given point. r(t) = 2 cos(t)i +2 sin(t)j + tk; t = 2 (), T. %3D ||

A: r(t)=(2 cos(t), 2 sin(t), t)r'(t)=-2sin(t), 2cos(t), 1r'(t)=4+1 =5T(t)=r(t)r'(t)T(t)=15-2sin(t),…

Q: Select the answer option that corresponds with polar coordinates (-1,-210\degree). 90° WIN 150° 4…

A: The given polar coordinates is (-1, -210°)

Q: D(X) is the price, in dollars per unit, that consumers are willing to pay for x units of an item,…

A: Here, the given functions are: D(x)=100x, S(x)=x

Q: x =r' +1, y =r -t = t a) Find dy/dx

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Q: Q9. (a) The nth term of a sequence is 6- 2n Work out the first three terms of the sequence. (b) Here…

A: We can solve the given problem as follows:

Q: In the year 2000, the population of a small city was 41,000. The population grows at a rate of…

A: 2037 -2000 = 37 =t at 2037 population growth is = 1300*e(0.03*37) population  growth= 1300e1.11…

Q: amplitude: period: phase shift: 6.

A: Follow the procedure given below.

Q: M. Vx? N. xe* O. 4 Р. cot x Q. cot?x R. 2 cot x

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Q: the area of the region enclosed by y = 2 – x´ and y = -x, identify the "a" and "b"

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Q: Find and classify the critical points of f(r, y) =r³ - 6ry + y³. %3D

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Q: 11 Convert the Cartesian equation y = 5 to a polar equation. r = 5cscθ r = 5secθ r = 5sinθ

A: We have to find the polar form

Q: Solve sin(2 – 62) = - Solve the equation for æ without evaluating the inverse function. (Your answer…

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Q: TT sin 5. Approximate dx by Simpson's rule with seventh ordinates?

A: Simpson's Rule:    ∫abf(x)dx=∆x3f(x0)+4f(x1)+2f(x2)+...+2f(xn-2)+4(fn-1)+f(xn) Where, ∆x=b-an We…

Q: 15 -8 -3

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Q: 1. Use the trapezoid (a) (b) (c) x In x dx; with (h = 0.1)

A: f(x)=x ln(x)   x 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 f(x) 0 0.10484 0.218785 0.341073…

Q: Ln (sin? (D-C)x) Find derivative of f(x) = %3D xD-C

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Q: Solve 8 sin (6x) = 3 for the two smallest positive solutions A and B , with A

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Q: Find the Taylor Series centered at 1 for the function f(x)= 4x3-2x2+x=5. Show with clear work.

A: We are asked to find the Taylor series centered at 1

Q: What two nonnegative real numbers with a sum of 50 have the largest possible product? The numbers…

A: We are asked to find the largest possible product of the two non negative number whose sum is 50

Q: A company finds that the marginal profit, in dollars per foot, from drilling a well that is x feet…

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Q: if 0 < x < 5, if 5 <x < 10. За-15 f(x) 15 - За Evaluate the definite integral by interpreting it in…

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Q: 1. Find the first derivative of the function g(I) = 81+ 12z - 48T. g'(z) = 2. Find the second…

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Q: Find an equation of the tangent plane to the surface z = læ? + 2y² + 2x + 1y +3 at the point (2, 4,…

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Q: x +6x, xa everywhere.

A: A function g(x) is continuous at x=a if and only if limx→a- g(x) = limx→a+ g(x) =g(a) .

Q: Biologists stocked a lake with 240 fish and estimated the carrying capacity (the maximal population…

A: Given: Biologists stocked a lake with 240 fish. The carrying capacity (the maximal population for…

Q: I. Write 2 – 7i in polar coordinates on the complex plane. II. Find (1+ i)° using DeMoivre's…

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Q: Find the centroid of the region. NOTE: Enter the exact answers. (7, 9) (?, ?) %3D y = 23

A: The expression for the centroid is: x¯=1A∬xdydx &amp; y¯=1A∬ydydx   Where; Area=A=∬dydx   From the…

Q: Determine the intervals on which the following function is concave up or concave down. Identify any…

A: The given function,  g(t)=3t5-20t4+30t3+80

Q: If line t is parallel to the line 5x-6y+10=0, What is the slope of line t? O a. 5 Оb. 5/6 О с. 6/5 O…

A: Slope of parallel lines are same

Q: Take the derivative of the following: Dy= 3xe y = e (3) e y = @y= In () 10 Y=ln (In x)

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Q: 4. Determine the general equation of the plane containing the points P(1, -4, –5), Q(2,0, 13) and R

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Q: Consider the graph of the function g(x): 4 y = g(x) 4 7 x The graph from x = 2 to x = 6 is a…

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Q: Find the intervals on which f is increasing and decreasing. f(x) = - cos 2x on [-1,1]

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Q: If $21.000 is invested in a savings account offering 4.5% per vear, compounded semiannually, how…

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Q: Absorption of Drugs The concentration of a drug in an organ at any time t (in seconds) is given by…

A: We have to find the concentration at given time t.

Q: State sec(cosec÷) in terms of x. Hence solve the equation 1 sec(cos ec 1 2x

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Q: Choose the point which shows the correct location for the polar coordinate (-3, 315). 90 2 WIN 135…

A: The given polar coordinate -3, 315°

Q: Use the summation formulas to rewrite the expression without the summation notation. 2j + 7 n2 j = 1…

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Q: 9. xInx dx

A: Here , we have given a indefinite integral in which two functions are given now we will solve this…

Q: The New River Gorge Bridge is 880 feet above the water below. A bottle rocket is launched upward off…

A: To find out the velocity and acceleration.

Q: Evaluate the integral using the following values. 9. x3 dx = 320, 9. dx = 4 dx = 16, %3D - 10x + 3)…

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