Set up the integral to find the area of the region bounded by y = r² − 1 and y = x + 5.

Q: -(;) > Let 7 (t) = < - 5ť² + 3, t² – 3t, In| a. Determine the coordinates of the point on the curve…

A: given: r(t)=-5t2+3,t2-3t,ln15

Q: Find the period of y=-3cos(3.7x). Round your answer to 1 decimal place.

A: " Since you have asked multiple question we will solve first one for you. Please specify question…

Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A: Height is given by f(t)f(t)=-16t2+420t+6t =11.5

Q: Use the method Laplace transform to solve the following. (a) 2r' + 7r=3e-t, x(0) = 4. (b) 2r' +…

A:

Q: Evaluate the following limit using L'Hospital's rule. Provide your answer below: دی lim (4x) X18

A:

Q: Evaluate the integral by interpreting it in terms of areas. *18 |x - 9| dx

A:

Q: Find the area of the surface x²-6y-2z=0 that lies above the triangle bounded by the lines x = 4, y =…

A: Surface Area :        Surface Area = ∫∫R 1+zx2+zy2 dA

Q: Given that the vectors X1 = () e- -2t ,X1 = (C)e-6t are solutions of a system x' = AX, do they form…

A:

Q: Identify and sketch by hand the graph of the quadric surface 25r2 – 25y? – 9z2 – 150r + 200 = 0. You…

A: An equation is given                              25x2-25y2-9z2-150x+200=0We have to identigy and…

Q: Click an item in the list or group of pictures at the bottom of the problem and, holding the button…

A: Given problem:-

Q: Let R(x), C(x), and P(x) be, respectively, the revenue, cost, and profit, in dollars, from the…

A: A)P(x)=R(x)-C(x)       =5x -(0.003x2+1.4x+60)P(x)=3.6x-0.003 x2-60b)R(50)=5(50)…

Q: 8) Find the unit tangent and unit normal vectors T(t) and N(t) for r(t) = (t, t², t²).

A:

Q: TC=575+2Q

A: ANSWER Is in next step

Q: 5. Does the function f(x) = e2x - 2x have any points of inflection? Justify your answer.

A:

Q: 1 dx x+1 1

A: Evaluate improper integral

Q: >(6k – 4)(7k + 3) - k=1 Enter your answer as a number without any arithmetic symbols. Sum =

A:

Q: Is the function a power function. If it is, write it in the form f(x) = kxP, and state the values of…

A:

Q: (x, y) is equal [where we set It is known that the area of a polygon with vertices (x1.₁), (x2.2).…

A:

Q: Find the center of mass of a thin wire lying along the curve r(t) = 2ti + 4tj+ (x,y,z) = ( (Type…

A:

Q: Suppose that sec(t) = 3/2 and that tis in quadrant IV. Find the exact value of tan(t). -3/2 -$5 O -…

A: 1 +tan2(t) = sec2(t) In Quadrant 4th , secant and cosine are positive. Note : As per our Guidelines…

Q: In order to solve with we first write and Setting to get sin 2xdx + cos 3ydy = 0 y(π/2) = π/3 cos…

A:

Q: Find all solutions in [0, 2π): 2 sin (x) - sin (2x) = 0: 4.8 00, π R/+ 4

A:

Q: For items 1-5 A 10-ft ladder is leaning against a house on flat ground. The house is to the left of…

A:

Q: Use an appropriate linear approximation to estimate cos(60.5" (Round your answer to three decimal…

A: To use the linear approximation to estimate cos(60.5°)

Q: Use the table to evaluate the expression. 1 2 3 4 f(x) g(x) 3 1 6 3 4. (g o f)(2)

A: Here (g∘f)(2)=g(f(2))But f(2)=3(g∘f)(2)=g(3)and g(3)=6Therefore(g∘f)(2)=6

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(s) : (t…

A: I am attaching image so that you understand each and every step.

Q: 6. A parallelogram is defined by the vectors (4, 3) and (1, 2). Determine the perimeter of the…

A: The parallelogram is defined by the vectors (4,3) and (1,2)  We have to determine the perimeter of…

Q: 3. Evaluate the double integral: ²₂2(x+3) dy dx 4. Evaluate the triple integral: ₂ dx dy dz Z

A: Topic:- multiple integration

Q: For a person at rest, the velocity v (in liters per second) of air flow into and out of the lungs…

A: Explained below

Q: Find the area under the graph of the function y=2-x-x² over the interval [-2,1].

A: Given query is to find the area under the curve.

Q: Consider the equation cos(3t) = 0.8. Find the smallest positive solution in radians and round your…

A: We can find the answer the as below.

Q: 2 Evaluate thefallowing cartesian integrats by - changing theminteequivalent Palar integralse 4- to…

A: Solving

Q: approximate sin 85° Sin a to 4 decimal poths. Compart to ne exact value if you using P(x) of me…

A: Here, to find the Taylor polynomial of the function f(x)=sin x around the point a=π2 which is given…

Q: Select all of the following graphs which represent y as a function of z, 24 REEF

A: Graphs are given, we have to find a graph that represents y as a function of x.

Q: A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with…

A: As per bartleby guidelines we only give first three question answers.

Q: Solve the triangle with the given information. a= 8.3, c= 2.8, p= 19.4° b 5.7 (Type an integer or a…

A:

Q: Find the limit. NOTE: Enter the answer using round brackets. t² + 8 1 = lim t+x6t²+7'2t (?, ?)

A: Explanation of the answer is as follows

Q: Show the repeating decimal .2727272727 repeating.... as an infinite geometric series. Give sum of…

A: This question can be solved using the concept of infinite geometric series.

Q: Determine if the following series converges. If the series converges, determine if it converges…

A:

Q: Find an equation of the line tangent to the curve r = sin 30 at the point where 0 =

A:

Q: Newton's Method will fail to approximate the solution to f(r) O with initial guess To when: O f(x)…

A: We have to choose correct option.

Q: A triangle is inscribed in a parabola such that the first vertex (point A) is at the origin and the…

A: This question can be solved using the concept of maxima and minima.

Q: 1. Find the first partial derivative of z with respect to x if x'y+ y°z+ z'x = 11.

A:

Q: Let the graph below represent f(x). For which values of x is f(x) increasing? 20 16- 12- -5-3-2 8+…

A: The graph of the function f'x is To evaluate: The values of x for which fx is increasing.

Q: nd the maximum profit and the number of units that must be produced and sold in order to yield the…

A: Given the query is to find the maximum profit.

Q: Find the volume of a solid bounded by y=(x2 -4) and y=(2x - x2) about the axis y=-4.

A: formula : here

Q: Rewrite cos(t+π/3) in terms of sin(t) and cos(t).

A:

Q: x²+2x+1 dx (x+2)(x−1)²

A:

Q: Numerical solution of Ordinary differential equations Consider the following initial value problem…

A: This is a problem of numerical method . Based on modified Euler method we will answer the question.

Q: Which of the following is a polynomial function?

A: