For 5, Sketch the region enclosed by the given curves. Find its area. Make sure you show how you find any points of intersection using algebra. 8 2 5. y = -x, y = x2+4 4

Q: k(а-2)+ k(5а) B- If k(a) = -43a+2, find 3

A: The objective of the question is evaluate the value .

Q: (Easy) For the following differential equations, state the independent and dependent variables, and…

A: Here we have to find the dependent and independent variable order and the degree of given…

Q: 3 2 2 3 1, find the matrix B Such that AB = 5 3 4 3 4 2 1 6 1 5 6 4 , If A = 1

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Q: (c) Find parametric equations to represent the red line in the graph below. 10 (-2, 7) (6, 3) -5 10…

A: This is a problem related to equation of line. Based on the general formula of line equation we will…

Q: Convert from rectangular to spherical coordinates. (Use symbolic notation and fractions where…

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Q: Verify that the function satisfies the three hypotheses of Rolle's theorem on the given interval.…

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Q: I FIND THE SECOND DERIVATIVE(y") OF THE FF IN ITS SIMPLIFIED FORM 3x-4 1. Y= Arctan

A: To find second derivative of the given function.

Q: 2. Y' = csc - y cot x ans. y sin x = x + C %3D

A: We know that; The standard form of the linear differential equation of first order is: dydx+Py=Q ;…

Q: Find the radius and height of the right circular cylinder of largest volume that can be inscribed in…

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Q: 10. ſ csc²e cot ôni- 5 cot ê dê

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Q: Evaluate the following IMPROPER INTEGRALS, It is optional to double check your answers/solution for…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Match the differential equation with its direction field. y' = sin(10x) sin(10y) y \ 20y 0.34 15 0,1…

A: Here, to match the graph of the given differential equation: y'=sin(10x)sin(10y)

Q: Find the 24th derivative of y = -sinx

A: Topic = Derivative    The 24th derivative isy24 =-sinx

Q: Consider the following planes. Sx+ 6y -2= 66 x- 12y + 22 0 (a) Find the angle between the two…

A:

Q: Find the minimum amount of tin sheet in square inches that can be made into a closed cylinder having…

A: Find the minimum amount of tin sheet in square inches that can be made into a closed cylinder having…

Q: ,x 1 Is the function k(x) = {x²-1 2,x = 1 continuous at x = 1?

A: We use L' hospital rule to find the limit.

Q: Which of the following integrals are improper? (Select all that apply.) 1 dr 6х — 1 1 dr 2.x – 1 sin…

A: We are asked to find which is improper integral

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: - ydy (y + 1) - J y + 1

A:

Q: Cost 3x dх

A: The objective of the question is evaluate the indefinite integral.

Q: Determine whether the plane passes through each point. x + 2y – 3z - 1 = 0 (a) (-4, 1, –1) O Yes O…

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Q: Seax sin bx dx

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Q: Determine if the given function is continuous on the given interval a. [2,5) , x <O f(x) = %3D 5x-8…

A: To determine whether the given function is continuous on the given interval.Interval=[2, 5)fx=1x,…

Q: 1„2 The graph shown is f (x) = ±x². 4 3 21 1 54 3-2 -14 1 2 3 4 5 -2 3 4 If g(x) = `f(t) dt, what is…

A: This is a problem of antiderivative function. Based on the general formula we will answer the…

Q: Use THIS standard form for a tangent plane: - fz (x1, yı) * (x – x1) – fy (x1, yı) * (y – y1) + (z –…

A: Given

Q: Find the Cartesian equation of the polar equation p² = 2[1+ r(cos 0 – sin 0)] and identify its…

A:

Q: Evaluate this path limit: 4.ry3 lim (z, y)¬(0, 0) 2x² + y6 I=y% =???

A: To find: Limit of the function of two variable along the given path.

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j…

A:

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 4 4x(1 – x²)dx = i -1

A: To find the value of given integral.

Q: 5)Let f ( x ) =3x4 + 4x3 Find the derivative. b)Find the critical numbers.

A: Given problem:- 5)Let f ( x ) =3x4 + 4x3   a) Find the derivative.   b) Find the critical numbers.

Q: The base of a three-dimensional figure is bound by the line y = x +2 on the interval [0, 4].…

A: Let's find.

Q: 6. Use parametric differentiation to find if x= 212 +2, y=t* -7 dx Solution:

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Q: . Y= In (- (x-2)2

A: To solve the second derivative of the function

Q: 30

A: Here, just to find the angle between F1 &amp; F2.

Q: Find the length of the arc of the given parabola: x²=4y from x=-2 to x=2

A: We know that the length of the arc of the parabola y=f(x) from x=a to x=b is given by L = ∫ab1+dydx2…

Q: 8)Suppose the total cost of a certain product is C(x) = 0.001 x2+ 5x + 300. The product can be sold…

A: Find your answer below

Q: Find parametric equations for the line whose vector equation is given. (a) (x, y) = (6, –5) + t(1,…

A: we can solve this as follows:

Q: Consider the following. u = (5, 0, -9), v = (8, 7, 3) (a) Find the projection of u onto v. (b) Find…

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Q: TOPIC Rational Frachon decomparition sx2 -9x-6 dx x3-2x2-4xt8

A: Given problem:- ∫(5x2-9x-6)x3-2x2-4x+8)dx

Q: B- Given 4x – 2y = 10 and 3x – 5y = 11, solve for x and y using Cramer's rule.

A: To solve given system of equations by Cramer's rule.

Q: Determine two positive values such that the sum of the two numbers is 105 and the product of the…

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Q: Streaming Music Consumers are spending more on music from digital sources than they do on CDs.…

A: f(t) =3.7+ln(t+1)(a)in 2012 , t=0f(0)= 3.7 +0.84 ln(0+1) = 3.7+ln1=3.7+0f(0)=3.7Amount spent by…

Q: Directions: In implicit differentiation, we differentiate each side of an equation with two…

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Q: Find the lengths of the sides of the triangle with the indicated vertices, and determine whether the…

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Q: Express the integral in terms of the variable u, but do not evaluate it. 12x-11 dx; u = 12x – 11…

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Q: Find the gradient of the function at the given point. f(x, y) = 2x + 4y2 + 1, (1, 5) Vf(1, 5) =

A: Let's find.

Q: The function g(x) is defined for-3 5xs3. The behaviour of g'(x) and g"(x) is given below. -3 <x<-2…

A: Given problem:-

Q: Determine whether the planes are parallel, orthogonal, or neither. 3x - 15y – 3z = 2 2x - 10y – 2z =…

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Q: Find the volume of the solid generated by revolving area of a circle: (x-2)²+y²=4

A: Rotate the circle:By rotating the circle around the y-axis, wegenerate a solid of revolution called…

Q: A swimming pool has a depth of 9 ft at the shallow end and 18ft at the deep end. The bottom of the…

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