Find the parametric equation of the line through (1, 0, -2) and parallel to the line ⅓ (x – 4) = ½ (y) = z + 2.

Q: Let w(1, y, z) = -zy arcsin(z) where z=t", y=t, z = 7t. dz dw dt dz dy dt' dt & and using the chain…

A: Given: wx,y,z=-xyarcsin(z)where x=t4,  y=t3, z=7t To find: dwdt

Q: Find the area of the region under the curve y = f(x) over the indicated interval. 6 1) 5/2 i f(x): =…

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Q: Order the functions by growth rate. a(x) = 55x c(x) = 6868².65 Select function ✓ Select function…

A: Given   Order the functions by growth rate. a(x)=55x b(x) = 60x2 c(x)= 68682*65 d(x) = 7x!

Q: f(x)= In(2+ sin(x)), 0≤x≤ 2x Find the interval(s) on which fis concave up. (Enter your answer using…

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Q: Transformation by trigonometric identities & integration by parts. Evaluate each of the following…

A: NOTE: Refresh your page if you can't see any equations. . use integration by parts method

Q: A couple from San Diego needs $20,000.64 as a down payment for their first home. If they invest the…

A: Solution- Initial amount (P)=$8000 Required future amount (A)=$20000.64 Rate(r)=6% n=2(compounded…

Q: Please show how to do cube rt. of 1.1

A: Given: g(x)=1+x3 at a=0L(x)≈x3+1

Q: Consider the following. Find g'(x). g'(x) = g(x): = X In(x) In(x) - 1 In(x) ² 2.72 Solve g'(x) = 0…

A: NOTE: Refresh your page if you can't see any equations. . the derivative of the function already…

Q: (10) Show that the following limits do not exist. (0,0) (b) lim y³ +2³ (p) (0,0) ry²

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Q: 6. If f(1) = 10 and f'(x) ≥ 2 for 1 ≤ x ≤ 4, how small can f(4) possibly be? Hint: Apply the Mean…

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Q: Next Find the volume of the solid bounded by the paraboloids z = −6+3x² + 3y² and z = 7 - 2x² – 2y²

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Q: Find the local minimum and maximum value of f. local minimum value local maximum value

A: Given function  f( x ) = 2x3 - 15x2 + 36x - 5f'( x ) = 6x2 - 30x + 36 critical points = ( 2 , 3 )

Q: In the xy-plane, the graph y=x^2+bx+c, where b and c are constants, has x-intercepts at x=-2 and…

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Q: e function based on the following headings: domain, x & y intercepts, critical points and intervals…

A: we will find the required.

Q: The profit function of a business is given as P (x) = −x2 + 54x + 70. How many units must be sold to…

A: Please see the below picture for detailed solution.

Q: In 58, find the critical points and the intervals on which the function is increasing or decreasing.…

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Q: tank is full of water. Find the work W required to pump the water out o T 1 m Ť 4 m 12 m 4 m

A: The volume of the water of thickness '∆x' at height of x from the bottom.  In △CGB & △CFEFE∥GB.…

Q: Use the graph of f to estimate the values of c that satisfy the conclusion of the Mean Value Theorem…

A: The given problem is solved below in detail.

Q: 1 Let C = 0 1 a) Find C-1 b) Use C¹ to solve the following system. 1 x + 3y 30 14 - 1 2 = 7 y + 4z =…

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Q: J exp (x+3) dr

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Q: Find the point on the line y=x that is closest to the point (-8, -4). [Hint: Express the distance d…

A: The given line is: y=x Find the point on the line that is closest to the point -8,-4

Q: Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of…

A: We have given the dimensions of the cardboard sheet i.e.   length= 11 in.  breadth = 7 in .

Q: 3. Determine the intersection (if any) of the following planes. Show your work clearly ₁: 2x + 3y z…

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Q: [-/4 Points] Suppose that f and g are functions that are differentiable at x = 1 and that f(1) = 4,…

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Q: 9. (a) A plane contains the point (1, -2,7), it is parallel to the y-axis and the x-slope is -5.…

A: Please see the below picture for detailed solution.

Q: Find the area of the shaded region. y 15 10 5 2 y=7x-x² y = 2x 4 (5, 10) 6 Co 8 X

A: Area between the two curves f(x) and g(x) can be calculated using theformula:Area=∫abf(x)-g(x)dx

Q: A ramp 20 ft long rises to a platform that is 17 ft off the ground. Find x , the angle of…

A: Given length of ramp = 20ft Height of ramp =17 ft

Q: can you please explain step by step in words

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Q: Approximate the sum of the series correct to four decimal places. (-1)^ 4^n! S≈ 00 n = 1

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Q: Estimate the area under the graph of f(x)=x^2+4x from x=5 to x=9 using 4 approximating rectangles…

A: Given: f(x)=x2+4x We are required to find Area under the graph of f(x) from x=5 to x=9 using 4…

Q: dw/st is incorrect but everything else is

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Q: Let f([]) = -6 u +2v be a real-valued function and let z = [] and y = be vectors. We find that f(x)…

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Q: Find the vector equation that represents the curve of intersection of the cylinder x² + y² = 1 and…

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Q: 1. Consider the function f(x) = 3x²+2x-4 x+2 b. Determine all critical numbers C. } a. Give the…

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Q: Omso Om = 1 Om=0 Omzo Om #0 If it is one-to-one, find its inverse. (If there is no solution, enter…

A: Work as shown below follow the steps:f(x)=mx+bRecall the function f is one to one if and only…

Q: Sketch the graph of f by hand and use your sketch to find the absolute maximum and minimum values of…

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Q: Find two numbers, and y, whose difference is 42 and whose product is a minimum. (Answer as a common…

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Q: (()* 2 2) y = 5. 20 18 16 14 12 10 y

A: We need to draw the curve.

Q: I would like to create a rectangular vegetable patch. The fencing for the east and west sides costs…

A: According to question, Given information, We have given the cost of east and west sides fencing is…

Q: 5. Determine if the following integral is convergent or divergent. Do not calculate it. 1+2 sin(¹)…

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Q: Suppose an oil spill covers a circular region. The radius in feet, r, increases according to the…

A: Solution: . as we can see from the graph, point (30,20) is on the graph  which means after 30…

Q: Find the distance between the skew lines: x=6+6t, y=4+7t, x = 5-t, y = 8, NOTE: Enter the exact…

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Q: 1 A 3 2 1 To find the blue shaded area above, we would calculate: [ f(x) dx Where: a = f(x) = area =…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = xe-x2/162,…

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Q: Let f([])---6 find that f(2) 수 수 - u +6v be a real-valued function and let - [³5] and 수 [2³] be…

A: Given : fuv=-6u+6v   To Find : a) f(x→)   ,     b) f(y→),             c) f(z→)

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and…

A: The given lines are: y=xy=2-x  The density function is δ=14x+9y+7  To find the center of mass of a…

Q: Compute the determinant of B [400 9501 3 2 28 800 101

A: The matrix is given by B = 40041056322880010 To determine: The value of determinant of the matrix.

Q: A circle is growing, its radius increasing by 4 mm per second. Find the rate at which the area is…

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Q: Find g[f(-2)]. f(x)=x² +4; g(x)=4x-1 g[f(-2)] = (Simplify your answer.)

A: Given: f(x)=x2+4; g(x)=4x-1

Q: 4 The volume of a cantaloupe is approximated by V=3. The radius is growing at the rate of 0.5…

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