Use Hooke's Law to determine the work done by the vaniable force in the spring problem. A force of 7 pounds compresses a 15-inch spring a total of 5 inches. How much work is done in compressing the spring 7 inches? in-lb

Q: 2. Write the given (total) area as an integral. a. The area above the x – axis and below y = 4 – x²…

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Q: Describe the graph of the equation. r = 10 cos ti + 8 sin tj – k O It is an ellipse in the z = – 1…

A: Given that       r = 10 cost i + 8 sint j - k

Q: 1 2 3 1+3* Use substitution to find the Taylor series at x= 0 of the function ... 1 What is the…

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Q: (2x – 3y) dx + (2y – 3x) dy

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Q: sheet of paper for a poster is to be 18 ft2 in area. The margins at the top and bottom are to be 9…

A: Ler the the dimensions of the sheet is  x and y in order to maximize the print area

Q: Of all rectangles with a perimeter of lo meters, which one has the maximum area? (GIve both the…

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Q: Find curl (4z i+ 5x j+ 8y k). curl(4z i+ 5x j+ 8y k) = ( )i +( i j+( i )k

A: To Find : curl(4z i + 5x j +8y k)   Note that : If F=〈P,Q,R〉 is a vector field in ℝ3, and Px,Qy, and…

Q: 1 T/2 3t/2 -1 - -2 + -3 + -4 - -5 The graph of the function f(x) = sec x is given above for the…

A: Topic:- function and calculus

Q: Evaluate the definite integral (cos(t), sin(t))dt

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Q: Use L'Hopital's rule to evaluate lim(1 – 2 sinh(x)) sch(a).

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Q: (4x-3) find dy/dх y = (2х-7)6

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Q: 2. Use the linear approximation of f(x) = x² ln(x + 1) to estimate (1.01)² ln(2.01).

A: We need to estimate value.

Q: If f(x) = V4x + 1 find f"(2). O 4/27 O 213 None of these O 2/3

A: Topic:- Derivatives

Q: d'y Find dx? 2 y = (2а-3)? dy 48 dx? (2г - 3)" O dy -12 da? (2г- 3)" O d'y 12 dx? (2a-3) dy -8 da?…

A: y=2(2x-3)2

Q: Consider the function f(x) on the interval [1, 11]. Find the average or mean slope of the function…

A: Given,  f(x)=1x

Q: At 10:17 a.m., you pass a police car at 55mph that is stopped on the freeway. You pass a second…

A: Here, note that the distance between two police cars is 39 miles and the time between them is…

Q: Evaluate: L7 3sin13 edx 512 1001 1024 1001 O 1024 1001 512 1001

A: Solution of given question is written in below steps.

Q: Find all real and complex solutions to the equation   x^3 − 3x^2 − 10x + 24 =0

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Q: 1 Given that 1 > x" with convergence in (-1, 1), find the power series for with center 1- 9x4 n=0 0.…

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Q: Peaive marima and, minima, 4 any tar the funchno If there is not an answers write N/A Wde ms wefs as…

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Q: Evaluate the iterated integral. /3 6. y cos(x) dy dx

A: I=∫0π3∫09y cos x dy dx =∫0π3cos(x) ∫09y dy dx  =∫0π3 cos(x) y2209 dx  =∫0π3 cos(x)812 dx

Q: 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4, 2)…

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Q: Given the vectors A = 3i – 5j + 2k and B = 7i + j – 2k. Find the vector projection of A onto B.

A: Given : A→=3i-5j+2kB→=7i+j-2k     To Find : Vctor Projection of A→  onto B→

Q: /hat is the area of the region bounded by the graphs of æ = y³ – 2y and DA = (3x – x² )dx DA = (? –…

A: Topic:- application of integration

Q: Consider the function f (x, y)=-2x'+3x'y+2 y°-9y+5

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Q: Use Hooke's Law to determine the work done by the variable force in the spring problem. A force of 5…

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Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

A: Here we have to find the volume.

Q: Evaluate sin 5x) lim, 0 (sin 5z ) 3x O 1 O 3/5 O 5/3

A: Topic:- limit calculus

Q: Use substitution to find the Taylor series at x = 0 of the function In (1+3x*). What is the general…

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Q: Evaluate: Lī 3sin13 xda 512 1001 1024 1001 1024 1001 512 1001

A: Solved below.

Q: Find the standard equatron of the sphere with the given chara ct eristics center:(-1,7 9) radius: 6

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Q: Find curl (8z i + 9x j + 8y k). curl (8z i + 9x j + 8y k) = ( i )i + ( i )j + ( i )k

A: We know: Where P, Q and R correspond to the components of a given vector field:F→=Pi→+Qj→+Rk→ curl…

Q: Given Sla- 3| 3 x – g(x) = What is lim,3- 9(x) ? x- 9- O O 1 O -1

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Q: ||r(t) x r"(t)|| Use the formula k(t) = to find k(t). ||r"(t)||° r(t) = t'i+ t°j K(t) =L

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Q: emplicit differuntintion to find an Use equaton of 44 tangent line to yle graph of ve equation given…

A: The given equation,       arcsin4x+arcsin3y=π2,  28,26

Q: Find div F and curl F if F(x, y, z) = xz°i+ 2y°x²j+2z²yk. %3D div F= curl F=

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Q: Let h(x)= f(g(x)) where f(x)=tanx. Then h'(x)= a) f'(tan x) g'(x) b) g'(x)tan(g(x)) c) g(x)…

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Q: Evaluate the definite integral. Using Fundamental Theorems of Calculus. (x?2 - х) dx x2 + x +1

A: ∫01x2-xx2+x+1dxit is a improper fraction ( degree of Numerator= Degree of denominator)Using long…

Q: View Policies Current Attempt in Progress Find curl (6z i + 7x j + 9y k). curl (6z i + 7x j + 9y k)…

A: Solution:

Q: Find the surface area of a sphere at the instant when the rate of increase of the volume of the…

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Q: Activity 1.5.3. A company manufactures rope, and the total cost of producing r feet of rope is C(r)…

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Q: Find the center and radius of the sphere that has (7, –6, 2) and (9, 12, –6) as endpoints of a…

A: The objective of the question is evaluate the center and radius of the circle

Q: manager sells 75 cakes per week at 650 pesos each and he knows that for every 10 pesos crease in the…

A: Given query is to find the price tk maximize the revenue.

Q: FIND THE INTEGRAL OF YOUR ANSWERS IN 2a and 2b  Note: My answer on 2a and 2b will be found on the…

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

Q: 10 *- 10-x (7) Solve for x. y =

A: Topic:- algebra

Q: t"(x) If t(x) = Vx find t'(x)' O -1/2x O 2x 1/2x -2x O None of these

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Q: What is the differential equation whose solution represents the family y = Ae3x + Be 3x+Ce4x? %3D O…

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Q: ||r(1) × r"(t)|| Use the formula «(t) to find «(t). r(t) = 11 cos(t)i + 11 sin(t)j + 6tk K(t) =

A: We can solve as follows

Q: 6) Find the linear approximation to R(t) = VE at t=32 Use the linear approximation to approximate…

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Q: write the equation of the tangent to the Eunction: 2(x? +y=J%=25(x* -y^) at the point (3, 1) %3D

A: First we calculate the slope of tangent at the given point