A kite 100 ft above the ground moves horizontally at a speed of 6 ft/s. At what rate (in rad/s) is the angle (in radians) between the string and the horizontal decreasing when 200 ft of string have been let out?   rad/s

Q: Find the moment of mass from the x-axis for y = x ln(x) − 3x and y = 1 bounded by x = 3 and x = 6.…

A: Given data:- Surface density is equal to 0.37 kg/unit2 y=xlnx-3xy=1 Bounded by, x=3 and x=6

Q: Use the definition of the Laplace transform to find L{f(t)}. (Enter your answer in terms of s.) 0,…

A: To find: L{f(t)} by the use of Laplace transform. Given information: The function is  ft=0…

Q: ven the revenue and cost functions R=28x -0.9x² and C = 7x + 12, where x is the daily production,…

A:

Q: 1.Find the derivative of the following functions. 2 a) F(x) = ²* 5 √t³ + 8dt et -dt et +3 b) G(x)=…

A: Topic:- application of integration

Q: Find a linear equation whose graph is the straight line with the given property. HINT [See Example…

A:

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = (t + 1)³ L{f(t)} =

A:

Q: In a chemical reaction, a certain compound changes into another compound at a rate proportional to…

A:

Q: Revenue The Better Baby Buggy Co. has just come out with a new model, the Turbo. The market research…

A:

Q: Find the values of x for which the series converges. (Enter your answer using interval notation.) Σ…

A:

Q: Lyra is designing a model of a solar system with a planet and a comet. The planet has a circular…

A:

Q: Given f(x,y,z)=√(−6x+5y+2z), find fx(x,y,z) = fy(x,y,z) = fz(x,y,z)=

A:

Q: Set up a double integral that gives the area of the surface of the graph of fover the region R. f(x,…

A:

Q: Find the curvature K of the plane curve at the given value of the parameter. r(t) = 8 +²³₁ t=2 11…

A:

Q: An inverted pyramid is being filled with water at a constant rate of 25 cubic centimeters per…

A:

Q: Question Given f(x)=√x+8, find f'(-7) using the definition of a derivative. Provide your answer…

A:

Q: Evaluate ₁² 2¹-132²+¹ dx .

A:

Q: Q4. Determine the first moment of the shaded area with respect to a axis. The equation of the curve…

A: Given data:- The given equation with respect to curve is, x2=9y

Q: Explain the meaning behind the expression foF-dr, for a curve C and vector field F.

A: To explain: The meaning behind the expression ∫CFdr for a curve C and vector field F.

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A:

Q: List the elements of the given set. the sets (A n B) U C and An (BU C), where A = {1, 2, 3, 4}, B =…

A:

Q: sketch and find the area of the region enclosed by the graph of the equation r=3 cos Θ....

A:

Q: 13. The fxs xsin 3xdx is equal to

A:

Q: y(t) = y" - 3y' = 8e²t - 2e-t, y(0) = 1, y'(0) = -1

A: Given

Q: Using geometry only, find the area under the curve. Include a sketch of graph for each region. Give…

A:

Q: For the sequence, determine if the divergence test applies and either state that lim n→∞ an does not…

A:

Q: 2. Set up the triple integral to find the volume inside x² + y² = 9, above z = 0, and below x+z = 4.…

A: Solution is given below:

Q: 21. Integrate x cos(2x² + 7)dx. sin (2x²+7) 4(x²+7) B. sin(2x²+7)+c A. +C C. D. 4 4 sin(2x² +7)+c…

A:

Q: 5. Use elementary Maclaurin series to find Maclaurin series for the following functions. a) 2²=-=-11…

A:

Q: An inverted pyramid is being filled with water at a constant rate of 60 cubic centimeters per…

A:

Q: H.w3: Used Newton-Raphson method to find solution accurate to with in 10-5 for the following…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Use the Gompertz growth model, y = Le y = Sketch its graph. L = 9000; y = 900 when t = 0; y = 1125…

A:

Q: (d) At which value(s) of x, if any, does the graph of f(x) have an inflection point? (e) It is known…

A:

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: Inverse laplace

Q: Fill in the blank. (Enter your answer in terms of t.) ਤੇ s 2 S | 14s + 53 -

A:

Q: Consider the following. - fx sec² t dt (a) Integrate to find F as a function of x. F(x) = F(x) = (b)…

A:

Q: 0.1 4 So V1+x* dx

A: Given : ∫00.11+x4

Q: Use the second derivative to determine the intervals over which the graph of the given function is…

A: The given function is fx=x13

Q: The equation of the plane containing the points (3,1,3), (4,0,-2), and (11,-5, 12).

A: Here we find the equation of plane using three points.

Q: For the function f(x) = 21² + 1, it is given that 3 f(x) dx = 21. At what value C does the function…

A:

Q: Let f(x, y, z) = eª + zy² and let C be a straight line segment connecting the points (4,2,1) and…

A:

Q: 3. Let R be the region between the functions y 2² and y = 8 - 2². Set up the iterated double…

A:

Q: The given family of functions is the general solution of the differential equation on the indicated…

A: The objective of the question is determine the particular solution of the given differential…

Q: This question has several parts that must be completed sequentially. If you skip a part of the…

A: The auxiliary equation is: m2+3m+2=0m2+m+2m+2=0m(m+1)+2(m+1)=0(m+2)(m+1)=0m=-2 or m=-1 smaller value…

Q: Find the area under the curve y = lines x = 1 and x = 5. 3x² + 4x + 1 bounded by the x-axis and the

A: Area under the curve y=3x2+4x+1 bounded by x-axis and x=1 to x=5.

Q: Find the fluid force on the vertical plate submerged in water, where the dimensions are given in…

A:

Q: 2. In a lab, the production cost, in dollars, per day of producing xbottles of given by: C(x)=4329…

A: Topic:- application of derivatives    Note:- as per our guideline if more than one question uploaded…

Q: 2. 2x² + 4x-3 ,2 X dx

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Consider the function f(x) and its derivatives:

A:

Q: Fill in the blank. (Enter your answer in terms of t.) { } [ 2 12s + 40 G S

A:

Q: Evaluate ľºm vy I 1-x² x² + y² dydx.

A: