A rock is thrown into a still pond. The circular ripples move outward from the point of impact of the rock so that the radius of the circle formed by a ripple increases at the rate of 5 feet per minute. Find the rate at which the area is changing at the instant the radius is 6 feet. When the radius is 6 feet, the area is changing at approximately (Round to the nearest thousandth as needed.) square feet per minute.

Q: 3. A rectangle with a fixed perimeter of 64 units is rotated about one of its sides, thus sweeping o...

A:

Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x2 + ...

A:   Intersection points:  x2 + y2 - 4ax = 0                                                          ...

Q: dy If y = sin='(cos x) then dx ||

A:

Q: Find the area bounded by y = sin²(x) and y = sin³(x) from < i< .

A:

Q: Definite Integral Instruction: Answer the following. Show all your solutions. 3. sin xdx (1 + w)(2w ...

A: As we know that; The Power rule: ∫xndx=xn+1n+1+C And ∫sinxdx=-cosx+C   From the given integration; (...

Q: 1 The time to failure, t, in hours, of a machine is often exponentially distributed with a probabili...

A: The probability density function is: f(t)=ke-kt, 0≤t&lt;∞ where k=1a and a is the average amount of ...

Q: 1. Answer the following question? A Let f '(x) = x - 2x – 3. For what value(s) of x does f(x) have a...

A:

Q: 3. Suppose that a function f has the following Maclaurin series: (-1)n+1 -(x – 3)" 3"n n=1 Find the ...

A:

Q: Evaluate the following limits. 1. lim(1+ Vw)(2–- w² + 3w*) w+1 12 - 1

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question fo...

Q: х* + аx — 2bx — 2аb - х3 —2ax* — 2bx* dx х4 + ах3 — 2bха — 2аbx?

A:

Q: Solve for the derivative of the following and simplify if possible. h(t) = t3 - t2 sin t

A:

Q: For a week, a clothing company tracks the amounts spent by its customers, with the results shown to ...

A:

Q: 5. The amount of a certain drug in a persons blood t minutes after admin- istering the drug is given...

A: The amount of a certain drug in a person's blood t minutes after administering the drug is given by ...

Q: 5. Find the derivative of y = In(cos v3x + 2 ), by using chain Rule.

A:

Q: Use the Root Test to determine if the series converges or diverges (-1)"2* (-1)"2ñ zuć en? (2n2 – 1)...

A: Given problem:-

Q: | In|Vi + 1| dx

A:

Q: 3. What is (Sin (6x)}? 4. What is (Cos (x²) dv 5. What is (tan x³) dx 6. What is (In x)7

A: we use the chain rule to find the derivative of the given function 

Q: In Exercises 39-42, the velocity v(t) of a particle moving in the plane is given, along with the pos...

A:

Q: Evaluate the moment M, and My of the region bounded by x- 2y - y? and the y-axis.

A: Given area is bounded by x=2y-y2 and y-axis.  On the y-axis, x=0. We try to find the point of inters...

Q: G(t), of the function g(t) = (2n?t? - t)V2n2 – t?. %3D

A:

Q: 1. lim 3" 5. lim tan r 2. lim 5 6. lim cos r 3. lim log r 4. lim cos r 7. lim sinr

A:

Q: In a psychology experiment, the time t, in seconds, that it takes a rat to learn its way through a m...

A: Given density function of time t in second for a rat for its way through maze  f(t)=0.04 e-0.04t

Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is...

A: To find out the volume of the tetrahedron whose vertices are given.  

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

A: This question can be solved as per the instruction given.

Q: 1. Fill in the following blanks for this function: y = - 4 cos 2x - 5 a)amplitude b) reflection c) p...

A: Given query is to find the Indicated points of the function.

Q: 11. A gate in an irrigation canal is constructed in the form of a trapezoid 3 ft wide at the bottom,...

A:

Q: Let a = ci + j and b = 8i + 15j. Find c so that the angle between a and bis Round your answers to fo...

A: To find the value of c

Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provide...

A:

Q: Va –2 -dx aㅎ (V+1)

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

A:

Q: The construction firm where you are working as an engineer plan to build a tunnel whose arch is in t...

A: The arch of the tunnel is in the shape of a parabola.Let road be the x-axis And given tunnel is 12m ...

Q: 6x Find an equation of the tangent line to the graph of y = 2 X +1 at the origin and at the point (-...

A: Given,          The line is y=6xx2+1 at the origin and at the point -1,-3.To find : Find an equation...

Q: Find the vector component of v = (4, – 1, 7) along b = (2, 3, –6) and the vector component of v orth...

A: We know that vector component of v along b is v→·b→b→ Vector component of v orthogonal to b is v→- v...

Q: ха + ах — 2bx -2ab — х3 — 2ах* — 2bx? x* + ax³ – 2bx³ – 2abx² dx

A: Given integration is: ∫x2+ax-2bx-2ab-x3-2ax2-2bx2x4+ax3-2bx3-2abx2dx

Q: 2. Scientists can determine the age of ancient objects by a method called Radiocarbon dating. The bo...

A:

Q: Find the volume generated by revolving bout the line x = 3 the area bounded by (y – 2)° = -4(x – 4) ...

A: Let's find. 

Q: 1. Complete the following tables of values to investigate lim(x¯ - 2x + 4). f(x) f(x) 1.6 0.5 x+1 li...

A:

Q: 2. A rectangular box has a square base with edges at least 10 cm long. It has no top, and the total ...

A:

Q: H-wr Phavethat D2 22=o far the funstions far the kunction -2y t- Rx,y) = e Ln JxZ+yZ CooS 2X

A:

Q: y=3-x + xlnx solves y' = Inx y = solves y' = y? 1-x

A: This question is based on differential equation.

Q: Do not write beyond this border. 3. 2. 1. Do not write beyond this border. ecessiv 3. 3 3. NO CALCUL...

A:

Q: cosx f(x) = 1+sinx

A:

Q: Consider the power series rvn(5– 2x)" 2n + 1 Vn(5 – 2x)* n=1 a. Show that the series is conditionall...

A:

Q: Find the area of the surface obtained by rotating the curve y = +, 1<1<2 about the y-axis. (a) 7(4 +...

A:

Q: Identify which below is a separable Ordinary Differential Equation 2xy a. y': х(у — 1) — у dy _x+ y ...

A:

Q: 12. Given f(x) - -5Vx + 2 and g(x) = vx+ 6, what are the restrictions on the domain for th 12. Given...

A:

Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provide...

A:

Q: x2+1 - dx x4-x²+1

A:

Q: 3x 3. lim х-0 sinx

A:

Q: 14. Find the orthogonal trajectories of the family of curves 1 y =- (x + k)³ (a) y = (3x+ C)/7 (d) y...

A: