Given cost and price (demand) functions C(q) = 100g + 42,000 and p(g) = - 2.1g + 870, what is the maximum revenue that can be earned? It would be $ (Round answer to nearest cent.)

Q: The radius of a sphere is increasing at a rate of 4.9 mm / s. How fast is the volume increasing when...

A: Volume of the sphere , V = 43πr3 ; where, 'r' is the radius of the sphere.

Q: rove that the given equation is a solution to the given DE: 5. x = 2t + C; y = Ct + 3 ; 2(y')² – xy'...

A: Topic:- application of derivatives

Q: Draw a line to show how the white can escape from check ,don’t forget:move ,block or capture

A: In this question we have to find how white can escape from check.

Q: I Find the second derivative(y") of the following functions and simplify the final results. 4. y = x...

A: 4 y = xcosx now fist derivative y' = x(cosx-1)cosx(-sinx) y' = (-1/2)sin2x x(cosx-1) now again diffe...

Q: tan x[cot x – cos x]dx |

A: Topic:- integration and trigonometry

Q: B. Use the properties of continuity to determine where each function is continuous. 1. f(x) = 2x*x +...

A: Let's find. 

Q: What is the integrating factor for the differential equation?

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Q: Question 3 Find the change in y = 2x -3 if the x changes from 3.3 to 3.5. А) 0.1 0.2 0.3 0.4

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Q: 1 1 9. dx I (# – 1)(x² + 4x + 5) In |x – 1|+ 10 In a? + 4x + 5| - 20 13 arctan(x + 2) +c 10

A: First we use partial fraction decomposition and then evaluate the integral.

Q: 4. Consider the surface S parametrized by R(u, v) = (uv, sin u, cos v). Find an equation for %3D the...

A: The given curve S is parametrized by: R→(u,v)=uv,sin u,cos v Now, to find the equation of the tangen...

Q: Choose from these statements. The proof starements in correct order. Let (2, y) satisfy R and (y, z)...

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Q: Prove that 3x +8 Viv = dr dy: %3D where R [-1,1] x [0, 2).

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Q: What is the equation of the tangent line to the function f(x) = a? + 5x at the point (1, 6)?

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Q: Consider the following. w = xy2 + x?z + yz?, x = t2, y = 6t, z = 6 (a) Find dw/dt using the appropri...

A: Here, the given functions are: w=xy2+x2z+yz2, x=t2,y=6t,z=6

Q: yi + yi = 1, when x = 0, y = 4 %3D

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Q: 1. Sand is being poured into a conical pile in such a way that the height is always one-third of the...

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Q: (2v² + 4u²v)du + (4uv + 3u³)dv = 0

A: The given differential equation is; (2v2+4u2v)du + (4uv+3u3)dv=0.

Q: 00 (-1)+12" n² +3 Determine the interval of convergence of

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Q: The half-life of cesium-137 is 30 years. Suppose we have a 130 mg sample. (a) Find the mass (in mg) ...

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Q: Integral from 0 to 1 of (3^x)/(e^x). The answer should be decimal

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Q: 1. f(x) 16x? – 4x +5 %3D

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: Give the Maclaurin series expansion of f(x) = ln(3 – 2x). Determine its interval of convergence. App...

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Q: 5. y- Br*-+습

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Q: Work Problems a) Evaluate the integral (4x + 1) ln x dx b) Evaluate the integral fou | 6 tan" x sec“...

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Q: By the fests. 2. a³y = x²(2a² – x²)

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Q: a) Show that f(x) = |5x+6| is continuous everywhere. (One point in particular is important to check)...

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Q: After some thought, you have decided that you will need $60,000 each year to live on after you retir...

A: This is a problem related to simple interest calculation. Based on the general formula of simple int...

Q: 1. Determine if if r2 /2r is differentiable at r 2.

A: First check for continuity then the derivative if both exist then function is differentiable. 

Q: Show that y1(t) = et and y2(t) = e−3t form a fundamental set of solutions for y'' +2y' −3y = 0, then...

A: If y1(t)  and y2(t) are two solutions to the differential equation                   p(t)y''+q(t)y'+...

Q: is differentiable at r 2. 2. (a) Using the definition of derivative, compute for the slope of the li...

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Q: Question Select your answer. Find the derivative of f(x) = 5/I with respect to r. 2x 5 Answer

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Q: (9xy-2y2) dx - (6x²- xy) dy =0

A: 9xy-2y2dx-6x2-xydy=0dydx=6x2-xy9xy-2y2dydx=x6x-yy9x-2y  

Q: I Find the second derivative(y") of the following functions and simplify the final results. 1. y = x...

A: Product  Rule of differentiation: du.vdx = u.dvdx +dudx.v dcos(x)dx = -sin(x) dsin(x)dx = cos(x) dxn...

Q: yi + yi = 1, when x = 0, y = 4

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Q: Question 1 Find the area bounded by the parabola x = y? and y = x-2. Answer in decimal form.

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Q: Find (f-1)'(a) for f(x) = ーX-3 when a = 3x +2 (Enter an exact answer.) Provide your answer below: ((...

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Q: INTEGRATE THE FOLLOWING (use integration techniques) -2y dy 2. Sy'e-24 dy

A: topic- indefinite integral

Q: 3x2+- 8(y + 1) = 0

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Q: substitution x = tan 0, then, the integral dx 1 + x2 transforms into tan 0 sec 0 d0 Select one:

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Q: Score! Question 16 The number line below shows a value on a log scale. 105 10-4 103 10 2 10-1 100 1...

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Q: SHOW YOUR SOLUTIONS. I. Eliminate the arbitrary constants. 3. x = c, cos wt + c2 sin wt ,w is a para...

A: topic - differential equations

Q: Assume that all the given functions have continuous second-order partial derivatives. If z = f(x, y)...

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Q: (b) Determine the equation of the line normal to f(r) =r²- 4r +5 at z = 1., Hint 1: The normal line ...

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Q: +o0 E(-1)" n=2 n?

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Q: +o0 (-1)" n (a) ► n! n=1 1 (b) E -3 n - -n n=1

A: Find the limit of the given functions at infinity

Q: 7. Find the volume of the solid formed when the graph of the region bounded by y = e", x = 0, x 2, a...

A: Explanation of the answer is as follows

Q: A waste management company is designing a rectangular construction dumpster that will be twice as lo...

A: Explained below

Q: 8. Using (4.6), find the polynomial P2(x) that interpolates the following data. In each case, simpli...

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Q: P where E is voltage and R is resistance. Approximate the maximum percent error in calculating power...

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Q: To evaluate the integral 1 dx x2 – 16 2х — we use the partial fraction decomposition of the integran...

A: Explained below