(b) Given the demand function P = 120 – 3Q, fixed cost, FC of 50 and variable cost, VC of 5 per unit express the profit function, a in its simplest form.

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A: This question is based on application of integration .

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A: We will find the roots.

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A: Given; I=∫4xsin4xdx   ....1   As we know that; ddxax=axlna∫sinxdx=-cosx+C And ∫a·fxdx=a·∫fxdx, where…

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Q: 6. Evaluate the following integrals. 1/4 (2) [¹ sec³ πt dt

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A: Solution

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Q: Find the length of the curve parameterized by x = 2 + 3t² and y = 3 + 2t³ from t=0 tot = 3.

A: A detailed solution is given below

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Q: 4. Elizabeth needs 2 1/3 cups of sugar for vanilla cake and 1 3/4 cups of sugar for chocolate cake.…

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Q: Evaluate the function at the indicated value of x =1. f(x)=loggx 8 -8 - 1011 8 0

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

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Q: Find the centroid of the given region. y = 2-x? y = x A (3/22,45/61) В) (5,15) c) (5/14,38/35)…

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Q: the z-axis is shaded. Figure 1: Graph of y = f(x) over [0,4]. t * f(x) dr = 16/3, [*f(2) dx = 37/12…

A: Given query is to find the value fi the integral.

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Q: 2. The following function S-60,000e models the decay of sales for a give product over time in months…

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Q: Determine whether the series converges. 1 k+11 The series

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A: The idea of ratio test must be there to understand it properly. The explanation part is given below.

Q: Find the arc length L of the graph of r(t). r(1) = t³ i+ t j+V6r? k, 2 <t< 5 k, 2 <t < 5 L = i

A: Given : r(t) = t3 i + t j + √6 t2/2 k 2 ≤ t ≤ 5 Now, r'(t) = 3t2 i + j + √6 t k Arc Length :

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A: Let 'x' be the number of  children's and 'y' be the number of adults. Now x≥0 and y≥0 since the…

Q: Graph the function using translations. f(x) = 3x+1

A: We will find the suitable graph.

Q: 6. Find the intervals on [0,27) where f(0) = sin² (0) is concave upward/ concave downward.

A:

Q: 10. Given the supply and demand functions: P = 10+2Q, P = 30 – Q Which of these statements are…

A: Here the given demand function is             P = 30 — Q Supply function is             P = 10 + Q…

Q: 9. 5- 8. 7- 4- h(x) 6- 3- 4 g(x) 3. 17 4 3. X-values 1 3. X-values 4 g(x) If f(x) then h(x) f'(1) =…

A: This is a problem related to derivative of the function. Based on the general formula and concept we…

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Q: 36. a6-72, a13 = 26

A: Student has specifically asked for the answer to the Question-36. Hence, solution to that problem is…

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Q: The logistic growth function f(t)= 116,000 1+5500 e describes the number of people, f(t), who have…

A: f(t)=116,0001+5500 e-tA)when epidemic begin;t=0f(0)=116,0001+5500=21.087The number of people…

Q: Q9. Which of these is not the derivative of the function, y = x": A. -½x-1½ B. –0.5x-1Vx-1 C. –0.5 1…

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Q: me origin is 6i + 8j, then the me direction of a = 3i + 4j at

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Q: Find the first four terms of the Taylor expansion of the solution to the given differential equation…

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Q: ||r'(t) × x r" (t)|| Use the formula k(t) to find k(t). r(t) = t’i + tl5j %3D K(t) :

A: The given formula is; κt=r't×r''tr't3 And rt=t2i+t15j   As we know that; The Power law; ddxxn=nxn-1