5. The profit, P(x), of a video company, in thousands of dollars, is given by the equation P(x) = -5x² + 500x - 4000, where x is the amount spent on advertising, in thousands of dollars. Determine the least amount spent on advertising that will result in a profit of at least $2 000 000.00

Q: 1. If y=tanx, prove that y=2(y² +1)(3y² +1).

A: y =tanx y'''=2(y2+1)(3y2+1).

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A:

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A: use implicit differentiation, I try to provide typed solution, if it is helpful like it.

Q: for the following P.d.f of x, find the p(x<1) and p(lx|<1),F(x)=x2/18 if -3<x<3 and 0 in other place

A: This is a problem related to probability distribution function. Please follow the procedure given…

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Q: 2. Solve the initial value problem x' = (t+1)/√t, x(1) = 4.

A: Given, x'=t+1t, x(1)=4

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Q: (3) Find explicit particular solutions of the initial value problems below. (a) + 1 = 2y, y(1) = 1.…

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Q: ] 8. In a company telephone tree, each employee is to phone two other employees. In the first round,…

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Q: Find each of the following for f(x) = 4x² - 7x+ 5. (A) f(x + h) (B) f(x+h)-f(x) (C) f(x+h)-f(x) h

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Q: If f(x)=x²+ax+b and the slope of tangent at x= -1 is 4 and the curve passes the point (2,4) Find…

A: I have stated the used formula in the solution

Q: 1. Evaluate the following integrals. [*(1+cos x)dx f. apa *1-√u -du

A: To evaluate the following integrals.

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A: Topic = Function As per guidelines , At a time only one question with three sub-parts can be…

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Q: 5. lim -00 2-1 5

A: limx→-∞x2-x45

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Q: 4 Find the roots of Z²+1=0 itt/2 Hint i = e 3

A: Given z4+1=0

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Q: Can you go into more detail? Why is the answer (4n+1)pi/2?

A: We want to find domain of the function.

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Q: 1. Calculate dy da for the following: (a) y ln(x + 2x³ - 6), =

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Q: 14. Evaluate to 4 decimal places: csc 153°

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Q: elimination 1 x³y 4- of arbitrary constant 16x² 3 کرا +30C =0

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Q: Hello good people, how are you, I need you to write these numbers in polar form for the complex in:…

A: Note that, if z=a+ib then z=reiθ=r(cos θ+i sin θ) where r=a2+b2 and θ=tan-1ba

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Q: 30. Use the fact that lim x→0 sin x X = 1 (shown in video) to show lim x-0 1 - cos x X = 0

A: we will find the required.

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A: Given y=sin3x-cos3x2

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A: Given

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A: Given thatgx=-3x+27fx =-x-52+16To find: Area bounded by the region with respect to y.Note: right to…

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A: The given matrix is A= 1 0 5 1        0 1 -1 5       2 5 1 0      0 0 4 1.

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A: Discontinuity of f can be removed by factorisation of the numerator

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Q: Q4:B/Simplify [cos 40+ i sin40 1³ [cos 20-i sin2015 using De Moivre's theorem?

A: