The function P(x) = - 0.25a² + 150x – 4000 gives the profit when a units of a certain product are sold. Find a) the profit when 50 units are sold dollars b) the average profit per unit when 50 units are sold dollars per unit c) the rate that profit is changing when exactly 50 units are sold dollars per unit d) the rate that profit changes on average when the number of units sold rises from 50 to 100. dollars per unit e) The number of units sold when profit stops increasing and starts decreasing. (Round to the nearest whole number if necessary.) units

Q: You are the Director of Infrastructure Management at the Nash Telecommunications Company. You are ta...

A:

Q: lve the differential equation y" + 16y =0 for y(r). || olve the differential equation y" +4y = e for...

A: Please refer to the image below

Q: Question 4 P4.5 If the 3rd term of a geometric progression is 52 and the 7th term is 832, then find ...

A:

Q: Use the limit comparison test to determine whether the series converges or diverges. 8k2 – 6k + 6 16...

A:

Q: Let f(x) = (3 – a) f(1) has one critical value at A = For I < A, f(r) is Select an answer Select an ...

A: We have to find the critical point and monotonic intervals.

Q: Rewrite the integration in terms of u. 1 x cos 10rx² dx = COs u du Apply the constant multiplication...

A:

Q: ove that the Solutm f y+ y = y CX) = A CoJ X + B sinx (hint y by using Bessel's Functron defin

A:

Q: 8. (x + 2y – 1)dx + (2x + 4y – 3)dy = 0 (r - 1)y' = v+ 2(x – 1)3 9

A:

Q: Find each function value and limit. Use ∞ or co where appropriate. 3x3 - 6x2 f(x) = 10x* +5 (A) f(- ...

A: given f(x) =3x3-6x210x4+5at x = -6f(-6) = 3×-63-6×-6210×-64+5f(-6) = -0.067at x = -12f(-12) = 3×-123...

Q: ermine the slope of the normal to f(x) = / 2r' – 18 at x = 3? %3D

A: Please refer to the image below

Q: Determine whether the series converges; if so, find its sum. Otherwise type N in the blank. 1 Σ k(k ...

A:

Q: Explain the following intervals on the line numbers-3<x<5

A: We will explain the given interval on the number line in the following step.

Q: The figure shows the median lifetime eamings E in dollars determined by the highest level of educati...

A:

Q: et Q(t) = t2. Find a value A + 1 such that the average rate of change of Q(t) from 1 to A equals the...

A: Given query is to find the value of A for which average rate of change will be equal to instantaneou...

Q: f(x+h) = 1/x+h+3 compute and simplify f(x+h)-f(x)

A: Given that, f(x+h) = 1x+h+3 We have to find the value of f(x + h) - f(x).

Q: First make a substitution and then use integration by parts to evaluate the integral. (Use C for the...

A:

Q: A parallelogram is determined by the vectors = (-2, 5) and 7= (3, 2). Determine the angle between th...

A:

Q: ompute the instantaneous slope at: (-1,-1) A: (-1,-1) and B: (x,-1/x+2) so triangle x = triangle ...

A: We have to find the instantaneous slope at: (-1,-1).

Q: 1 xp2 xV9x²-4

A:

Q: Q 3/ Find the psints the Curve y=2x=3=? 12 x+20 on where the tangent is parallel to the X-aXis

A:

Q: Let f(x) = x(x-4). (a) Find the critical numbers of the function f. (Enter your answers from smalles...

A:

Q: Determine

A:

Q: f(x) = 8 +3/x f'(x) =D f'(1)=D (Simplify your answer. Type an exact answer, using radicals as needed...

A: f(x)= 8+√3x  Find f'(x) , f'(1), f'(2) and f'(3) 

Q: Find the length of the bath Y on these states a) z = 2t + it where 0 <t < 1 TT b) z = 2 sin(÷) where...

A:

Q: dx using the Trapezoid Rule, and n=6. Your answer should be to the tenths place (so of the form X.x)...

A:

Q: 4. The two sides forming the right angle of a right-angled triangle are denoted by a and b. The hypo...

A:

Q: 10. Do the required operations and simplify. State any restrictions. (x+1}*x (x-1)? x+2x-3x+4x+3 a)....

A: We can simplify the given questions as below.

Q: Find the maximum and minimum values attained by f(x,y,z) = xyz on the unit ball x2+y2+z2 ≤ 1

A:

Q: Find the maximum value of f(x, y) = 2x? y + 5 on the unit circle. (Give an exact answer. Use symboli...

A: Given fx,y=2x2y3+5 on unit circle. We have to find maximum value.  

Q: Inventory cost A retailer has determined that the cost C of ordering and storing x units of a produc...

A:

Q: 11. If 16% less than a certain quantity is 441, find the quantity. Ans. 525

A: 11. Let the certain quantity be x From the given statement x-16% of x=441

Q: Find all critical values for f(x) (x 10) (x + 1)". The critical values occur at x = (Enter your answ...

A: Topic:- function and application of derivatives

Q: f (x, y) = 5ye" – e5x – yð

A: for critical points equate the first derivative wrt x and y to zero.  

Q: Determine the equation of the tangent to the graph of y = x³ - 3x² + x+ 3 at the point x = -1

A:

Q: ve the given boundary-value problem. (If an answer does not exist, enter DNE.) y" + y = 0, y'(0) = 0...

A: Topic:- differential equations

Q: x3 – 1 When you evaluate: dx The sum of the coefficient of for any constant n is 16 7 (c) None of th...

A: We know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power rule: ∫xndx=xn+1n+1+C ; n≠-1   Given: I=∫...

Q: dx 2+ Vx-4

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you wa...

Q: (- 4,3). a) Let f(x, y)= x²y°. Find the directional derivative of f at P(-1,1) in the direction of ū...

A: a)

Q: 8. Svay y3 y²dy 2-

A: We have ∫y2dy2-y3

Q: Prove the following claim: At least two powers of 3 have exactly 100 digits

A: The number of digits in an number x is log10x+1, where · is the greatest integer function. The Claim...

Q: Use LaGrange multipliers to find the maximum and minimum for the function f(x, y)=x² +2y² restricted...

A:

Q: -7 h'(s) (s – 12)2 Find the s values in the interval [-6, 3 where h(s) takes its minimum. S =

A: We have to find the s values in the interval [-6, 3] where h(s) takes its minimum.

Q: III. Find the maximum point, minimum point, and inflection point 2. y = x* - 2x? +3

A:

Q: y^2dy=x(xdy-ydx)e^x/y solve using homogeneous equations (diff eq)

A:

Q: f(x+h) = x^2+2xh+h^2-3x-3h compute and simplify. f(x+h)-f(x) =

A:

Q: Consider the function f() For this function there are three important intervals: (- 00, A, [4, B, an...

A:

Q: Use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). f(x) = 1+ -

A:

Q: Compute the discriminant D(x, y) of the function. f(x, y) = x' + yt – 6x – 2y² + 1 (Express numbers ...

A:

Q: 3sec(2x-45)-2 amplitude,period,horizontal,vertical

A: We have to find the amplitude period horizontal and vertical shifts of the secent  function.

Q: Use the definition of the Taylor series to find the Taylor series of each of the following functions...

A: Given f (x) = sin x, c = π/4  We have to find the Taylor series and  radius of convergence.