A business that produces color copies is trying to minimize its average cost per copy​ (total cost divided by the number of​ copies). This average cost in cents is given by

​f(x)equals=0.00000093x^2−0.0146+60​,

where x represents the total number of copies produced.

​(a) Describe the graph of f.

​(b) Find the minimum average cost per copy and the corresponding number of copies made.

1)

Let y be the solution of the equation

y ′ = 4(x^4)*sin(x^4) satisfying the condition y ( 0 ) = − 1.

Find y ( pi^1/3 ).

2)

Find the largest value of the parameter r

for which the function y = e^(rx) is a solution of the

equation y ″ − 14 y ′ + 28 y = 0.

3)

Let y ′ = − 4x^2*e^(-x^4) and let y ( 0 ) = 1.

Find ln ⁡ ( y ( 2 ) ).

Could you clarify what you mean by "typing error"?

Find the general solution of this differential equation: y'''+y''+y'+y=4e^(-t)+4sin(t)

The following exercise is designed to be solved using technology such as calculators or computer spreadsheets.

Interest paid on a home mortgage is normally tax deductible. That is, you can subtract the total mortgage interest paid over the year in determining your taxable income. This is one advantage of buying a home. Suppose you take out a 30-year home mortgage for $250,000 at an APR of 8% compounded monthly. The mortgage payments details for the first year are given below.

Suppose that your marginal tax rate is 30%. What is your actual tax savings due to mortgage payments? (Round your answer to the nearest cent.)

Use Green’s theorem in the plane to evaluate∮C(4x+ 1)x2ydx+x(x3−y3)dy where C is the circle whose equation is x2+y2= 2x transversed once in an anti cloickwise direction.

1-Prove the identity.

cosh(x) + sinh(x) = e^x

2-Prove the identity.

sinh(x + y) = sinh(x) cosh(y) + cosh(x) sinh(y)

3-Prove the identity.

sinh(2x) = 2 sinh(x) cosh(x)

4-Prove the identity.

= e^2x

5-If

tanh(x) =

,

find the values of the other hyperbolic functions at x.

1. Consider the region bounded by the graph of y^2 = r^2 −x^2

(a) When this region is rotated about the x-axis a sphere of radius r is generated. Use integration to find its volume V (b) Use integration to find the surface area of such a sphere

2. Find the arc length of the curve y = 1 3 x 3/2 on [0, 60] (

3. Consider the graph of y = x^3 . Compute the surface area of revolution about the x-axis over the interval [0, 2]

4. A spring whose equilibrium length of 15in. exerts a force of 50 lbs when it is stretched to 20in. Find the work required to stretch the spring from 22in. to 24in.

Find the local maximum and minimum values and saddle point(s) of the function. If you have three dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter NONE in any unused answer blanks.) f(x, y) = x^3 – 27xy + 27y^3

EvaluateRC F·dr where F = hyzexz,exz,xyexzi and C : r = ht2 + 1,t2 −1,t2 −2ti, 0 ≤ t ≤ 2. Hint: Check whether F is conservative. If so, the Fundamental Theorem for Line Integrals might be useful

A piece of wire 28 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (Give your answers correct to two decimal places.)
(a) How much wire should be used for the square in order to maximize the total area?
(b) How much wire should be used for the square in order to minimize the total area?

Answer all the question below.

Table 2:

1.     Visualize data in table 2 in a 2-dimensional plot using Matlab.
2.     Interpolate data in table 2 to determine a value of temperature when t = 8 and t = 20.
3.     Formulate a mathematical function for data in table 2 using a curve fitting technique.
4.     Determine temperature value at t = 8 and t =20 and explain a different with a result from the interpolation technique.

Need to solve this all question. Please Provide the proper solution. Thank you

find the riemann sum f(x)=x^2 +3x over the interval [0,8] where x₀ =o, x₁=1 , x₂=6, x₄=8, and c₁=1, c₂=2, c₃=4, c₄=6

An economy is based on three sectors, agriculture, manufacturing, and energy. Production of adollar’s worth of agriculture requires inputs of $0.30 from agriculture, $ 0.30 frommanufacturing, and $0.30 from energy. Production of a dollar’s worth of manufacturing requires inputs of $0.30 from agriculture, $0.20 from manufacturing, and $0.20 from energy. Production of a dollar’s worth of energy requires inputs of $0.20 from agriculture, $0.30 frommanufacturing, and $0.30 from energy.

Find the output for each sector that is needed to satisfy a final demand of $67 billion foragriculture, $34 billion formanufacturing, and $14 billion for energy.

1) The output of the agricultural sector is ___ billion dollars

2) The output of the manufacturing sector is __ billion dollars

3) The output of the energy sector is __ billion dollars

Consider a region R bound by the coordinate axes and y = ( 9 + x 2 ) − 1 2 on 0 ≤ x ≤ 4.

a. Find the area of R.

b. Suppose R is revolved about the x-axis to form a solid. Find the volume of the solid.

c. Suppose R is revolved about the y-axis to form a solid. Find the volume of the solid.

Is this true or false? The foci for the hyperbola ((x-2)^(2))/(36)-((y+1)^(2))/(64)=1 are (2, -1 +4\sqrt(7) and (2, -1 - 4\sqrt(7)