Calculus Problems

[Amu]

Hello Everyone,

I need help on these problems as soon as possible (probably by today's midnight). I am stuck as I don't know where to begin. ): Any help will be appreciated, thank you!

1) The revenue (in thousand of dollars) from the sale of x thousand units of food processors is given by f(x) = 10xe^(-0.05x). How many processors must be sold to generate a revenue of $60,000.00?

2) The following table gives the distance between Math street and Robin's creek at various locations (every 10 feet) along Math street from Algebra avenue. The x values are the distances from Algebra ave and the y distances from Math street to Robin's creek. (Math street and Algebra ave meet in a right angle). Find the area of the lot.

x -> 0 10 20 30 40 50 60 70 80 90 100 110 120 x is in feet
y -> 75 81 84 76 67 68 69 72 68 56 42 23 0 y is in feet

(Do numbers 3 and 4 using a Trapezoid AND a Simpson's method, both methods)

3) The circumference of an ellipse whose major axis is 4√3 inches long and minor axis is 4 inches long is = 8√3 ∫ √1-(2/3)(sin(θ))dθ from (0, (π/2)). Find the circumference.

(Do number 4 by Trapezoid method)

4) A hanger is 100 ft long and 40 ft wide. A cross section of the hanger is the inverted catenary y = 31-10(e^(x/20)+e^(-x/20). Find the number of square ft of roofing on the hanger. (Hint: Find the arc length of the catenary and multiply by the length of the hanger).

(Do number 5 by Simpson's method)

5) The Gateway Arch in St. Louis, Missouri in anc arc with the equation y = 693.8597-68.7872cosh(0.0100333x) with -299.2239 ≤x≤299.2239. Find the length of the curve that is the arch. (Note: Coshx is the hyperbolic cosine the derivative of which is sinhx).

 

[Deleted member 4993]

Hello Everyone,

I need help on these problems as soon as possible (probably by today's midnight). I am stuck as I don't know where to begin. ): Any help will be appreciated, thank you!

1) The revenue (in thousand of dollars) from the sale of x thousand units of food processors is given by f(x) = 10xe^(-0.05x). How many processors must be sold to generate a revenue of $60,000.00?

2) The following table gives the distance between Math street and Robin's creek at various locations (every 10 feet) along Math street from Algebra avenue. The x values are the distances from Algebra ave and the y distances from Math street to Robin's creek. (Math street and Algebra ave meet in a right angle). Find the area of the lot.

x -> 0 10 20 30 40 50 60 70 80 90 100 110 120 x is in feet
y -> 75 81 84 76 67 68 69 72 68 56 42 23 0 y is in feet

(Do numbers 3 and 4 using a Trapezoid AND a Simpson's method, both methods)

3) The circumference of an ellipse whose major axis is 4√3 inches long and minor axis is 4 inches long is = 8√3 ∫ √1-(2/3)(sin(θ))dθ from (0, (π/2)). Find the circumference.

(Do number 4 by Trapezoid method)

4) A hanger is 100 ft long and 40 ft wide. A cross section of the hanger is the inverted catenary y = 31-10(e^(x/20)+e^(-x/20). Find the number of square ft of roofing on the hanger. (Hint: Find the arc length of the catenary and multiply by the length of the hanger).

(Do number 5 by Simpson's method)

5) The Gateway Arch in St. Louis, Missouri in anc arc with the equation y = 693.8597-68.7872cosh(0.0100333x) with -299.2239 ≤x≤299.2239. Find the length of the curve that is the arch. (Note: Coshx is the hyperbolic cosine the derivative of which is sinhx).

These are nice set of problems - looks like a take-home-test!

Are you supposed to seek external help for test?

Anyway, in this site, most of us want to know how much you know so that we can help you properly.

Please share your work with us.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (e.g. "are these correct?")

 

[DrPhil]

We need to see your work! What have you tried - what tools you know . . .

Hello Everyone,

I need help on these problems as soon as possible (probably by today's midnight). I am stuck as I don't know where to begin. ): Any help will be appreciated, thank you!

1) The revenue (in thousand of dollars) from the sale of x thousand units of food processors is given by f(x) = 10xe^(-0.05x). How many processors must be sold to generate a revenue of $60,000.00?

If you ignore the 4exponential correction, you can get a first apprioximation. Then refine with "successive approximations".

2) The following table gives the distance between Math street and Robin's creek at various locations (every 10 feet) along Math street from Algebra avenue. The x values are the distances from Algebra ave and the y distances from Math street to Robin's creek. (Math street and Algebra ave meet in a right angle). Find the area of the lot.

x -> 0 10 20 30 40 50 60 70 80 90 100 110 120 x is in feet
y -> 75 81 84 76 67 68 69 72 68 56 42 23 0 y is in feet

(Do numbers 3 and 4 using a Trapezoid AND a Simpson's method, both methods)

Both methods use weighted sums of the data points. You should know those patterns - or be able to find them in your text.

3) The circumference of an ellipse whose major axis is 4√3 inches long and minor axis is 4 inches long is = 8√3 ∫ √1-(2/3)(sin(θ))dθ from (0, (π/2)). Find the circumference.

The integral is 4 times the length of the portion of the ellipse in the first quadrant. You need to make a table of values of theta (evenly spaced from 0 to pi/2) and then calculate the integrand for each. Then use trapezoidal and Simpson's rules.

(Do number 4 by Trapezoid method)

4) A hanger is 100 ft long and 40 ft wide. A cross section of the hanger is the inverted catenary y = 31-10(e^(x/20)+e^(-x/20). Find the number of square ft of roofing on the hanger. (Hint: Find the arc length of the catenary and multiply by the length of the hanger).

(Do number 5 by Simpson's method)

5) The Gateway Arch in St. Louis, Missouri in anc arc with the equation y = 693.8597-68.7872cosh(0.0100333x) with -299.2239 ≤x≤299.2239. Find the length of the curve that is the arch. (Note: Coshx is the hyperbolic cosine the derivative of which is sinhx).

Likewise, make tbles of values and find the indicated weighted sums.

When you have more work to show us, we can help where you get stuck.

 

[Deleted member 4993]

Hello Everyone,

I need help on these problems as soon as possible (probably by today's midnight). I am stuck as I don't know where to begin. ): Any help will be appreciated, thank you!

1) The revenue (in thousand of dollars) from the sale of x thousand units of food processors is given by f(x) = 10xe^(-0.05x). How many processors must be sold to generate a revenue of $60,000.00?

Finding zero by Newton-Raphson we get x = 9.788

2) The following table gives the distance between Math street and Robin's creek at various locations (every 10 feet) along Math street from Algebra avenue. The x values are the distances from Algebra ave and the y distances from Math street to Robin's creek. (Math street and Algebra ave meet in a right angle). Find the area of the lot.

x -> 0 10 20 30 40 50 60 70 80 90 100 110 120 x is in feet
y -> 75 81 84 76 67 68 69 72 68 56 42 23 0 y is in feet

Area = 10*(75+81)/2 +10*(81+84)/2 + ... +10*(23+0)/2

= 5*75 + 10*(81+84+76+67+68+56+42+23) ........sq.ft

(Do numbers 3 and 4 using a Trapezoid AND a Simpson's method, both methods)

3) The circumference of an ellipse whose major axis is 4√3 inches long and minor axis is 4 inches long is = 8√3 ∫ √1-(2/3)(sin(θ))dθ from (0, (π/2)). Find the circumference.

(Do number 4 by Trapezoid method)

4) A hanger is 100 ft long and 40 ft wide. A cross section of the hanger is the inverted catenary y = 31-10(e^(x/20)+e^(-x/20). Find the number of square ft of roofing on the hanger. (Hint: Find the arc length of the catenary and multiply by the length of the hanger).

(Do number 5 by Simpson's method)

5) The Gateway Arch in St. Louis, Missouri in anc arc with the equation y = 693.8597-68.7872cosh(0.0100333x) with -299.2239 ≤x≤299.2239. Find the length of the curve that is the arch. (Note: Coshx is the hyperbolic cosine the derivative of which is sinhx).

.

 

[HallsofIvy]

Hello Everyone,

I need help on these problems as soon as possible (probably by today's midnight). I am stuck as I don't know where to begin. ): Any help will be appreciated, thank you!

1) The revenue (in thousand of dollars) from the sale of x thousand units of food processors is given by f(x) = 10xe^(-0.05x). How many processors must be sold to generate a revenue of $60,000.00?

If you want an exact solution, let t= -.05x. Then x= -20t so the equation becomes 10(-20t)e^t= -200te^t= 60000 or te^t= -300. The solution to that is t= W(-300) where W is the Lambert W function, defined as the inverse function to f(x)= xe^x. Then since x= -20t, x= -20W(-300)