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A 2400 hp diesel locomotive burns 160 gals of fuel per hour. If the heat of combustion of the diesel oil used is 1.2*10^5 Btu/gal, find the efficiency of the motor.

Please show your work.

A tire contain 1 cubic foot of air at gauge pressure of 28 lb/in2. How much additonal air at atmospheric pressure must be pumped into the tire to raise the pressure to 36 lb/in2 at the same temperature?

Please show your work.

Hi.

I have 3 resistors, two of them are connected in series and they are 100 and 50 ohms. These 2 are in parallel with the third resistor which is 100 ohms. I thought the total was 250 but I was wrong. Then I tried again and came up with 60 ohms which is also wrong. How do I do this?

Hi.

I am looking at a working in a book and there is a step I don´t understand, I need some help with what happens.

Here is the original problem:

6x^2y´´ + 7xy´ - (1+x^2)y = 0 ;

Then there are a number of steps shown which I understand until:

1) Sum (from 0 to infinity) (6(n+r)(n+r-1) + 7(n+r) -1) subscript (a) x^n+r - sum (from 2 to infinity) a sub (m-2) * x^m+r = 0

2) Sum (from 0 to infinity) (6(n+r)^2 + n + r - 1) a (sub n) - a (sub n-2)) * x^n+r = 0

I don´t understand how to get from 1 to 2. 1 I understand but not how to get from 1 to 2. Where is the 7 in 2?

Please explain that and what happens.

Thank you.

Hi.

I have the following double integral to evaluate and I need to turn the limits into polar coordinates. Here is the integral with Cartesian limits:

∫ ∫ x dx dy ; for first integral the upper limit is 6 and lower 0. For the second integral the upper limit is y and the lower limit is 0.

Please show your work.

Also, is the some method for translating the limits from polar to cartesian and vice versa?

Thank you.

Hi.

How do I go about finding the area of a a half circle from x = -1 to x = 1

and y = 0 to y = 1. This half circle is in quadrants 1 and 2.

How is this done using double integral?

Please show steps.

Thank you.

Hi.

How does one integrate the following:

int : sin (xy) dx

Thanks

Hi

A projectile is fired with an initial speed of 500m/sec at an angle of elevation of 45°.

How high overhead will the projectile be when it has traveled 5 km?

Please show how you get the answer.

Thanks

Hi.

I am wondering how one finds the equation in x and y from a vector function and vice versa? It would be good if you could explain from these 2 examples:

1) r(t) = (cos t)i + (sin t) j + tk

2) r(t) = (t+1)i + (t^2 -1)k

Please show your work.

Thank you.

Hi.

How do I integrate the following function:

∫ (x+1)*sqrt(5-x) dx.

I want to know how to do it using substitution, not integration by parts. Please show how you do it and explain the steps.

Thank you!

Hi.

Sometimes one needs to use integration by parts more than once.

∫ e^x * x^3 dx needs to be done 3 times and ∫ e^x * x^2 dx needs to be done twice. Sometimes it is obvious how many times one needs to integrate but sometimes not. Take the following as an example:

∫ e^2x * sin (x) dx. How does one know that it is enough to integrate it twice? Is there some general rule?

Thank you!

Hi.

I need to integrate the following fraction:

(3x^2 + 2x +4) / ((x+1)*(x^2 + 4))

I know the upper one is the derivative of the lower one so this is no major deal. What I am looking for is how to simplify this fraction so I can tackle fractions that aren´t so "neat".

I know this one simplfies to (2x/x^2 + 4) + (1/x+1) but I don´t know how it becomes like that. Can someone please walk me through how to simplify it or break it up?

Thank you!

Hi.

How do I change the following function into partial fractions so I can integrate it:

(1-3x) / (x(1+x^2))

Show me how it is done, please.

Thank you.

Hi.

How do I find the solution to:

x^2 + 4x +13 = 0

Please walk me through how to solve an equation like this.

Thank you!

Hi.

How does one solve equations that have complex numbers as answers? Perhaps someone can walk me through how to solve this one:

x^2 - 2x + 5 = 0

Thank you!

Hi.

I need to evaluate the function f(x,y,z) = 1 / sqrt(x^2 + y^2 + z^2) over the bottom half of the sphere of radius 5 centered at the origin.

Can you please show work? I have the solution but don´t know how to get there.

Thank you!

Hi.

I am supposed to find the area here:

f(x,y,z) = x^2 + y^2 + z^2 and W (region) has radius between 0 and 4, θ is between π/4 and 3π/4 and z is from -1 to 1.

Please show work, I have the solution but don´t know how to get it.

Thank you!

Hi.

I think I am supposed to find the area here.

f(x,y,z) = x^2 + y^2 + z^2 and W (region) has radius between 0 and 4, θ is between π/4 and 3π/4 and z is from -1 to 1.

Please show work, I have the solution but don´t know how to get it.

Thank you!

Hi.

I am supposed to evaluate a double integral for the function x^2 - y^2 where R is in the first quadrant between the circles of radius 1 and radius 2. I need to use polar coordinates.

Can someone please walk me through the solution? I am supposed to find the area.

Also, is the a website where I can enter the function to see what it looks like?

Thank you!

Hi.

I am having some problem understanding changing of signs when I differentiate.

Let´s consider 1/(x-y) and we differentiate with respect to y. That becomes 1/ (y-x)^2. Why the changing of signs. Further differentiation with respect to y yields: -2/(y-x)^3. Why don´t the signs change back to what they were originally?

Thank you!