Alan

Answered here: https://web2.0calc.com/questions/reposted-because-the-answer-i-got-last-time-was-incorrect#r9 

Look at the right hand side of   x+y = 37 +15/30 -(x-y)/30 

There are two fractions on that side, namely  15/30 and -(x-y)/30 

We could rewrite them as [15 - (x-y)]/30 

We want the fractional parts to vanish because we must be left with an integer on the right hand side in order to be compatible with the integers on the left hand side.  For this to happen we simply need to make 15 - (x-y) vanish, which happens if we set x-y equal to 15.

"A pair of positive integers (x, y) satisfies the equation 31x + 29y = 1125. What is x + y?"

Write 31x as 30x + x

Write 29y as 30y - y

Then you can write 31x + 29y = 1125 as 30x + x + 30y - y = 1125  or  30(x+y) + (x-y) = 1125

Subtract x-y from both sides:    30(x+y) = 1125 - (x-y)

Divide both sides by 30:     x+y = 1125/30 - (x-y)/30 

Now 1125/30 = 37 + 15/30 so we have   x+y = 37 +15/30 -(x-y)/30  

If x and y are positive integers, the fractional terms on the right hand side must cancel each other out.

For this to happen we set (x-y) = 15, then we are left with 

x+y = 37

Use the constant acceleration formulae.

(a)   Use s = ut + (1/2)at²  where s = displacement in time t, with initial velocity u and acceleration a.

For the vertical direction we have:

 a = -32 ft/s² , u = 70*sin(30°) ft/s  and s = -3 ft  (taking the height when hit as the zero height).

So:   -3 = 70*sin(30°)*t - (1/2)*32*t²    or  16t² - 35t - 3 = 0  (noting that sin(30°) = 1/2)

Solve this for t (using the positive solution of course!).

(b)  For the horizontal direction there is zero acceleration, so:   distance = 70*cos(30°)*t  where t is the value found from part (a).

Change in F = 1.8*change in C.

To see this, let F1 = 32 + 1.8*C1  and F2 = 32 + 1.8*C2

F2 - F1 = (32 + 1.8*C2) - (32 + 1.8C1)  = 1.8*(C2 - C1)

"Divide. 2+4i/−3+2i"

As follows:

If (x, y) are the rectangular coordinates and (r, theta) are the corresponding polar coordinates, then use

r² = x² + y² 

and 

tan(theta) = y/x

to get from rectangular to polar.

This graph should help with parts a and b:

For part c, note that the denominator can be factored as (x+4)(x-3).

If you just put x = -4 in the original denominator you get zero, but if you put the denominator in factored form, and then cancel the (x+4) term you will have removed the singularity at x = -4. 

See https://web2.0calc.com/questions/can-anyone-imagine-what-happened#r3