Answer:
The answer is 
Step-by-step explanation:
To calculate the volumen of the solid we solve the next double integral:

Solving:

![[6x^{2} ]{{1} \atop {0}} \right. * [\frac{y^{3}}{3}]{{1} \atop {0}} \right.](https://tex.z-dn.net/?f=%5B6x%5E%7B2%7D%20%5D%7B%7B1%7D%20%5Catop%20%7B0%7D%7D%20%5Cright.%20%2A%20%5B%5Cfrac%7By%5E%7B3%7D%7D%7B3%7D%5D%7B%7B1%7D%20%5Catop%20%7B0%7D%7D%20%5Cright.)
Replacing the limits:

The plane y=mx divides this volume in two equal parts. So volume of one part is 1.
Since m > 1, hence mx ≤ y ≤ 1, 0 ≤ x ≤ 
Solving the double integral with these new limits we have:

This part is a little bit tricky so let's solve the integral first for dy:
![\int\limits^\frac{1}{m}_0 [{12x \frac{y^{3}}{3}}]{{1} \atop {mx}} \right.\, dx =\int\limits^\frac{1}{m}_0 [{4x y^{3 }]{{1} \atop {mx}} \right.\, dx](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%5Cfrac%7B1%7D%7Bm%7D_0%20%5B%7B12x%20%5Cfrac%7By%5E%7B3%7D%7D%7B3%7D%7D%5D%7B%7B1%7D%20%5Catop%20%7Bmx%7D%7D%20%5Cright.%5C%2C%20dx%20%3D%5Cint%5Climits%5E%5Cfrac%7B1%7D%7Bm%7D_0%20%5B%7B4x%20y%5E%7B3%20%7D%5D%7B%7B1%7D%20%5Catop%20%7Bmx%7D%7D%20%5Cright.%5C%2C%20dx)
Replacing the limits:

Solving now for dx:
![[{\frac{4x^{2}}{2} -\frac{4m^{3} x^{5}}{5} ]{{\frac{1}{m} } \atop {0}} \right. = [{2x^{2} -\frac{4m^{3} x^{5}}{5} ]{{\frac{1}{m} } \atop {0}} \right.](https://tex.z-dn.net/?f=%5B%7B%5Cfrac%7B4x%5E%7B2%7D%7D%7B2%7D%20-%5Cfrac%7B4m%5E%7B3%7D%20x%5E%7B5%7D%7D%7B5%7D%20%5D%7B%7B%5Cfrac%7B1%7D%7Bm%7D%20%7D%20%5Catop%20%7B0%7D%7D%20%5Cright.%20%3D%20%5B%7B2x%5E%7B2%7D%20-%5Cfrac%7B4m%5E%7B3%7D%20x%5E%7B5%7D%7D%7B5%7D%20%5D%7B%7B%5Cfrac%7B1%7D%7Bm%7D%20%7D%20%5Catop%20%7B0%7D%7D%20%5Cright.)
Replacing the limits:

As I mentioned before, this volume is equal to 1, hence:

you find what they both divide by and then divide each one and then you keep doing that until you cant no more
Answer:
$18.36
Step-by-step explanation:
In this question, we have to find the cost of the cake for the customer who orders a month early.
We know that the original price of the cake is $30.
We also know that there was a 28% discount and a 15% discount added to the purchase.
Remember, You don't add discount percentages together, you discount the prices separately.
Solve:
First, apply the 28% discount.
30 · 0.28 = 8.40
30 - 8.40 = 21.60
Now apply the 15% discount to the new price.
21.60 · 0.15 = 3.24
21.60 - 3.24 = $18.36
They needed to pay $18.36 for the cake.
Answer:
2
-1
x=4,y=11 (same in both equations)
L x w x h
3/8=0.375
5/8=0.625
7/8=0.875
0.375x0.625x0.875 =
0.205078125.......... doesn't seem right but that's what i got