Check the picture below.
so, bearing in mind that, the radius and height are two sides in a right-triangle, thus both are at a ratio of each other, thus the radius is at 3:4 ratio in relation to the height.
![\bf 12\pi =\cfrac{\pi \cdot 3^2h^2 h}{4^2}\implies 12\pi =\cfrac{9\pi h^3}{16}\implies \cfrac{192\pi }{9\pi }=h^3 \\\\\\ \sqrt[3]{\cfrac{192\pi }{9\pi }}=h\implies \sqrt[3]{\cfrac{64}{3}}=h\implies \cfrac{4}{\sqrt[3]{3}}=h \\\\\\ \cfrac{4}{\sqrt[3]{3}}\cdot \cfrac{\sqrt[3]{3^2}}{\sqrt[3]{3^2}}=h\implies \cfrac{4\sqrt[3]{9}}{\sqrt[3]{3^3}}=h\implies \cfrac{4\sqrt[3]{9}}{3}=h](https://tex.z-dn.net/?f=%5Cbf%2012%5Cpi%20%3D%5Ccfrac%7B%5Cpi%20%5Ccdot%203%5E2h%5E2%20h%7D%7B4%5E2%7D%5Cimplies%2012%5Cpi%20%3D%5Ccfrac%7B9%5Cpi%20h%5E3%7D%7B16%7D%5Cimplies%20%5Ccfrac%7B192%5Cpi%20%7D%7B9%5Cpi%20%7D%3Dh%5E3%0A%5C%5C%5C%5C%5C%5C%0A%5Csqrt%5B3%5D%7B%5Ccfrac%7B192%5Cpi%20%7D%7B9%5Cpi%20%7D%7D%3Dh%5Cimplies%20%5Csqrt%5B3%5D%7B%5Ccfrac%7B64%7D%7B3%7D%7D%3Dh%5Cimplies%20%5Ccfrac%7B4%7D%7B%5Csqrt%5B3%5D%7B3%7D%7D%3Dh%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B4%7D%7B%5Csqrt%5B3%5D%7B3%7D%7D%5Ccdot%20%5Ccfrac%7B%5Csqrt%5B3%5D%7B3%5E2%7D%7D%7B%5Csqrt%5B3%5D%7B3%5E2%7D%7D%3Dh%5Cimplies%20%5Ccfrac%7B4%5Csqrt%5B3%5D%7B9%7D%7D%7B%5Csqrt%5B3%5D%7B3%5E3%7D%7D%3Dh%5Cimplies%20%5Ccfrac%7B4%5Csqrt%5B3%5D%7B9%7D%7D%7B3%7D%3Dh)
It’s B
If y-x=6
Y +X =_10
then y= 6 + x, instead of y insert this no
6+ x+ x =-10
6 + 2x =-10 then collect like terms
2x =-10-6
2x=-16 then multiple both side by 1/2
X=-8
Y=6+x instead of x insert -8
Y=6-8
=-2
The unit rate is 24÷8
Answer 3 grams
Answer:
4 inches
Step-by-step explanation:
First, we find how much fits into one inch of soil. We do this by multiplying 4 by 3. This equals 12. For every 12 cubic inches, the soil will be one inch deep. We divide 48 by 12 to see how many inches deep is it. This equals 4. The soil is 4 inches deep.
Answer:
<h3>36 and 12</h3>
Step-by-step explanation:
Let the two positive integers be x and y.
If their product is 432, then
xy = 432 ......... 1
Also if the sum of the first plus three times the second is a minimum, then;
p(x) = x + 3y
From 1;
y = 432/x ..... 3
Substitute 3 into 2;
p(x) = x+3y
p(x)= x + 3(432/x)
p(x) = x + 1296/x
Since the expression is at minimum when dp(x)/dx = 0
dp/dx = 1 + (-1296)/x²
dp/dx = 1 -1296/x²
0 = 1 -1296/x²
0 = (x²-1296)/x²
cross multiply
0 = x²-1296
x² = 1296
x = √1296
x = 36
Since xy = 432
36y = 432
y = 432/36
y = 12
Hence the two positive numbers are 36 and 12
