Answer:
The factorization of
is 
Step-by-step explanation:
This is a case of factorization by <em>sum and difference of cubes</em>, this type of factorization applies only in binomials of the form
or
. It is easy to recognize because the coefficients of the terms are <u><em>perfect cube numbers</em></u> (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).
Let's solve the factorization of
by using the <em>sum and difference of cubes </em>factorization.
1.) We calculate the cubic root of each term in the equation
, and the exponent of the letter x is divided by 3.
![\sqrt[3]{729x^{15}} =9x^{5}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B729x%5E%7B15%7D%7D%20%3D9x%5E%7B5%7D)
then ![\sqrt[3]{10^{3}} =10](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B10%5E%7B3%7D%7D%20%3D10)
So, we got that
which has the form of
which means is a <em>sum of cubes.</em>
<em>Sum of cubes</em>

with
y 
2.) Solving the sum of cubes.


.
Answer:
The height of the rock formation is 
Step-by-step explanation:
see the attached figure to better understand the problem
we know that

solve for h

After it is fully simplified, it will be 5x+1-3y
Answer:
y = (2/5) OR y = (6/5)
Step-by-step explanation:
The first step is isolating the expression within the absolute value bars. The first thing we can do is subtract both sides by 8. If we do that, we get -2|4-5y| = -4. Now, to completely isolate the absolute value, we would have to divide by -2. This yields |4 - 5y| = 2. Finally, we can remove the absolute value bars. However, to do this, we need to first understand what an absolute value bar does to an equation. Lets say that |x| = 2. Absolute value describes the DISTANCE of some quantity from 0 (on the number line). Therefore, x (which is inside the absolute value bars) can be either positive or negative 2 (they are BOTH two units away from 0). Similarly, in this case, (4 - 5y) can either be 2 or -2 (because the absolute value of both is 2). Now we have two possible solutions to solve for:
4 - 5y = 2 OR 4 - 5y = -2
5y = 2 OR 5y = 6
y = (2/5) OR y = (6/5)
If we plug both of these answers back into the equation we can see that they both check out.
We need to find the percent increase from 38.8 to 82.4, so
x * 38.8 = 82.4
x = 82.4/38.8
x = 2.1237
Multiply by 100 to convert to percentage (move decimal 2 places to the right)
2.1237 = 212.37%
Now we can apply this percentage increase to the onion dip...
0.48 x 212.37% =
0.48 x 2.1237 = 1.019
Round to the nearest cent $1.02 is the amount of increase. Now add it to the original price to get today's price...
$1.02 + .48 = $1.50