Answer: a = 3∛2
<u>Step-by-step explanation:</u>
ab⁴ = 384 --> a = 384/b⁴
Substitute a = 384/b⁴ into the second equation to solve for "b".
a²b⁵ = 4608
![\bigg(\dfrac{384}{b^4}\bigg)^2\cdot b^5=4608\\\\\\\dfrac{147,456b^5}{b^8}=4608\\\\\\\dfrac{147,456}{b^3}=4608\\\\\\\dfrac{147,456}{4608}=b^3\\\\\\32=b^3\\\\\\\sqrt[3]{32} =b\\\\\\2\sqrt[3]{4} =b](https://tex.z-dn.net/?f=%5Cbigg%28%5Cdfrac%7B384%7D%7Bb%5E4%7D%5Cbigg%29%5E2%5Ccdot%20b%5E5%3D4608%5C%5C%5C%5C%5C%5C%5Cdfrac%7B147%2C456b%5E5%7D%7Bb%5E8%7D%3D4608%5C%5C%5C%5C%5C%5C%5Cdfrac%7B147%2C456%7D%7Bb%5E3%7D%3D4608%5C%5C%5C%5C%5C%5C%5Cdfrac%7B147%2C456%7D%7B4608%7D%3Db%5E3%5C%5C%5C%5C%5C%5C32%3Db%5E3%5C%5C%5C%5C%5C%5C%5Csqrt%5B3%5D%7B32%7D%20%3Db%5C%5C%5C%5C%5C%5C2%5Csqrt%5B3%5D%7B4%7D%20%3Db)
Substitute b = 2∛4 into the first equation to solve for "a".
ab⁴ = 384
a(2∛4)⁴ = 384
a = 384/(2∛4)⁴
a = 24/4∛4
= 6/∛4
= 6(∛2)/2
= 3∛2
For every 6 apple pie, you need 2 pounds of apples.
So, how many pounds of apples do you need for 10 apple pies?
Well, first to figure out this question we first need to make a conversion factor.
I see in the fraction 6/3 we can simplify that to 2/1. Now we got our conversion factor.
We need to invert the fraction in order for the pie unit to cancel out.
1/2 * 10 = 5
You will need 5 pounds of apples to make 10 apple pies.
Basically, you are looking for the ARC SINE of .994 which is
83.72 Degrees
You could also use an online calculator:
http://www.1728.org/trigcalc.htm
This is the diference of 2 perfect squares. 4 is a perfect square, x^2 is a perfect square, and 25 is a perfect square. The pattern for this is (ax + b)(ax - b). Our a is 2 since 2*2 = 4, and our b is 5 since 5*5 = 25. So your factors are (2a+5)(2a-5), choice C.
