Answer:
The factorization of
is ![(9x^{5} +10)(81x^{10} -90x^{5} +100)](https://tex.z-dn.net/?f=%289x%5E%7B5%7D%20%2B10%29%2881x%5E%7B10%7D%20-90x%5E%7B5%7D%20%2B100%29)
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>
![(a^{3} +b^{3} )=(a+b)(a^{2} -ab+b^{2})](https://tex.z-dn.net/?f=%28a%5E%7B3%7D%20%2Bb%5E%7B3%7D%20%29%3D%28a%2Bb%29%28a%5E%7B2%7D%20-ab%2Bb%5E%7B2%7D%29)
with
y ![b=10](https://tex.z-dn.net/?f=b%3D10)
2.) Solving the sum of cubes.
![(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)((9x^{5})^{2}-(9x^{5})(10)+10^{2} )](https://tex.z-dn.net/?f=%289x%5E%7B5%7D%29%5E%7B3%7D%20%2B%20%2810%29%5E%7B3%7D%3D%289x%5E%7B5%7D%20%2B10%29%28%289x%5E%7B5%7D%29%5E%7B2%7D-%289x%5E%7B5%7D%29%2810%29%2B10%5E%7B2%7D%20%29)
![(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)(81x^{10}-90x^{5}+100)](https://tex.z-dn.net/?f=%289x%5E%7B5%7D%29%5E%7B3%7D%20%2B%20%2810%29%5E%7B3%7D%3D%289x%5E%7B5%7D%20%2B10%29%2881x%5E%7B10%7D-90x%5E%7B5%7D%2B100%29)
.
Answer:
She will have $71.32.
Step-by-step explanation:
135-(44.8+18.88)=71.32
Answer:my
The height of the stack will be 9.15×10^20_m
Or 9.15×10^17_Km
Which is 6 billion times more more than the distance to the sun
Or 22.9 million times further than the star Proxima Centauri
Step-by-step explanation:
Given
Avogadro's number = 6.02×10^23 particles
And the thickness of a penny = 1.52_mm
The height of the stack will be
1.52 × 6.02 ×10^23 = 9.15×10^23_mm 9.15×10^20_m
Answer:
37.931%
Step-by-step explanation:
11 / (11+18)
Answer:
B and E
Step-by-step explanation:
The zero of a function is whatever point on the function where the y-value is zero. Hope this helped.