John invests $5625 into a savings account with a fixed annual interest rate of 7% compounded continuously. How many years will i
1 answer:
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To get rid of 
, you have to take the third root of both sides:
![\sqrt[3]{x^{3}} = \sqrt[3]{1}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7Bx%5E%7B3%7D%7D%20%3D%20%5Csqrt%5B3%5D%7B1%7D%20)
But that won't help you with understanding the problem. It is better to write
as a product of 2 polynomials:
From this we know, that
is the solution. Another solutions (complex roots) are the roots of quadratic equation.
But that won't help you with understanding the problem. It is better to write
From this we know, that
Answer:
Part A : 2y( x³ + 9x - 5x² - 45 ), Part B : 2y( x - 5 )( x² + 9 )
Step-by-step explanation:
Part A : Let's break every term down here to their " prime factors ", and see what is common among them,
2x³y + 18xy − 10x²y − 90y -
2x³y = 2 x³
y,
18xy = 2 3
3
x
y,
− 10x²y = 2 - 5
x²
y, - so as you can see for this example I purposely broke down - 10 into 2 and - 5. I could have placed the negative on the 2, but as that value was must likely common among all the terms, I decided to place it on the 5. The same goes for " − 90y. " I placed the negative there on the 5 once more.
− 90y = 2 - 5
3
3
y
The terms common among each term are 2 and y. Therefore, the GCF ( greatest common factor ) is 2x. Let's now factor the expression using this value.
2y( x³ + 9x - 5x² - 45 )
Part B : Let's simply factor this entire expression. Of course starting with the " factored " expression : 2y( x³ + 9x - 5x² - 45 ),
- Factor out "
" by grouping,
- Factor 9 from 9x - 45 and x² from x³ - 5x²,
- Factor out common term x - 5,
- And our solution is thus 2y( x - 5 )( x² + 9 )