(v - 1)² = 2v² - 5v - 17
(v - 2)(v - 2) = 2v² - 5v - 17
v² - 2v - 2v + 4 = 2v² - 5v - 17
v² - 4v + 4 = 2v² - 5v - 17
<u>- v² - v² </u>
-4v + 4 = v² - 5v - 17
<u>+ 5v + 5v </u>
v + 4 = v² - 17
<u> + 17 + 17</u>
v + 21 = v²
0 = v² + v + 21
v² + v + 21 = 0
v = <u>-(1) +/- √((1)² - 4(1)(21))</u>
2(1)
v = <u>-1 +/- √(1 - 84)</u>
2
v = <u>-1 +/- √(-83)
</u> 2<u>
</u> v = <u>-1 +/- 9.11i
</u> 2<u>
</u> v = -1 <u>+</u> 4.555i<u>
</u> v = -1 + 4.555i v = -1 - 4.555i
There is more than one solution.
<u />
We want to find

, for

.
Recall the product rule: for 2 differentiable functions f and g, the derivative of their product is as follows:

.
Thus,
![y'=[(x^2+2)^3]'[(x^3+3)^2]+[(x^3+3)^2]'[(x^2+2)^3]\\\\ =3(x^2+2)^2(x^3+3)^2+2(x^3+3)(x^2+2)^3](https://tex.z-dn.net/?f=y%27%3D%5B%28x%5E2%2B2%29%5E3%5D%27%5B%28x%5E3%2B3%29%5E2%5D%2B%5B%28x%5E3%2B3%29%5E2%5D%27%5B%28x%5E2%2B2%29%5E3%5D%5C%5C%5C%5C%20%3D3%28x%5E2%2B2%29%5E2%28x%5E3%2B3%29%5E2%2B2%28x%5E3%2B3%29%28x%5E2%2B2%29%5E3)
Answer: A)

.
Answer:
Part 1) 
Part 2) 
Step-by-step explanation:
The picture of the question in the attached figure
Part 1
Find the length side AB
we know that
----> by SOH (opposite side divided by the hypotenuse)
substitute the given values

solve for AB

Part 2
Find the length side AC
we know that
----> by TOA (opposite side divided by the adjacent side)
substitute the given values

solve for AC

The mass of radioactive material remaining after 50 years would be 48.79 kilograms
<h3>How to determine the amount</h3>
It is important to note that half - life is the time it takes for the amount of a substance to reduce by half its original size.
Given the radioactive decay formula as
m(t)=120e−0.018t
Where
t= 50 years
m(t) is the remaining amount
Substitute the value of t


Find the exponential value
m(t) = 48.788399
m(t) = 48.79 kilograms to 2 decimal places
Thus, the mass of radioactive material remaining after 50 years would be 48.79 kilograms
Learn more about half-life here:
brainly.com/question/26148784
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