The time it takes for 1g of strontium-90 to decay to 250 mg is; 57.6 years
<h3>What is the half life of an element?</h3>
The formula for half life is;
A(t) = A₀ * (¹/₂)^(t/t_1/2)
Where;
A(t) is amount left after t years
A₀ the initial quantity of the substance that will undergo decay;
t_1/2 is the half-life of the decaying quantity.
We are given;
t_1/2 = 28.8 years
A₀ = 1 g
A(t) = 250 mg = 0.25 g
Thus;
0.25 = 1 * (¹/₂)^(t/28.8)
log 0.25 = (t/28.8) log (1/2)
-0.60206 = (t/28.8) * -0.3010
t = 2 * 28.8
t = 57.6 years
Read more about half life at; brainly.com/question/11152793
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The first thing you have to realize is that
tangent is the
slope of a curve on a given point. You can solve for the slope by finding the derivative of the given function. So:

Next use
product rule (I recommend watching videos if you're confused):
![= [sin(x)] + [x*cos(x)]](https://tex.z-dn.net/?f=%3D%20%5Bsin%28x%29%5D%20%2B%20%5Bx%2Acos%28x%29%5D)
Next substitute you x-value (π/2) into your derivative:
![= [sin( \frac{ \pi}{2} )] +[ \frac{\pi}{2}*cos( \frac{\pi}{2})]](https://tex.z-dn.net/?f=%3D%20%5Bsin%28%20%20%5Cfrac%7B%20%5Cpi%7D%7B2%7D%20%29%5D%20%2B%5B%20%5Cfrac%7B%5Cpi%7D%7B2%7D%2Acos%28%20%5Cfrac%7B%5Cpi%7D%7B2%7D%29%5D%20%20)


So our slope at π/2 is 1. Next we use our slope-form and substitute our given value and solve for y-intercept (algebra-stuff)


So we get our equation:

So our answer is E
Feel free to ask any questions.
Hopes this helps!
A is the answer because it is eligil and black beans