4 years ago

Which set of line segments could create a right triangle? a 15, 30, 35 b 15, 36, 39 c 15, 20, 29 d 5, 15, 30

1 answer:

7 0

Which set of line segments could create a right triangle? a 15, 30, 35 b 15, 36, 39 c 15, 20, 29 d 5, 15, 30 = b 15, 36, 39

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What is the expression (cscx+cotx)^2 the same as?

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c)1 + 2cot^2x + 2cscx cotx

because cosc^2x=1+cot^2x

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a stainless steel garbage can is in the shape of a right circular cylinder. If its radius is 6 inches and its volume is 864 pi c

lubasha [3.4K]

$\bf \textit{volume of a cylinder}=v=\pi r^2 h\qquad 
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The core melt- down and explosions at the nuclear reactor in Chernobyl in 1986 released large amounts of strontium-90, which dec

elena-14-01-66 [18.8K]

If $S(t)$ is the amount of strontium-90 present in the area in year $t$ , and it decays at a rate of 2.5% per year, then

$S(t+1)=(1-0.025)S(t)=0.975S(t)$

Let $S(0)=s$ be the starting amount immediately after the nuclear reactor explodes. Then

$S(t+1)=0.975S(t)=0.975^2S(t-1)=0.975^3S(t-2)=\cdots=0.975^{t+1}S(0)$

or simply

$S(t)=0.975^ts$

So that after 50 years, the amount of strontium-90 that remains is approximately

$S(50)=0.975^{50}s\approx0.282s$

or about 28% of the original amount.

We can confirm this another way; recall the exponential decay formula,

$S(t)=se^{kt}$

where $t$ is measured in years. We're told that 2.5% of the starting amount $s$ decays after 1 year, so that

$0.975s=se^k\implies k=\ln0.975$

Then after 50 years, we have

$S(50)=se^{50k}\approx0.282s$

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