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3 years ago

6

How far is the top of the lampost from the tip of its shadow?

1 answer:

astraxan [27]3 years ago

3 0

Answer:

About 14.58 ft

Step-by-step explanation:

We have an angle, the side <em>opposite</em> that angle, and the <em>hypotenuse</em> of that triangle. If you remember SOH CAH TOA, the right trig ratio for this problem is <em>sine</em>. In this case, $\sin{49^{\circ}=\frac{11}{x}$ . We want to solve for x, so we can multiply both sides by x to get $x\sin{49^{\circ}}=11$ and then divide both sides by $\sin{49^{\circ}}$ to get $x=\frac{11}{\sin{49^{\circ}}} \approx 14.58$

So, the top of the lamppost is about 14.58 ft from the tip of its shadow

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2 years ago

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4 years ago

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3 years ago

At the beginning of an experiment, a scientist has 300 grams of radioactive goo. After 150 minutes, her sample has decayed to 37

monitta

Answer:

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Step-by-step explanation:

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Here, t denotes time and k denotes decay constant.

$\ln \left ( \frac{M_f}{M_0} \right )=-kt\\\ln \left ( \frac{37.5}{300} \right )=-k(150)\\-2.079=-k(150)\\k=\frac{2.079}{150}=0.014$

So, half-life of the goo in minutes is calculated as follows:

$\ln \left ( \frac{50}{100} \right )=-kt\\\ln \left ( \frac{50}{100} \right )=-(0.014)t\\t=\frac{-0.693}{-0.014}=49.5\,\,minutes$

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3 years ago