NO LINKS!!! Please help fill in the blanks. Part 8a

Mathematics

2 answers:

viva [34]2 years ago

7 0

$\\ \tt\hookrightarrow 2(3)^{12t}=1200$

Isolate the term

$\\ \tt\hookrightarrow (3)^{12t}=600$

Apply log on both sides

$\\ \tt\hookrightarrow log(3)^{12t}=log600$

$\boxed{\sf log_a b=bloga}$

$\\ \tt\hookrightarrow 12tlog3=log600$

$\\ \tt\hookrightarrow t=\dfrac{log600}{12log3}$

$\\ \tt\hookrightarrow t=\dfrac{2.778}{12(0.477)}$

$\\ \tt\hookrightarrow t=\dfrac{2.778}{5.724}$

$\\ \tt\hookrightarrow t=0.485$

Aloiza [94]2 years ago

7 0

MisterBrainly has already solved part 1, so I'll go over part 2 only.

Check out the screenshot below.

Side note: The portion "Time in years" at the very end could easily be something like "time in days" or "time in "months". It's not clear what time unit your teacher wants. Also, it will depend on how the half-life is set up.

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A detective knows what time of day it is based on the angle at which the sun is hitting a man. Suppose a detective is looking at

soldi70 [24.7K]

Answer:

The angle $\theta$ at which the sun is hitting the ground is:

$\theta\approx 59.74^o$

Step-by-step explanation:

You can use right angle trigonometry to solve this, since the man (6 ft tall) and the shadow on the ground (3.5 ft long) form a right angle triangle as shown on the attached image.

The use the tangent function to find the angle that the sun's rays make with the ground:

$tan(\theta)=\frac{opposite}{adjacent} \\tan(\theta)=\frac{6}{3.5} \\\theta=arctan(\frac{6}{3.5})\\\theta\approx 59.74^o$