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2 years ago

Help with #5 above!!!!!

Mathematics

1 answer:

Serggg [28]2 years ago

5 0

<h3>Answer: 38.66 degrees</h3>

==========================================

Explanation:

As you stated in problem 4, tan(angle) = opposite/adjacent

We'll use this idea to help find angle Z. First lets set up the proper tangent ratio for this problem

tan(Z) = XY/YZ

tan(Z) = 8/10

tan(Z) = 0.8

To isolate Z, we need to undo the tangent function. We will use the inverse tangent or the arctangent function to do this.

tan(Z) = 0.8

arctan( tan(Z) ) = arctan(0.8)

Z = 38.6598 which is approximate

This rounds to 38.66

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If 3,000 bacteria, with a growth constant (k) of 2.8 per hour, are present at the beginning of an experiment, in how many hours

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Given:

Initial number of bacteria = 3000

With a growth constant (k) of 2.8 per hour.

To find:

The number of hours it will take to be 15,000 bacteria.

Solution:

Let P(t) be the number of bacteria after t number of hours.

The exponential growth model (continuously) is:

$P(t)=P_0e^{kt}$

Where, $P_0$ is the initial value, k is the growth constant and t is the number of years.

Putting $P(t)=15000,P_0=3000, k=2.8$ in the above formula, we get

$15000=3000e^{2.8t}$

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2 years ago

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