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3 years ago

If GHJ is equal to LMK, with a scale factor of 5:6, find the perimeter of GHJ.

Mathematics

1 answer:

xxTIMURxx [149]3 years ago

4 0

Answer: Weeeell, 35

Step-by-step explanation:

1. By definition, the perimeter of a triangle is the sum of the lenght of each side.

2. Then, the perimeter of the triangle LMK is:

P_{LMK}=14+17+11\\P_{LMK}=42

3. If both triangles are congruent and the scale factor is 5:6 (Which you can rewrite as a fraction: 5/6), you must multiply the perimeter of the triangle LMK by this scale factor.

4. Then, you have that the perimeter of the triangle GHJ is:

P_{GHJ}=42*\frac{5}{6}=35

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Answer:

15595 bacteria will be present after 13 hours.

Step-by-step explanation:

Continuous population growth:

The continuous population growth model, for the population after t hours, is given by:

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In which P(0) is the initial population and r is the growth rate.

Started with 5000 bacteria

This means that $P(0) = 5000$

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This means that $P(3) = 6500$ . We use this to find r.

$P(t) = 5000e^{rt}$

$6500 = 5000e^{3r}$

$e^{3r} = \frac{65}{50}$

$\ln{e^{3r}} = \ln{\frac{65}{50}}$

$3r = \ln{\frac{65}{50}}$

$r = \frac{\ln{\frac{65}{50}}}{3}$

$r = 0.0875$

$P(t) = 5000e^{0.0875t}$

How many bacteria will be present after 13 hours?

This is P(13). So

$P(13) = 5000e^{0.0875*13} = 15594.8$

Rounding to the nearest whole number

15595 bacteria will be present after 13 hours.

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