Prove that the line passing through points A (4.1) and B (-1.3) is perpendicular to the line passing through points G (4, -2) an
1 answer:
Answer:
- See below
Step-by-step explanation:
<u>Find the slope of each line:</u>
- m(AB) = (3 - 1)/(- 1 - 4) = 2 / - 5 = - 2/5
- m(GD) = (3 + 2)/(6 - 4) = 5/2
<u>The product of the slopes is - 1, hence the lines are perpendicular:</u>
- - 2/5 * 5/2 = - 1
Equation of each line
<u>Line AB</u>
- y - 1 = -2/5(x - 4) ⇒ y = - 2/5x + 8/5 + 1 ⇒ y = - 2/5x + 13/5
<u>line GD</u>
- y + 2 = 5/2(x - 4) ⇒ y = 5/2x - 10 - 2 ⇒ y = 5/2x - 12
<em>Their graph and intersection point is given in the attached picture</em>
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The amount of drugs that will be left after 12 hours is 17.42 mg provided Sarah takes 550 mg of an antibiotic every hour.
<h3>What is exponential decay?</h3>Exponential decay can be described as a reduced amount of an original substance by a definite percentage over a period of time. It can be determined by using the formula:
where;
- y = total amount,
- a = initial amount = 550 mg
- r = the growth rate = 0.25
- t = number of growth periods = 12 hours
y = 17.42 mg
Therefore, we can conclude that the amount of drugs that will be left after 12 hours is 17.42 mg.
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