Henry's current age is 10 times Justin's current age. In 6 years Henry's age will be 4 times Justin's age. Which system of equat
1 answer:
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Answer:
a =
x = 27y
Step-by-step explanation:
Order of Operations: BPEMDAS
<u>Question 1</u>
Step 1: Write out discriminant
d = b² - 4ac
Step 2: Subtract b² on both sides
d - b² = -4ac
Step 3: Divide both sides by -1
b² - d = 4ac
Step 4: Divide both sides by 4c
a =
<u>Question 2</u>
Step 1: Write out equation
2/3(x - 18y) = 6y
Step 2: Distribute parenthesis
2/3x - 12y = 6y
Step 3: Isolate <em>x </em>by adding 12y on both sides
2/3x = 18y
Step 4: Divide both sides by 2/3
x = 27y
Answer:
- h ≥ 0
- C = 0; concentration eventually decays to nothing
- (0, 0) is the only intercept in the domain. It means the concentration in the bloodstream is zero at the time the drug is injected.
- 1.95 hours
Step-by-step explanation:
1. a. The domain of the function in the context of this problem is h ≥ 0. The maximum value of h will correspond to the time at which the concentration is considered to be negligible. If that time is when the concentration decays to 1% of its peak value, then perhaps the suitable domain is 0 ≤ h ≤ 180.
b. The equation of the vertical asymptote of this function is where the denominator of C(h) is zero, that is ...
h^3 +8 = 0
h = ∛(-8)
h = -2 . . . . the equation of the vertical asymptote
This is not a concern for a medical professional because it is outside the domain of the function.
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2. As h gets large the value of the function approaches 2/h, which is to say the horizontal asymptote is C = 0. It means the concentration of medication in the blood eventually decays to zero.
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3. C(0) = 0 is the only intercept in the domain of the function. (h, C(h)) = (0, 0)
In the context of this problem, it means the blood concentration of medication is zero at the time of the injection.
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4. About 1.95 hours after injection, a maximum concentration of the drug occur in the bloodstream. This value is easily found using a graphing calculator.
Taking the derivative of the function gives you ...
C'(h) = -2(h^4 +5h^3 -16h -20)/(h^3 +8)^2
This has two real zeros and two complex zeros. The positive real zero is near h = 1.94527, about 1.95.
That is, the concentration in the bloodstream reaches a maximum about 1.95 hours after injection into the muscle.
