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Svetllana [295]
3 years ago
6

In Triangle LMN, < M is a right angle. If MN = 10 and LN = 20.4, determine m < N to the nearest degree.

Mathematics
1 answer:
UNO [17]3 years ago
6 0

cos θ = \frac{adjacent}{hypotenuse}

cos ∠N = \frac{10}{20.4}

      ∠N = cos⁻¹ (\frac{10}{20.4})

      ∠N = 60.65°

Answer: 61°

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The function C(h)=(2h^2+5h)/(h^3+8) models the concentration of medication in the bloodstream (as a percent) h hours after its i
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  3. (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.
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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.

__

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.

__

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.

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