1. Given the triangle below, what is the value of sin 8 ? 12 6 ก 65
2 answers:
Answer:
(2/5)√5
Step-by-step explanation:
from the sine rule (see attached for reference), we can construct the following relationship
12/sinθ = (6√5) / sin 90°
recall that sin 90° = 1, hence our equation becomes:
12/sinθ = (6√5) / 1
12/sinθ = (6√5) (rearranging)
12 ÷ (6√5) = sin θ
sin θ = 12 / (6√5)
sin θ = 2 / √5 (moving radical to numerator by multiplying by √5/√5)
= 2 / √5 x √5/√5
= 2√5 / 5
= (2/5)√5
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<h3>Answer: 15x^(7/3) - 8x^(7/4) + x + 9000</h3>
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Explanation:
If you know the cost function C(x), to find the marginal cost, we apply the derivative.
Marginal cost = derivative of cost function
Marginal cost = C ' (x)
Since we're given the marginal cost, we'll apply the antiderivative (aka integral) to figure out what C(x) is. This reverses the process described above.
D represents a fixed constant. I would have used C as the constant of integration, but it's already taken by the cost function C(x).
To determine the value of D, we plug in x = 0 and C(x) = 9000. This is because we're told the fixed costs are $9000. This means that when x = 0 units are made, you still have $9000 in costs to pay. This is the initial value. You'll find that all of this leads to D = 9000 because everything else zeros out.
Therefore, we go from this
to this
which is the final answer.