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kenny6666 [7]
2 years ago
9

Find the function value of cos^2 (7pi/8)

Mathematics
1 answer:
Kamila [148]2 years ago
7 0
\cos^2\dfrac{7\pi}8=\dfrac12\left(1+\cos\dfrac{7\pi}4\right)
=\dfrac12+\dfrac12\cos\left(-\dfrac\pi4\right)
=\dfrac12+\dfrac12\cos\dfrac\pi4
=\dfrac12+\dfrac1{2\sqrt2}
=\dfrac{\sqrt2+1}{2\sqrt2}
=\dfrac{2+\sqrt2}4
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Answer:

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Step-by-step explanation:

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3 years ago
adam prepares a meal of shrimp and brown rice. it must contain exactly 6 g of fat and 10 mg of iron. each 5oz serving of shrimp
jasenka [17]

Answer:

Adam needs 9/8 of a 5oz serving of shrimps (which equals to 5.625 oz) and 5/8 of a cup of brown rice (which is around 10 tablespoons).


Explanation:

You are given:

every serving of shrimp contains 2g of fat and 5mg of iron;

every serving of rice contains 6g of fat and 7mg of iron;

each meal should have 6g of total fat and 10mg of total iron.


You need to set a system of equation: let's call

s = quantity of shrimps

r = quantity of rice

The equation for the total fat will be: the quantity of fat in the serving of shrimps plus the quantity of fat in the serving of rice must be equal to 6g

2s + 6r = 6    (1)

Similarily:

the quantity of iron in the serving of shrimps plus the quantity of iron in the serving of rice must be equal to 10g

5s + 7r = 10     (2)


In order to solve the system, solve for s in equation (1):

s = (6-6r)/2 = 3 - 3r        (3)

Substitute in equation (2):

5(3 - 3r) + 7r = 10

and solve for r:

15 - 15r + 7r = 10

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Substitute the value of r in equation (3):

s = 3 - 3×5/8 = 9/8


Therefore Adam would need 9/8 of a 5oz serving of shrimps and 5/8 of a 1 cup of brown rice for each meal.

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Answer:

1/10

Step-by-step explanation:

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