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timurjin [86]
3 years ago
11

Find the exact value of cos(7\pi /12)

Mathematics
1 answer:
Naya [18.7K]3 years ago
7 0

7π/12 lies in the second quadrant, so we expect cos(7π/12) to be negative.

Recall that

\cos^2x=\dfrac{1+\cos(2x)}2

which tells us

\cos\left(\dfrac{7\pi}{12}\right)=-\sqrt{\dfrac{1+\cos\left(\frac{7\pi}6\right)}2}

Now,

\cos\left(\dfrac{7\pi}6\right)=-\cos\left(\dfrac\pi6\right)=-\dfrac{\sqrt3}2

and so

\cos\left(\dfrac{7\pi}{12}\right)=-\sqrt{\dfrac{1-\frac{\sqrt3}2}2}=\boxed{-\dfrac{\sqrt{2-\sqrt3}}2}

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Whats equivalent expression to 48j+36 with __(4j+__)
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On a certain hot summer day, 481 people used the public swimming pool. The daily prices are 1.25 for children and 2.25 for adult
spayn [35]

Answer:the number of children that swam in the public pool that day is 222

the number of adult that swam in the public pool that day is 259

Step-by-step explanation:

Let x represent the number of children that swam in the public pool that day.

Let y represent the number of adult that swam in the public pool that day.

On a certain hot summer day, 481 people used the public swimming pool. This means that

x + y = 481

The daily prices are 1.25 for children and 2.25 for adults. The receipts for admission totaled to 86.25. This means that

1.25x + 2.25y = 860.25 - - - - - - - -1

Substituting x = 481 - y into equation 1, it becomes

1.25(481 - y) + 2.25y = 860.25

601.25 - 1.25y + 2.25y = 860.25

- 1.25y + 2.25y = 860.25 - 601.25

y = 259

Substituting y = 259 into x = 481 - y, it becomes

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8 0
3 years ago
Please help me!!!!!!!!!!!
shutvik [7]

The given parabola is y+4=12(x-7)^2. Compare with the standard equation of a parabola in vertex form, y-c=a(x-b)^2.

The vertex of this parabola is (b,c). Compare y+4=12(x-7)^2 with the standard equation y-c=a(x-b)^2.

we see c=-4,b=7. Thus, the vertex of the given parabola is (7,-4).


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3 years ago
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