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liberstina [14]
3 years ago
11

Find the centroid of the region bounded by the given curves y=8sin(4x), y=8cos(4x)

Mathematics
1 answer:
Luba_88 [7]3 years ago
5 0
A cosine is just a sine shifted to the left by π/2. A cosine of 4x is shifted to the left by only π/8 because of the factor 4. Sketch them.

The region we're looking for is this sausage-shaped part between the cos and the sin.

The x intercepts are at π/8 for the cosine and π/4 for the sine. The midpoint between them is at (π/8 + π/4)/2 = 3/16π.

The region is point symmetric around the x axis, so the y coordinate of the centroid is 0.

So the centroid is at (3/16π, 0)
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3 years ago
The admision fee at a basket ball game is 350$ for children and 750$ for adults. On a certain night,1500 people enter the basket
Hoochie [10]

<u>Note: The only way to solve this problem is by adjusting the fees to $3.50 and $7.50.</u>

Answer:

<em>1300 children attended the basketball game</em>

Step-by-step explanation:

System of Equations

Let's call:

x = number of children attending the basketball game

y = number of adults attending the basketball game

On a certain night, 1500 people enter the game, thus:

x + y = 1500           [1]

Since each admission fee for children cost $3.50 and $7.50 for adults and it was collected $6050, thus:

3.50x + 7.50y = 6050            [2]

From [1]:

y = 1500 - x

Substituting in [2]:

3.50x + 7.50(1500 - x) = 6050

Operating:

3.50x +  11250 - 7.50 = 6050

-4x = 6050 - 11250

Solving:

x = 1300

1300 children attended the basketball game

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3 years ago
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The dot plot below shows the number of books 26 students read in a month:



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