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2 years ago

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

1 answer:

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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Work out the shaded area

Dennis_Churaev [7]

Answer:

Step-by-step explanation:

Shaded area:

Area of big rectangle - Area of small rectangle

$= 10 \times 12 - (10 - 5) \times (12 - 2)$

Calculate the difference

$= 10 \times 12 - 5 \times 10$

Calculate the product

$= 120 - 50$

Calculate the difference

$= 70 \: {cm}^{2}$

Hope this helps...

Best regards!!

7 0

3 years ago

6. A prism has bases that are equilateral triangles with sides lengths of 10 inches and a length of 30 inches.

eimsori [14]

Answer:

The volume of the prism is $1,299\ in^{3}$

Step-by-step explanation:

we know that

The volume of the prism is equal to

$V=BL$

where

B is the area of the triangular base

L is the length of the prism

we have

$L=30\ in$

The area of a equilateral triangle is equal to

$B=\frac{1}{2}(10)^{2} sin(60\°)$

$B=25\sqrt{3}\ in^{2}$

substitute

$V=(25\sqrt{3})(30)=1,299\ in^{3}$

8 0

2 years ago

Point A’ is the image of Point A when point A is rotated about the origin B. What angle in the counterclockwise direction is A r

liberstina [14]

Answer:

90 degrees

Step-by-step explanation:

8 0

2 years ago

A chef makes 1 in a half gallons of soup in a large pot. how many 1-cup sevings can the chef get from this large pot of soup?

attashe74 [19]

There are 16 cups in one gallon so a half would be 8
Answer: 8 cups

4 0

3 years ago

Read 2 more answers

The height, h, of the equilateral triangle is given by h =5cotΘ, where Θ is 30 degrees. Can someone help me with this? I don't u

Hoochie [10]

You don't even need the picture to solve this one.

You said that h = 5 cot(Θ) , and you said that Θ is 30 degrees.
All you need now is to find the cotangent of Θ, plop that into the equation,
and the solution practically jumps off the paper into your lap.

To find the cotangent of 30 degrees, you can use a calculator, look it up
in a book, read it off of a slide rule if you have one, draw a picture of a
30-60-90 right triangle etc. You'll find that the cotangent of 30 degrees
is √3 . That's about 1.732 .

So your equation is h = 5 (1.732) = <em>8.66 </em>(rounded)

Apparently, somebody gave you the equation, and asked you to find 'h'.
Once you had the equation, you didn't even need to know that 'h' has
anything to do with a triangle.

5 0

2 years ago