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3 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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Which function's graph has x-intercepts at x=−1 and x=3, and a vertex at point (1,−4)?

Luda [366]

Answer:

Top right option: g(x) = (x+1)(x-3)

Step-by-step explanation:

x=-1 is the solution to x+1=0

x=3 is the solution to x-3=0

Therefore, your expression so far is (x+1)(x-3) or x²-2x-3.

Since the vertex must be (1,-4) we must check if x=1 satisfies the equation x=-b/2a:

x=-b/2a

1=-(-2)/2(1)

1=2/2

1=1

Both sides are equal to each other, so the final function is g(x) = (x+1)(x-3)

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3 years ago

A case in riverhead, new york, nine different crime victims listened to voice recordings of five different men. all nine victims

Alexus [3.1K]

the complete question in the attached figure

1) Find the probability that all nine victims would select the same person. You should enter your answer as a decimal, not as a percent. Do not round, as your answer should be a terminating decimal.

P=(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)=0.000000512

2) what is the probability that the first victim picks SOMEONE? ANYONE?

P=(1/5)=0.20 ---------------- > 20%

3) Now let’s look at victim #2. What is the probability that they pick the same person as victim #1?

P=(1/5)*(1/5)=0.04 --------------> 4%

4) Now let’s look at victim #3. What is the probability that they pick the same person as victim #1?

P=(1/5)*(1/5)*(1/5)=0.008 --------------> 0.8%

5) Now let's look at victim #9. What is the probability that they pick the same person as victim #1?

P=(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)=0.000000512

6) Once you find all those probabilities, what rule would apply?

the probability is given by (1/5)^n

n=number of victims that pick the same person---------> in this problem = 9

P=(1/5)^9= 0.000000512

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4 years ago

ASAP HELP ANSWER ALL THESE AND I WILL GIVE THE BRAINLEST

alexandr1967 [171]

The second question is number 3 for the polygon translation.
Question 3 is 2 units right and four units down.

3 0

3 years ago

Read 2 more answers

The assets division should contain what accounts

fredd [130]

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4 years ago

What is the area of a 4.2 yard square?

SOVA2 [1]

Answer:

37.8 square feet

Step-by-step explanation:

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3 years ago