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Ann [662]
3 years ago
7

The first three terms of a geometric sequence are as follows.

Mathematics
1 answer:
Katen [24]3 years ago
4 0

Answer:

3 and 1

Step-by-step explanation:

the sequence is dividing each # by 2

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Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the s
Furkat [3]

Answer:

\frac{16\pi}{3}.

Step-by-step explanation:

I graphed the region in the image below. The blue line is y=3, the purple line is x=1 and the green curve is y = 4x-x^{2}. The shaded region in blue is the region we are going to rotate.

Now, to find the volume  v= 2\pi \int\limits^a_b {p(x)h(x)} \, dx where a=1, b=3 (left and right points of the region), p(x) is the distance from the rotation axis to the diferential Δx, we say p(x)=x and h(x) is the height of the region, in this case is h(x)= 4x-x^{2}-3. Then,

v =  2\pi \int\limits^1_3 {x(4x-x^{2}-3)} \, dx

=  2\pi \int\limits^1_3 {4x^{2}-x^{3}-3x} \, dx

= 2\pi (\frac{4x^{3}}{3}-\frac{x^{4}}{4}-\frac{3x^{2}}{2})^{3}_1

= 2\pi (36-\frac{81}{4}-\frac{27}{2}-\frac{4}{3}+\frac{1}{4}+\frac{3}{2})

= 2\pi*\frac{8}{3}

=  \frac{16\pi}{3}.

8 0
3 years ago
Cammie can mow 1/2 acre in 25 minutes. If her rate is constant, Cammie says she can mow 1 1/4 acres in one hour. Is Cammie corre
Sergeu [11.5K]

Answer: No, Cammie is not correct. She can mow  1\frac{1}{5}\ acres in one hour (See explanation).

Step-by-step explanation:

Convert the mixed number to an impoper fraction:

1. Multiply the whole number part by the denominator of the fraction and add the product to the numerator.

2. The denominator does not change.

Then:

1\frac{1}{4}=\frac{(1*4)+1}{4}=\frac{5}{4}

Let be "x" the acres Cammie can mow in one hour.

You know that she can mow \frac{1}{2}\ acre in 25 minutes, then you can set up the following proportion (Remember that 1 hour has 60 minutes):

\frac{\frac{1}{2}}{25}=\frac{x}{60}

Solving for "x", you get:

\frac{\frac{1}{2}}{25}=\frac{x}{60}\\\\(60)(\frac{1}{50})=x\\\\x=\frac{6}{5}

Convert from improper fraction to mixed number:

1. When you divide 6 by 5, the quotient is 1. This will be the whole number part.

2. The remainder is 1. This will be the numerator.

3. The denominator does not change.

Then:

x=1\frac{1}{5}

Therefore, she can mow  1\frac{1}{5}\ acres in one hour.

3 0
3 years ago
Hours After Sunset, X
Sloan [31]

Answer:

The answer is slope: -9/2  y-intercept: 75

Step-by-step explanation:

I just took the test :]

5 0
3 years ago
PLEASE HELP THIS IS REALLY IMPORTANT
Svet_ta [14]

Answer:

a) x^2-x-20\\

b) what?

c) -70

Step-by-step explanation:

If you have any questions feel free to ask in the comments - Mark

sorry for the terrible answer

3 0
3 years ago
From 99° to 70°f what is the percent decrease
SSSSS [86.1K]

Answer:

should be -29.29 %

Step-by-step explanation:

8 0
3 years ago
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