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3 years ago

Find the volume of the cylinder. 1607.7 in 3 2845.7 in 3 6430.7 in 3 401.9 in 3

Mathematics

1 answer:

Musya8 [376]3 years ago

6 0

Answer:

$\Huge\boxed{1607.7in^3}$

Step-by-step explanation:

Hello There

The volume of a cylinder can be found using this formula

$V=\pi r^2h$

where r = radius and h = height

The cylinder shown has a radius of 8 inches and a height of 8 inches

Knowing this information we plug it in into the formula

$V=\pi 8^28\\8^2=64\\64*8=512\\512\pi=1607.68$

Finally we round to the nearest tenth and get that the volume of the cylinder is 1607.7 in ^3

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[need math help] Study buddies part #2

rosijanka [135]

Answer:

Part A) The distance between Whitney's house and Anh's house is 6.5 miles.

Part B) The total distance traveled by Whitney during the trip was 9.5 miles.

Step-by-step explanation:

Part A)

Notice that during Whitney's journey to Anh's house, her velocity was negative for some time. So, Whitney was travelling backwards. Hence, the total distance Whitney traveled will be greater than the actual distance from Whitney's house to Anh's.

So, instead, we can calculate Whitney's total displacement. Total displacement is given by:

$\displaystyle \text{Displacement}=\int_a^bv(t)\, dt$

Where v(t) is the velocity function.

So, the displacement of Whitney when she traveled from her house to Anh's house will be:

$\displaystyle \text{Displacement}=\int_0^{24}v(t)\, dt$

To calculate the integral, we can split it off at t = 11, t = 16, and t = 24.

The three regions represent three geometric figures, which we can use to calculate the area and then find the integral. Rewriting:

$\displaystyle \text{Displacement}=\int_0^{11}v(t)\, dt+\int_{11}^{16}v(t)\, dt+\int_{16}^{24}v(t)\, dt$

Now, we can calculate the area of each figure.

The first figure is a trapezoid with a height of 0.8 and two bases of 11 and 3. So, its area is:

$\displaystyle A_1=\frac{1}{2}(0.8)(11+3)=5.6\text{ miles}$

The second figure is a triangle with a height of 0.6 and a base of 5. So, its area is:

$\displaystyle A_2=\frac{1}{2}(0.6)(5)=1.5\text{ miles}$

Lastly, the third figure is another triangle will a height of 0.6 and a base of 8. So, its area is:

$\displaystyle A_3=\frac{1}{2}(0.6)(8)=2.4\text{ miles}$

However, notice that the second figure is below the x-axis. During that interval, Whitney was traveling backwards. Hence, we will subtract the second area from the rest of the areas.

Then the displacement will be:

$\displaystyle \text{Displacement}=5.6-1.5+2.4=6.5\text{ miles}$

So, the distance between Whitney's house and Anh's house is 6.5 miles.

Part B)

The total distance differs from displacement in that it includes all the distances in both directions. It is given by:

$\displaystyle \text{Distance}=\int_a^b|v(t)|\, dt$

In other words, all of our values are now positive. We will utilize the same strategy:

$\displaystyle \text{Distance}=\int_0^{11}|v(t)|\, dt+\int_{11}^{16}|v(t)|\, dt+\int_{16}^{24}|v(t)|\, dt$

Substitute. The only difference is that we will add 1.5 instead of subtracting it. So:

$\displaystyle \text{Distance} =5.6+1.5+2.4=9.5$

Therefore, in this instance, Whitney traveled a total of 9.5 miles to get to Anh's house.

6 0

3 years ago

the summer camps had a field trip from the campus to fragrance hill. they traveled at an average speed of 65km/h in the first tw

sergejj [24]

Answer:

I took them a total of 5 hours

Step-by-step explanation:

First you multiply 65 by 2 because of the first two hours

Then you subtract 130 out of 364 to get 234, those were the first two hours

The next hours you simply divide 234/78, which is 3

3 + 2 = 5 hours

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2 years ago

Grandma uses 2/3 of a pumpkin to make a pumpkin pie. How many pumpkins should she buy to make 4 pumpkin pies?

Pachacha [2.7K]

she needs to use 8/12 of pumpkins

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2 years ago

Paul owes PAula $.35 and has a pocket full of five cents $.10 coins and $.25 coins that he can use to pay her what is the differ

coldgirl [10]

He can use:
a quarter and a dime (difference: 15)
a quarter and two nickels (difference: 20)
a dime and three nickels (difference: 5)
two dimes and a nickel (difference: 5)

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3 years ago

A farmer sells 8.7 kilograms of pears and apples at the farmer's market. 2 5 of this weight is pears, and the rest is apples. Ho

Ivenika [448]

Answer: 5.22kg

Step-by-step explanation:

From the question, a farmer sells 8.7 kilograms of pears and apples at the market. Of the pears and apples sold, 2/5 of this weight is pears, and the rest is apples. To calculate the kilograms of apple sold goes thus:

Total kilograms sold = 8.7kg

Fraction of pears weight = 2/5

Pears kilograms sold = 2/5 × 8.7

= 0.4 × 8.7

= 3.48kg

Since the kilograms of pears sold is , 3.48kg, to get the kilograms of apple sold, we subtract 3.48kg from 8.7kg. This will be:

= 8.7kg - 3.48kg

= 5.22kg

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3 years ago