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bija089 [108]
3 years ago
15

What is the circumference of a circle if the diameter is 25 feet. Show answer as a decimal.

Mathematics
1 answer:
vitfil [10]3 years ago
4 0

Answer:

Step-by-step explanation:

C≈78.54 i think

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Calculus Problem
Roman55 [17]

The two parabolas intersect for

8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2

and so the base of each solid is the set

B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, |x^2-(8-x^2)| = 2|x^2-4|. But since -2 ≤ x ≤ 2, this reduces to 2(x^2-4).

a. Square cross sections will contribute a volume of

\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x

where ∆x is the thickness of the section. Then the volume would be

\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x

We end up with the same integral as before except for the leading constant:

\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx

Using the result of part (a), the volume is

\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x

and using the result of part (a) again, the volume is

\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}

7 0
2 years ago
I need help with this ASAPP
torisob [31]

Answer:

6

Step-by-step explanation:

you can see the factors in the green section of the venn diagram. Of all the factors, 6 is the largest.

Hope this helps!

7 0
3 years ago
Read 2 more answers
Please hurry!!!
algol [13]

Answer:

Gallons of punch used = 4.94 gallons

Step-by-step explanation:

Given that:

Liters of punch purchased = 25 liters

Liters of punch left over = 6 liters

Liters of punch used = 25 - 6 = 19 liters

According to the given statement;

1 liter = 0.26 gallons

19 liters = 0.26*19 gallons

19 liters = 4.94 gallons

Hence,

Gallons of punch used = 4.94 gallons

7 0
2 years ago
I need help it’s for a very hard test
Mumz [18]

Answer:

C

Step-by-step explanation

This has a factor of 6% or 0.06. But, you are adding and not subtracting so it is 1.06. ( If you multiply by a number less than 1 then it is actually dividing) So C is the only on that is correct.

6 0
2 years ago
A family has two cars. The first car has a fuel efficiency of 40 miles per gallon of gas and the second has a fuel efficiency of
lesya692 [45]

Answer:

first car = 35, second car= 15

Step-by-step explanation:

40x+15y=1625

x+y=50

multiplying the 2nd by -15 and add the 2 equations, we get x= 35 and by substituting on second equation we get y= 15

4 0
2 years ago
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