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3 years ago

Please help me solve this problem

Mathematics

1 answer:

goblinko [34]3 years ago

5 0

Answer:

iv, ii, i, iii, vi, v

Step-by-step explanation:

First, it is better if you fix all of these into fractions:

2/3--> 0.6666

-4/5--> -0.8

7/4--> 1.75

-21/8--> -2.625

11/4--> 2.75

root 5--> 2.24...

Hope this helps!!

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use the general slicing method to find the volume of The solid whose base is the triangle with vertices (0 comma 0 ), (15 comma

lyudmila [28]

Answer:

volume V of the solid

$\boxed{V=\displaystyle\frac{125\pi}{12}}$

Step-by-step explanation:

The situation is depicted in the picture attached

(see picture)

First, we divide the segment [0, 5] on the X-axis into n equal parts of length 5/n each

[0, 5/n], [5/n, 2(5/n)], [2(5/n), 3(5/n)],..., [(n-1)(5/n), 5]

Now, we slice our solid into n slices.

Each slice is a quarter of cylinder 5/n thick and has a radius of

-k(5/n) + 5 for each k = 1,2,..., n (see picture)

So the volume of each slice is

$\displaystyle\frac{\pi(-k(5/n) + 5 )^2*(5/n)}{4}$

for k=1,2,..., n

We then add up the volumes of all these slices

$\displaystyle\frac{\pi(-(5/n) + 5 )^2*(5/n)}{4}+\displaystyle\frac{\pi(-2(5/n) + 5 )^2*(5/n)}{4}+...+\displaystyle\frac{\pi(-n(5/n) + 5 )^2*(5/n)}{4}$

Notice that the last term of the sum vanishes. After making up the expression a little, we get

$\displaystyle\frac{5\pi}{4n}\left[(-(5/n)+5)^2+(-2(5/n)+5)^2+...+(-(n-1)(5/n)+5)^2\right]=\\\\\displaystyle\frac{5\pi}{4n}\displaystyle\sum_{k=1}^{n-1}(-k(5/n)+5)^2$

But

$\displaystyle\frac{5\pi}{4n}\displaystyle\sum_{k=1}^{n-1}(-k(5/n)+5)^2=\displaystyle\frac{5\pi}{4n}\displaystyle\sum_{k=1}^{n-1}((5/n)^2k^2-(50/n)k+25)=\\\\\displaystyle\frac{5\pi}{4n}\left((5/n)^2\displaystyle\sum_{k=1}^{n-1}k^2-(50/n)\displaystyle\sum_{k=1}^{n-1}k+25(n-1)\right)$

we also know that

$\displaystyle\sum_{k=1}^{n-1}k^2=\displaystyle\frac{n(n-1)(2n-1)}{6}$

and

$\displaystyle\sum_{k=1}^{n-1}k=\displaystyle\frac{n(n-1)}{2}$

so we have, after replacing and simplifying, the sum of the slices equals

$\displaystyle\frac{5\pi}{4n}\left((5/n)^2\displaystyle\sum_{k=1}^{n-1}k^2-(50/n)\displaystyle\sum_{k=1}^{n-1}k+25(n-1)\right)=\\\\=\displaystyle\frac{5\pi}{4n}\left(\displaystyle\frac{25}{n^2}.\displaystyle\frac{n(n-1)(2n-1)}{6}-\displaystyle\frac{50}{n}.\displaystyle\frac{n(n-1)}{2}+25(n-1)\right)=\\\\=\displaystyle\frac{125\pi}{24}.\displaystyle\frac{n(n-1)(2n-1)}{n^3}$

Now we take the limit when n tends to infinite (the slices get thinner and thinner)

$\displaystyle\frac{125\pi}{24}\displaystyle\lim_{n \rightarrow \infty}\displaystyle\frac{n(n-1)(2n-1)}{n^3}=\displaystyle\frac{125\pi}{24}\displaystyle\lim_{n \rightarrow \infty}(2-3/n+1/n^2)=\\\\=\displaystyle\frac{125\pi}{24}.2=\displaystyle\frac{125\pi}{12}$

and the volume V of our solid is

$\boxed{V=\displaystyle\frac{125\pi}{12}}$

3 0

3 years ago

Find the area of the following circles. a. A circle with a 8-inch radius b. A circle with a 10-kilometer radius c. A circle with

Thepotemich [5.8K]

Area of a circle is $A= \pi r^2$ . The first one, a, the radius squared is 8*8=64. So $A=64 \pi$ . If you multiply in pi as 3.14, you'll have 200.96 square inches. The second one, b, the radius squared is 10*10=100. So $A=100 \pi$ square kilometers. If you multiply in pi as 3.14 you'll have 314 square kilometers. The third one, c, the radius squared is 14*14=196. So $A=196 \pi yd^2$ . Or you could multiply in pi as 3.14 to get 615.44 yd squared. For the last one, d, the radius squared is 22*22=484 cm. Therefore, $A=484 \pi cm^2$ , or multiply in 3.14 for pi to get 1519.76 cm squared. There you go!

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3 years ago

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Hannah sold 48 flowers in 3 hours at the farmers market if she continues to sell at that rate how many flowers will she sell in

igomit [66]

First, find the rate of flowers bought per hour:
48 / 3 = 16 flowers per hour.
Then, to find the amount bought after 2 hours, multiply the 16 flowers per hour by 2.
16 * 2 = 32.
After 2 hours, she will have bought 32 flowers.

5 0

3 years ago

Tony’s club is selling oranges to raise money. For every box they sell, they get 1 1/8 dollars profit. They have sold 75 boxes a

dmitriy555 [2]

Tony’s club is selling oranges to raise money. For every box they sell, they get 1 1/8 dollars profit. They have sold 75 boxes already. How many more boxes must they sell to raise 180 dollars?

Answer: We are given:

The amount of money Tony's club get for every box they sell $=1 \frac{1}{8} =1.125$ dollar

They amount of money Tony's club has raised by selling 75 boxes is:

$75 \times 1.125=84.375$ dollars

The amount of money Tony's club is required to raise = 180 dollars

The remaining need to be raised is :

$180-84.375=95.625$ dollars

Therefore, the number of more boxes to be sold are:

$\frac{95.625}{1.125}=85$

Hence, 85 more boxes they must sell to raise 180 dollars

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3 years ago

What does 1,580÷25=I know the answer, I need to show how I got it.

ziro4ka [17]

$\begin{gathered} \sqrt[25]{1580} \\ 1\text{ and 15 cannot divide 25 therefore, we use the first three numbers to divide 25} \\ \frac{158}{25}\text{ = }6\text{ remainder 8} \\ \text{You have to carry that remainder which is 8 and combine it with the 0 in 1580.} \\ \frac{80}{25}\text{ = }3\text{ remainder 5} \\ The\text{ remainder 5 will also divide 25} \\ \frac{5}{25}=0.2 \\ The\text{ quotient values are 63 + 0.2 = 63.2} \end{gathered}$

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1 year ago