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2 years ago

Need help solving for y

Mathematics

1 answer:

alukav5142 [94]2 years ago

5 0

Answer:

I think it is 45 not for exactly sure if I'm right. But I think it is.

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Aurora has a cell phone plan that charges $65 for phone service plus $12 for eachgigabyte of data used each month. If her bill f

Ivahew [28]

Answer:

4 gigabytes

Step-by-step explanation:

64+12+12+12+12=113

7 0

2 years ago

Read 2 more answers

How can you divide 3 4 by 65

Aleks04 [339]

Answer:

48 3/4

Step-by-step explanation:

65/1

3 x65/4x1=195/4 which equal 48 3/4

3 0

1 year ago

Read 2 more answers

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

2 years ago

A baker uses 8.5 lbs of flour daily.How many ounces of flour will he use in two weeks?

kicyunya [14]

The answer would be 1,904 because a pound is 16 ounces so 8.5 times 14 (how many days are in two weeks) which is 119. Then 119 times 16 (how many ounces are in a pound) would be 1,904. hope i am helpful :D

7 0

2 years ago

Find two positive numbers whose product is 25 and whose sum is a minimum. (if both values are the same number, enter it into bot

pshichka [43]

Let xy = 25, x and y > 0.

$y = \frac{25}{x}$
$\text{Denote S as: } x + y$
$S(x) = x + \frac{25}{x}$

$\text{Minimum: }S'(x) = 0, S''(x) > 0$
$S'(x) = 1 - \frac{25}{x^{2}}$
$1 - \frac{25}{x^{2}} = 0$
$x^{2} = 25$
$x = 5 (x > 0)$

$S''(x) = \frac{50}{x^{3}} > 0, (x > 0)$

Thus, at x = 5, there lies a minimum summation, and this forms a square with side length of 5.

4 0

2 years ago

Need help solving for y​

Need help solving for y