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2 years ago

What is the solution to the system of equations?

Mathematics

1 answer:

goldfiish [28.3K]2 years ago

8 0

Answer:

y=-5x+30

y=-5×10+30

y=-50+30

y=-20

x=10

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Find the quotient 17)------ 3145

madreJ [45]

185 * 17 = 3145 so that means 3145 / 17 = 185

5 0

2 years ago

The world brand of rivet placement is 11209 rivets in 9 hours and belongs to J. Mair of Ireland. If another person places 11209

Ilya [14]

Answer:

4.74 hours

Step-by-step explanation:

Given that both person have to place same number of rivets that is

11209

first person take 9 hours to complete the work

hence 1 hour work of 1st person is $\frac{1}{9}$ of total work

second person takes 10 hours to complete the same work

hence 1 hour work of 2nd person is $\frac{1}{10}$

Now if both work together then

1 hour work of both person = $\frac{1}{9} +\frac{1}{10}$ = $\frac{19}{90}$

thus working together they need $\frac{90}{19}$ hours = 4.74 hours to complete the whole work which is placing 11209 rivets

5 0

3 years ago

There are 30 students in Mrs. Woodward’s class, and 1/5 of the class has their own cell phone. Of this group of students, 1/2 of

olga_2 [115]

Answer:

3 students

Step-by-step explanation:

There are 30 students in Mrs. Woodward’s class.

$\dfrac{1}{5}$ of the class has their own cell phone, so

$\dfrac{1}{5}\cdot 30=\dfrac{1}{5}\cdot \dfrac{30}{1}=6$

students have their own cell phones.

$\dfrac{1}{2}$ of those 6 students are allowed to use social media. So,

$\dfrac{1}{2}\cdot 6=\dfrac{1}{2}\cdot \dfrac{6}{1}=3$

students are allowed to use social media.

3 0

3 years ago

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

1. A trapezoid has an area of 91 m2. The height of the trapezoid is 7 m and the measure of one base is twice the height. What is

Lynna [10]

The area of the trapezoid is given by:
A = (1/2) * (b1 + b2) * (h)
Where,
b1, b2: bases of the trapezoid
h: height
Substituting values we have:
91 = (1/2) * ((2 * 7) + b2) * (7)
Rewriting we have:
91 = (1/2) * (14 + b2) * (7)
(2/7) * 91 = 14 + b2
b2 = (2/7) * 91 - 14
b2 = 12 m
Answer:
The measure of the other base of the trapezoid is:
b2 = 12 m

6 0

2 years ago

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