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Andrei [34K]
3 years ago
14

Write (2 4) and (6 16) in the form y=mx+b

Mathematics
1 answer:
Lena [83]3 years ago
3 0

Answer:

y = 3x-2

Step-by-step explanation:

We can find the slope using the formula

m = (y2-y1)/(x2-x1)

  = (16-4)/(6-2)

  =12/4

 =3

We then use the point slope form of a line

y-y1= m(x-x1)

y-4 = 3(x-2)

Distribute the 3

y-4= 3x-6

Add 4 to each side

y-4+4 = 3x-6+4

y = 3x-2

This is in slope intercept form

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Give the domain and range. Tell if it is a function.
Anna [14]
It’s not a function
That’s all I know sorry!
6 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
A child from a class of 30 students is chosen to pick one of five prizes. How many outcomes are there
Mamont248 [21]

Answer: 5?

Step-by-step explanation:

there are 5 prizes to be chosen from.

4 0
3 years ago
Graph the following lines and write the equation in slope-intercept form. With y intercept of −3 and an x intercept of −4.5.
makvit [3.9K]

Answer:

y=-\frac{2}{3}x-3

Step-by-step explanation:

To write the equation of a line we need 2 points. We know:

  • If the y-intercept of the line is -3 then the point is (0,-3).
  • If the x-intercept of the line is -4.5 then the point is (-4.5,0).

Using these two point, we will find the slope and then substitute it into the point slope form y-y_1=m(x-x_1) with a point.

Slope: m=\frac{0--3}{-4.5-0}=\frac{0+3}{-4.5}=\frac{3}{-4.5}=-0.6667

This decimal is -2/3. We will now substitute -2/3 and (0,-3) into the point slope form.

y--3=-\frac{2}{3}(x-0)\\y+3=-\frac{2}{3}(x)\\y+3=-\frac{2}{3}x\\y=-\frac{2}{3}x-3


6 0
3 years ago
Pyramid A is a square pyramid with a base side length of 12 inches and a height of 8 inches. Pyramid B is a square pyramid with
yan [13]

Answer:

<em>The volume of pyramid B is 64 times the volume of pyramid A.</em>

<em></em>

Step-by-step explanation:

Given:

Two square pyramids A and B.

Side Length of A, s_A = 12 inches

Height of A, h_A = 8 inches

Side Length of B, s_B = 48 inches

Height of B, h_B = 32 inches

To find:

How many times bigger is the volume of pyramid B than pyramid A?

OR

V_B is how many times bigger than V_A ?

Solution:

First of all, let us have a look at the formula for volume of a pyramid:

V=\dfrac{1}{3} \times \text{Area of Base} \times \text{Height}

Here, base is square, so:

V=\dfrac{1}{3} \times s^2 \times h

Volume of pyramid A:

V_A=\dfrac{1}{3} \times s_A^2 \times h_A

\Rightarrow V_A=\dfrac{1}{3} \times 12^2 \times 8 = 384\ inch^3

Volume of pyramid B:

V_B=\dfrac{1}{3} \times s_B^2 \times h_B

\Rightarrow V_B=\dfrac{1}{3} \times 48^2 \times 32 \\\Rightarrow V_B=\dfrac{1}{3} \times 12^2 \times 8 \times 4^2 \times 4\\\Rightarrow V_B=\dfrac{1}{3} \times 12^2 \times 8 \times 64\\\Rightarrow V_B= 24576\ inch^3 = 384\times 64\ inch^3\\\Rightarrow V_B = V_A\times 64\ inch^3

<em>The volume of pyramid B is 64 times the volume of pyramid A.</em>

3 0
3 years ago
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