The volume of the cylinder would be:
282.74
Question # 17 Solution
Answer:
![x_{1}= \frac{mx_{2}-y_{2}+y_{1}}{m}](https://tex.z-dn.net/?f=x_%7B1%7D%3D%20%5Cfrac%7Bmx_%7B2%7D-y_%7B2%7D%2By_%7B1%7D%7D%7Bm%7D)
Step-by-step Explanation:
The given expression
![m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
And we have to solve for x₁
So,
Lets solve for x₁.
![m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
Multiply both sides by x₂ - x₁
![m(x_{2}-x_{1})= (x_{2}-x_{1})\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=m%28x_%7B2%7D-x_%7B1%7D%29%3D%20%28x_%7B2%7D-x_%7B1%7D%29%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
![m(x_{2}-x_{1})= (y_{2}-y_{1})](https://tex.z-dn.net/?f=m%28x_%7B2%7D-x_%7B1%7D%29%3D%20%28y_%7B2%7D-y_%7B1%7D%29)
![mx_{2}-mx_{1}= (y_{2}-y_{1})](https://tex.z-dn.net/?f=mx_%7B2%7D-mx_%7B1%7D%3D%20%28y_%7B2%7D-y_%7B1%7D%29)
![-mx_{1}= y_{2}-y_{1}-mx_{2}](https://tex.z-dn.net/?f=-mx_%7B1%7D%3D%20y_%7B2%7D-y_%7B1%7D-mx_%7B2%7D)
Divide both sides by -m
![\frac{-mx_{1}}{-m}= \frac{y_{2}-y_{1}-mx_{2}}{-m}](https://tex.z-dn.net/?f=%5Cfrac%7B-mx_%7B1%7D%7D%7B-m%7D%3D%20%5Cfrac%7By_%7B2%7D-y_%7B1%7D-mx_%7B2%7D%7D%7B-m%7D)
![x_{1}= \frac{mx_{2}-y_{2}+y_{1}}{m}](https://tex.z-dn.net/?f=x_%7B1%7D%3D%20%5Cfrac%7Bmx_%7B2%7D-y_%7B2%7D%2By_%7B1%7D%7D%7Bm%7D)
Therefore, ![x_{1}= \frac{mx_{2}-y_{2}+y_{1}}{m}](https://tex.z-dn.net/?f=x_%7B1%7D%3D%20%5Cfrac%7Bmx_%7B2%7D-y_%7B2%7D%2By_%7B1%7D%7D%7Bm%7D)
Question # 23 Solution
Answer:
![n= \frac{bx}{-b + x}](https://tex.z-dn.net/?f=n%3D%20%5Cfrac%7Bbx%7D%7B-b%20%2B%20x%7D)
Step-by-step Explanation:
The given expression
![\frac{nx}{b}-x=x](https://tex.z-dn.net/?f=%5Cfrac%7Bnx%7D%7Bb%7D-x%3Dx)
And we have to solve for n
So,
Let's solve for n.
![\frac{nx}{b}-x=x](https://tex.z-dn.net/?f=%5Cfrac%7Bnx%7D%7Bb%7D-x%3Dx)
Multiply both sides by b.
![-bn + nx = bx](https://tex.z-dn.net/?f=-bn%20%2B%20nx%20%3D%20bx)
Factor out n.
![n(-b + x)= bx](https://tex.z-dn.net/?f=n%28-b%20%2B%20x%29%3D%20bx)
Divide both sides by -b + x.
![\frac{n(-b + x)}{-b + x}= \frac{bx}{-b + x}](https://tex.z-dn.net/?f=%5Cfrac%7Bn%28-b%20%2B%20x%29%7D%7B-b%20%2B%20x%7D%3D%20%5Cfrac%7Bbx%7D%7B-b%20%2B%20x%7D)
![n= \frac{bx}{-b + x}](https://tex.z-dn.net/?f=n%3D%20%5Cfrac%7Bbx%7D%7B-b%20%2B%20x%7D)
Therefore, ![n= \frac{bx}{-b + x}](https://tex.z-dn.net/?f=n%3D%20%5Cfrac%7Bbx%7D%7B-b%20%2B%20x%7D)
<em>Keywords: solution, equation</em>
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Answer:(a=5,b=3)
7a-3b = 26--------(1)
a + 2b =11---------(2)
on mutlplying by7 in eq 2
= 7a+14b=77-------(3)
from eq(1) and (3) (on substracting)
7a+14b=77
7a-3b=26
________
=-17b=51
b=51/17
b=3
on putting value of b in eq 1
7a-3b = 26
=7a-9=26
7a=35
a=5
Step-by-step explanation:
hope it helps
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The missing justification in the proof is
<span>B) Substitution property of equality
The expression for sin</span>² x and cos² x is substituted to the other side of the equation. Since sin x = a/c, then sin² x = a²/c². Similarly, since cos x = b/c, then cos² x = b²/c². Adding to two results to the third statement.
For the first question (f - &)(x) = 5xcubed - 7xsquared + 8