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Calculus Examples
Popular Problems Calculus Find the Domain and Range f(x)=5x-3
f
(
x
)
=
5
x
−
3
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
(
−
∞
,
∞
)
Set-Builder Notation:
{
x
|
x
∈
R
}
The range is the set of all valid
y
values. Use the graph to find the range.
Interval Notation:
(
−
∞
,
∞
)
Set-Builder Notation:
{
y
|
y
∈
R
}
Determine the domain and range.
Domain:
(
−
∞
,
∞
)
,
{
x
|
x
∈
R
}
Range:
(
−
∞
,
∞
)
,
{
y
|
y
∈
R
}
Answer:
![(x,y) = \left(\dfrac{18}{5},\dfrac{67}{15}\right)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%5Cleft%28%5Cdfrac%7B18%7D%7B5%7D%2C%5Cdfrac%7B67%7D%7B15%7D%5Cright%29)
Step-by-step explanation:
First rearrange all equations into this format:
![ax+by=c](https://tex.z-dn.net/?f=ax%2Bby%3Dc)
that will result in:
![3x-4y=-1](https://tex.z-dn.net/?f=3x-4y%3D-1)
![9x-7y=15](https://tex.z-dn.net/?f=9x-7y%3D15)
then we'll multiply an equation with a number such that we have same numbers on both equations (with only different signs). So we can add them
Here you can see that we've multiplied the first equation with (-3) so that we have -9x on one equation and 9x on the other. Now when we add the two equations the 9x and -9x terms will cancel out (or eliminate)
![\[\begin{array}{r@{}l@{\quad}l@{\quad}r@{}l@{}c}3x-4y&{}=-1&\xrightarrow{\times (-3)}&-9x +12y&{}=+3\\[\jot]9x -7y&{}=15&\xrightarrow{\phantom{\times (-3)}}&9x-y&{}=15&~\smash{\raisebox{.8\normalbaselineskip}{$+$}}\\\cline{4-5}&&&+5y&{}=18\\[\jot]&&&y&{}=\dfrac{18}{5}\\\end{array}\]\\](https://tex.z-dn.net/?f=%5C%5B%5Cbegin%7Barray%7D%7Br%40%7B%7Dl%40%7B%5Cquad%7Dl%40%7B%5Cquad%7Dr%40%7B%7Dl%40%7B%7Dc%7D3x-4y%26%7B%7D%3D-1%26%5Cxrightarrow%7B%5Ctimes%20%28-3%29%7D%26-9x%20%2B12y%26%7B%7D%3D%2B3%5C%5C%5B%5Cjot%5D9x%20-7y%26%7B%7D%3D15%26%5Cxrightarrow%7B%5Cphantom%7B%5Ctimes%20%28-3%29%7D%7D%269x-y%26%7B%7D%3D15%26~%5Csmash%7B%5Craisebox%7B.8%5Cnormalbaselineskip%7D%7B%24%2B%24%7D%7D%5C%5C%5Ccline%7B4-5%7D%26%26%26%2B5y%26%7B%7D%3D18%5C%5C%5B%5Cjot%5D%26%26%26y%26%7B%7D%3D%5Cdfrac%7B18%7D%7B5%7D%5C%5C%5Cend%7Barray%7D%5C%5D%5C%5C)
now that we've found the value of y
we'll use this value in any of the two equations to get the value of x.
let's put y in the first equation:
![3x-4y=-1](https://tex.z-dn.net/?f=3x-4y%3D-1)
![3x-4\left( \dfrac{18}{5}\right)=-1](https://tex.z-dn.net/?f=3x-4%5Cleft%28%20%5Cdfrac%7B18%7D%7B5%7D%5Cright%29%3D-1)
![3x=-1+4\left( \dfrac{18}{5}\right)](https://tex.z-dn.net/?f=3x%3D-1%2B4%5Cleft%28%20%5Cdfrac%7B18%7D%7B5%7D%5Cright%29)
![3x=-1+\dfrac{72}{5}](https://tex.z-dn.net/?f=3x%3D-1%2B%5Cdfrac%7B72%7D%7B5%7D)
![3x=\dfrac{67}{5}](https://tex.z-dn.net/?f=3x%3D%5Cdfrac%7B67%7D%7B5%7D)
![x=\dfrac{67}{3(5)}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B67%7D%7B3%285%29%7D)
![x=\dfrac{67}{15}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B67%7D%7B15%7D)
Answer:
0.46
Step-by-step explanation:
42.78/m = 93
=> m = 42.78/93
=> m = 0.46
Hope my answer helps :)
9514 1404 393
Answer:
50°
Step-by-step explanation:
The measure of an inscribed angle is half the measure of the arc it intercepts.
∠ACB = 1/2 arc AB = (100°)/2
∠ACB = 50°
Answer:
the answer is 2o.
Step-by-step explanation:
the width is always the longest and wider!!!
Let me know if the answer is right, thank u.