5/4. first, convert the mixed fraction into an improper fraction to get 5/2. multiply the 5/2 to the 1/2. multiplying the numerators gets you 5. the denominators being multiplied gets you 4. 5 is the new numerator, 4 is the new denominator. 5/4 is in simplest form
Answer:
V(cylinder) = πr²h
h=3 cm
r=2 cm
V(cylinder) = πr²h = π*2²*3 =12π cm³
Answer : 12π cm³.
Given:
Equation of line
.
To find:
The equation of line that goes through the point ( − 21 , 2 ) and is perpendicular to the given line.
Solution:
The given equation of line can be written as
![7x-4y+12=0](https://tex.z-dn.net/?f=7x-4y%2B12%3D0)
Slope of line is
![\text{Slope}=-\dfrac{\text{Coefficient of x}}{\text{Coefficient of y}}](https://tex.z-dn.net/?f=%5Ctext%7BSlope%7D%3D-%5Cdfrac%7B%5Ctext%7BCoefficient%20of%20x%7D%7D%7B%5Ctext%7BCoefficient%20of%20y%7D%7D)
![m_1=-\dfrac{7}{(-4)}](https://tex.z-dn.net/?f=m_1%3D-%5Cdfrac%7B7%7D%7B%28-4%29%7D)
![m_1=\dfrac{7}{4}](https://tex.z-dn.net/?f=m_1%3D%5Cdfrac%7B7%7D%7B4%7D)
Product of slopes of two perpendicular lines is -1. So, slope of perpendicular line is
![m_1m_2=-1](https://tex.z-dn.net/?f=m_1m_2%3D-1)
![m_2=-\dfrac{1}{m_1}](https://tex.z-dn.net/?f=m_2%3D-%5Cdfrac%7B1%7D%7Bm_1%7D)
![[\because m_1=\dfrac{7}{4}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20m_1%3D%5Cdfrac%7B7%7D%7B4%7D%5D)
Now, the slope of perpendicular line is
and it goes through (-21,2). So, the equation of line is
![y-y_1=m_2(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm_2%28x-x_1%29)
![y-2=-\dfrac{4}{7}(x-(-21))](https://tex.z-dn.net/?f=y-2%3D-%5Cdfrac%7B4%7D%7B7%7D%28x-%28-21%29%29)
![y-2=-\dfrac{4}{7}x-\dfrac{4}{7}(21)](https://tex.z-dn.net/?f=y-2%3D-%5Cdfrac%7B4%7D%7B7%7Dx-%5Cdfrac%7B4%7D%7B7%7D%2821%29)
![y-2=-\dfrac{4}{7}x-12](https://tex.z-dn.net/?f=y-2%3D-%5Cdfrac%7B4%7D%7B7%7Dx-12)
![y=-\dfrac{4}{7}x-12+2](https://tex.z-dn.net/?f=y%3D-%5Cdfrac%7B4%7D%7B7%7Dx-12%2B2)
![y=-\dfrac{4}{7}x-10](https://tex.z-dn.net/?f=y%3D-%5Cdfrac%7B4%7D%7B7%7Dx-10)
Therefore, the required equation in slope intercept form is
.
Step-by-step explanation:
martha-12
0+6+12
i think thats the answer