Answer:
![15\pi\ cm^{2}](https://tex.z-dn.net/?f=15%5Cpi%5C%20cm%5E%7B2%7D)
Step-by-step explanation:
we know that
The lateral area of the cone is equal to
![LA=\pi rl](https://tex.z-dn.net/?f=LA%3D%5Cpi%20rl)
where
r is the radius of the base
l is the slant height
we have
![r=3\ cm](https://tex.z-dn.net/?f=r%3D3%5C%20cm)
Applying the Pythagoras Theorem find the slant height
![l^{2}=3^{2} +4^{2}\\ \\l^{2}=25\\ \\l=5\ cm](https://tex.z-dn.net/?f=l%5E%7B2%7D%3D3%5E%7B2%7D%20%2B4%5E%7B2%7D%5C%5C%20%5C%5Cl%5E%7B2%7D%3D25%5C%5C%20%5C%5Cl%3D5%5C%20cm)
substitute in the formula
![LA=\pi (3)(5)=15\pi\ cm^{2}](https://tex.z-dn.net/?f=LA%3D%5Cpi%20%283%29%285%29%3D15%5Cpi%5C%20cm%5E%7B2%7D)
Given :
![\:](https://tex.z-dn.net/?f=%20%5C%3A%20)
![\:](https://tex.z-dn.net/?f=%20%5C%3A%20)
![\gray{ \frak{The \: given \: two \: \: points \: are(x_{1 },y_{1})=(−6 , -10)and(x_{ 2 },y_{2} )=( 2,5 )\:}}](https://tex.z-dn.net/?f=%20%5Cgray%7B%20%5Cfrak%7BThe%20%5C%3A%20%20given%20%5C%3A%20%20two%20%5C%3A%20%20%20%5C%3A%20points%20%20%5C%3A%20are%28x_%7B1%20%7D%2Cy_%7B1%7D%29%3D%28%E2%88%926%20%2C%20-10%29and%28x_%7B%202%20%7D%2Cy_%7B2%7D%20%29%3D%28%202%2C5%20%29%5C%3A%7D%7D)
![\:](https://tex.z-dn.net/?f=%20%5C%3A%20)
Let's solve by using midpoint formula :
![\:](https://tex.z-dn.net/?f=%20%5C%3A%20)
![\bf \boxed{\color{red}\frak{Midpoint \: \: Formula : {( \: x ,\:y \: ) = }( \frak{ \frac{x_{1 } + y_{1}}{2} , \frac{x_{2 } + y_{2}}{2} )}}}](https://tex.z-dn.net/?f=%20%20%20%5Cbf%20%5Cboxed%7B%5Ccolor%7Bred%7D%5Cfrak%7BMidpoint%20%5C%3A%20%20%20%5C%3A%20Formula%20%3A%20%20%7B%28%20%5C%3A%20x%20%2C%5C%3Ay%20%5C%3A%20%20%29%20%3D%20%7D%28%20%20%5Cfrak%7B%20%5Cfrac%7Bx_%7B1%20%7D%20%2B%20y_%7B1%7D%7D%7B2%7D%20%2C%20%5Cfrac%7Bx_%7B2%20%7D%20%2B%20y_%7B2%7D%7D%7B2%7D%20%29%7D%7D%7D)
![\:](https://tex.z-dn.net/?f=%20%5C%3A%20)
![\large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \frac{ -6 + 2}{2} , \frac{ - 10 + 5}{2} )}}](https://tex.z-dn.net/?f=%20%5Clarge%20%5Cgray%7B%20%5Cfrak%7B%28%20%5C%3A%20x%20%2C%5C%3Ay%20%5C%3A%20%20%29%20%3D%20%7D%28%20%20%5Cfrak%7B%20%5Cfrac%7B%20-6%20%2B%202%7D%7B2%7D%20%2C%20%5Cfrac%7B%20-%2010%20%2B%205%7D%7B2%7D%20%29%7D%7D)
![\:](https://tex.z-dn.net/?f=%20%5C%3A%20)
![\: \large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \frac{ -4}{2} , \frac{ - 5}{2} )}}](https://tex.z-dn.net/?f=%20%5C%3A%20%5Clarge%20%5Cgray%7B%20%5Cfrak%7B%28%20%5C%3A%20x%20%2C%5C%3Ay%20%5C%3A%20%20%29%20%3D%20%7D%28%20%20%5Cfrak%7B%20%5Cfrac%7B%20-4%7D%7B2%7D%20%2C%20%5Cfrac%7B%20-%205%7D%7B2%7D%20%29%7D%7D)
![\:](https://tex.z-dn.net/?f=%20%5C%3A%20)
![\large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \cancel\frac{ -4}{2} , \cancel\frac{ - 5}{2} )}}](https://tex.z-dn.net/?f=%5Clarge%20%5Cgray%7B%20%5Cfrak%7B%28%20%5C%3A%20x%20%2C%5C%3Ay%20%5C%3A%20%20%29%20%3D%20%7D%28%20%20%5Cfrak%7B%20%20%5Ccancel%5Cfrac%7B%20-4%7D%7B2%7D%20%2C%20%20%5Ccancel%5Cfrac%7B%20-%205%7D%7B2%7D%20%29%7D%7D)
![\: \:](https://tex.z-dn.net/?f=%20%5C%3A%20%20%5C%3A%20)
![\underline{ \boxed{ \large \red{ \frak{option \: d }( \frak{ - 2, - 2.5)}}}}✓](https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Cboxed%7B%20%5Clarge%20%5Cred%7B%20%5Cfrak%7Boption%20%5C%3A%20d%20%7D%28%20%20%5Cfrak%7B%20%20%20-%202%2C%20-%202.5%29%7D%7D%7D%7D%E2%9C%93)
Hope Helps! :)
Answer:
3.66666666667
Step-by-step explanation:
If you multiply the number of batches he makes and the amount of grape juice he needs for every quart, you get and answer of 3.66666666667.
1/3 * 11= 3.66666666667
If you need to round the answer it would be 3.67
step 2 i believe is the answer
Answer:
Small no. is 15
Larger no. is 15 + 27 = 42
Step-by-step explanation:
Let the small no. be x
Larger no. will be x + 27
5x + x + 27 = 117
6x + 27 = 117
6x = 117-27
x = 90/6
x = 15