Answer:
r^2 = 45÷2 x^2
Step-by-step explanation:
Details of cone:
Radius(r) = 5x cm
Height(h) = 12x cm
Slant height(l) = √(12x^2 + 5x^2)
l = 13x cm
Total surface area of a cone (T. S. A) = πrl + πr²
T. S. A = π * 5x * 13x + π5x^2
T.S.A = π65x^2 + π5x^2
T.S.A = π65x^2 + π25x^2
T.S.A = 90πx^2 - - - - - (1)
Details of sphere:
Radius (r) = r cm
Total surface area = 4πr²
Total Surface area of sphere= 4πr²cm - - - (2)
Equating (1) and (2) to calculate r
4πr² = 90πx^2
r^2 = 90πx^2 / 4π
r^2 = 90π (x^2) / 4π
r^2 = 45/2 (x^2) ;
r^2 = 45÷2 x^2
Hence the proof
Answer:
B
Step-by-step explanation:
x − 3 − 2(6 − 2x) = 2(2x − 5)
Firstly, we will find slope of the given lne
we can select any two points from the graph
(-4,-5) and (4,-1)
so, x1=-4 , y1=-5 m x2=4 , y2=-1
now, we can use formula
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
now, we can plug values
![m=\frac{-1+5}{4+4}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-1%2B5%7D%7B4%2B4%7D)
![m=\frac{1}{2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B2%7D)
(B)
we are given
line parallel to the nline shown
and we know that
slope of two parallel lines are always equal
so, slope will also be
![m=\frac{1}{2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B2%7D)
we have point as (3,4)
now, we can use point slope form of line
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
we can plug values
![y-4=\frac{1}{2}(x-3)](https://tex.z-dn.net/?f=y-4%3D%5Cfrac%7B1%7D%7B2%7D%28x-3%29)
we get
![y=\frac{1}{2}x+\frac{5}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7Dx%2B%5Cfrac%7B5%7D%7B2%7D)
(D)
we have point as (-3, 2)
and we know that
slope of perpendicular line is -1/m
so,
![m_p=-2](https://tex.z-dn.net/?f=m_p%3D-2)
now, we can use point slope form of line
![y-2=-2(x+3)](https://tex.z-dn.net/?f=y-2%3D-2%28x%2B3%29)
we get
.............Answer
Answer:
x=6
Step-by-step explanation:
Mean is another word for average. It is found by adding up all of the values, and dividing that number by the amount of values you added together.
You have 5 values that get a mean or, average, of 7.4
1) We can write this as the following:
(11+12+5+3+x)/5=7.4
2) To solve, multiply both sides by 5:
11+12+5+3+x=37
3) Now combine all of the numbers on the left:
31+x=37
4) Now subtract 31 from both sides:
x=6