Answer:
The diameter of the hemisphere is 20.4 centimeters.
Step-by-step explanation:
The volume of an hemisphere is given by:

In this problem, we have that:

So



![r = \sqrt[3]{\frac{3*2233}{2\pi}}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B3%2A2233%7D%7B2%5Cpi%7D%7D)

The radius is 10.2 centimeters.
The diameter is double the radius. So:
2*10.2 = 20.4
The diameter of the hemisphere is 20.4 centimeters.
Answer:
Step-by-step explanation:
6/4=(6-1)/(4-x)
6/4=5/(4-x)
6(4-x)=4(5)
24-6x=20
-6x=-4
x=4/6
x=2/3
2/3 of an inch should be cut off the width.
Answer:
-7
Step-by-step explanation:
Lets assume the number Peggy is thinking of be "x".
Now as given, when twice the number is added to three times one more than the number. We can write it as
∴
--- Equation 1
Again, it is given that Peggy gets the same result as when she multiplies four times one less than the number.
∴
-- equation 2
Next, we can equate both the equation 1 and 2 as it is given that result is same.

Let´s distribute 3 into
and 4 into 
⇒ 
⇒ 
Subtract both side by 4x and 3
∴ 
∴ Peggy was thinking of -7
∈ ≤ ≥
-6 ≤ 2x + 6 ≤ 6 ( seperate the two inequalities)
2x + 6 ≥ - 6
2x + 6 ≤ 6 (solve the inequalities)
x ≥ -6
x ≤ 0 (find the intersection)
solution is : x ∈ { -6, 0 }