4/3pi *r3 = 972pi
Divide both side by pi
4/3 *r3 = 972
r3 = 972* 3/4
r3 = 729
r = the square root of 729 to the third power (I don't know if I'm expressing this correctly but answer is 9, hope you get that)
r = 9 that's your answer.
Hope it's correct, appreciate if you could let me know
Answer:
Option 1 - 
Step-by-step explanation:
Given : The goals against average (A) for a professional hockey goalie is determined using the formula 
. In the formula, g represents the number of goals scored against the goalie and t represents the time played, in minutes.
To find : Which is an equivalent equation solved for g?
Solution :
Solve the formula in terms of g,
Multiply both side by t,
Divide both side by 60,
Therefore, option 1 is correct.
Here's link to the answer:
tinyurl.com/wpazsebu
Answer:
Constructive Proof
Step-by-step explanation:
Let x be a positive integer
x must be equal to sum of all positive integers exceeding it
i.e.
x = x + (x - 1) + ( x - 2) + ......... + 2 + 1
Equivalently,
x = ∑i (where i = 1 to x)
The property finite sum;
∑i (i = 1 to x) = x(x + 1)/2
So,
x = x(x + 1)/2 ------- Multiply both sides by 2
2 * x = 2 * x(x + 1)/2
2x = x(x + 1)
2x = x² + x ------- subtract 2x from both sides
2x - 2x = x² + x - 2x
0 = x² + x - 2x ----- Rearrange
x² + x - 2x = 0
x² - x = 0 ------ Factorise
x(x - 1) = 0
So,
x = 0 or x - 1 = 0
x = 0 or x = 1 + 0
x = 0 or x = 1
But x ≠ 0
So, x = 1
The statement is only true for x = 1
This makes sense because 1 is the only positive integer not exceeding 1
1 = 1
It is a Constructive Proof
A proof is constructive when we find an element for which the statement is true.
Answer:
11.718
Step-by-step explanation:
Answer given above. Pls check
