Answer:
diameter = 3,600 units
Step-by-step explanation:
Let 
= 3.14
C = 2r
11,304 = 2(3.14)r
r = 1,800
d = 2r = 2(1,800) = 3,600
Answer:
t=x+44
Step-by-step explanation:
the x ounces are being added to the vase's pre-existing 44 ounces so therefore the equation is t=x+44
Answer:
3pi/4 and -pi/4
Step-by-step explanation:
We can simplify -6/6 to -1.
Therefore, this function can be simplified to arctan(-1).
Recall that the meaning of arctan is to find a value that will get the value inside the parenthesis when taken the tangent of it. In other words, tan(x) = -1.
Recall that tan(x) = sin(x)/cos(x). Now recall that sin(pi/4) and cos(pi/4) are both sqrt(2)/2, meaning that tan(pi/4) is 1. To make it -1, we can either make sin(x) -1 while keeping cos(x) 1, or the other way around.
If x is -pi/4, cos(x) will still be 1, but sin(x) will be -1, so tan(-pi/4) will be -1.
If x is 3pi/4, cos(x) will be -1, but sin(x) will still be 1, so tan(3pi/4) will be -1.
Side note: there are still infinite more answers. You can attain them by adding or subtracting 2pi as many times as you want from 3pi/4 or -pi/4 and still get an arctan of -1.
Answer:
4512.
Step-by-step explanation:
We are asked to find the number of five-card hands (drawn from a standard deck) that contain exactly three fives.
The number of ways, in which 3 fives can be picked out of 4 available fives would be 4C3. The number of ways in which 2 non-five cards can be picked out of the 48 available non-five cards would be 48C2.
We can choose exactly three fives from five-card hands in 
ways.
Therefore, 4512 five card hands contain exactly three fives.
