The complete question is
Three tennis balls are stored in a cylindrical container with a height of 8 inches and a radius of 1.43 inches. The circumference of a tennis ball is 8 inches. a) Find the volume of a tennis ball b) There are 3 tennis ball in the container Find the amount of space within the cylinder not taken up by the tennis balls. Round your answers to the nearest hundredth.
Part a)
we know that
length of a circumference=2*pi*r----------> r=length/(2*pi)---> 8/(2*pi)
r=1.27 in------> radius of tennis ball
volume of a tennis ball is equals to the volume of a sphere
[volume of a sphere]=(4/3)*pi*r³----> (4/3)*pi*1.27³---> 8.58 in³
the answer Part a) is
the volume of a tennis ball is 8.58 in³
Part b)
[volume of the container]=pi*r²*h-----> pi*1.43²*8----> 51.39 in³
[volume of 3 tennis balls]=8.58*3-----> 25.74 in³
the amount of space within the cylinder not taken up by the tennis balls is
51.39-25.74-----> 25.65 in³
the answer Part b) is
25.65 in³
Answer:
the answer is 2 + i.
Step-by-step explanation:
Let the square root of 3 + 4i be x + iy.
So (x + iy) (x +iy) = 3 +4i
=> x^2 + xyi + xyi + i^2*y^2 = 3 + 4i
=> x^2 – y^2 + 2xyi = 3 + 4i
Equate the real and complex terms
=> x^2 - y^2 = 3 and 2xy = 4
2xy = 4
=> xy = 2
=> x = 2/y
Substitute in
=> x^2 - y^2 = 3
=> 4/y^2 - y^2 = 3
=> 4 – y^4 = 3y^2
=> y^4 + 3y^2 – 4 = 0
=> y^4 + 4y^2 – y^2 – 4 =0
=> y^2(y^2 + 4) – 1(y^2 + 4) =0
=> (y^2 – 1) (y^2 + 4) =0
Therefore y^2 = 1, we ignore y^2 = -4 as it gives complex values of y.
Therefore y = 1 and x = 2/1 = 2
The required square root of 3 + 4i is 2 + i.
Answer:52
Step-by-step explanation:
2^4 = 16
Then..
16+81 =97
Then..
97-50 = 47
Lastly..
47+5 = 52
Let the third angle be x.
The sum of the interior angles of all triangles is 180 degrees. Thus, you can set the interior angles' sum equal to 180 and solve for the third angle, x.
44 + 72 + x = 180
116 + x = 180 (collect like terms)
x = 64 (subtract 116 from both sides)
Answer:
The measure of the third angle is 64 degrees.
