What is the y-intercept of the function f(x)=4 - 5x? -5 -4 4 5
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The number of basketball that will fill up the entire office is <u>approximately 16,615.</u>
<em><u>Recall:</u></em>
Volume of a spherical shape =
Volume of a rectangular prism =
<em><u>Given:</u></em>
Diameter of basketball = 9.5 in.
Radius of the ball = 1/2 of 9.5 = 4.75 in.
Radius of the ball in ft = 0.4 ft (12 inches = 1 ft)
Dimension of the office (rectangular prism) = 20 ft by 18 ft by 12 ft
- First, find the volume of the basketball:
Volume of ball =
Volume of basketball =
- Convert to
<em>Therefore,</em>
- Volume of basketball =
- Find the volume of the office (rectangular prism):
Volume of the office =
- Number of basket ball that will fill the office = Volume of office / volume of basketball
- <em>Thus:</em>
Number of basket ball that will fill the office =
Therefore, it will take approximately <u>16,615 balls</u><u> to fill up the entire office</u>.
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The airplane reaches its maximum height of 81 feet in 12 seconds.
<h3>Behavior of curves</h3>If y = , it means that the second derivate is 2 which is positive, then there is a minimum turning point.
If y = - , it means that the second derivative will be -2 which is negative, then there is a maximum turning point.
Analysis:
h(t) = - + 81
By expanding,
h(t) = -( - 24t + 144) +81
h(t) = - + 24t - 144 + 81
h(t) = - + 24t - 63
at turning point d/dt(h(t)) = 0
d/dt (h(t)) = -2t +24
-2t +24 = 0
if we differentiate again, second derivative is -2 which is negative, so it is a maximum point.
2t = 24
t = 12 seconds
h(t) at t = 12
h(t) = + 24(12) - 63 = 81 feet
In conclusion, the maximum height of the airplane after 12 seconds is 81 feet.
Learn more about minimum and maximum points: brainly.com/question/14993153
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