Determine whether the graphs of x+y=3 and x-y=8 are perpendicular
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The radius of each of the smaller molds is r = 1/3 ft. Using the volume of the given hemisphere, the required radius is calculated.
<h3>How to calculate the volume of a hemisphere?</h3>The volume of the hemisphere is calculated by using the formula,
= × π × r³ cubic units
where r is the radius of the hemisphere.
<h3>Calculation:</h3>It is given that,
A hemisphere-shaped bowl with a radius r = 1 ft is filled with chocolate.
So, the volume of the bowl is
V = × π × (1)³
= × π cubic feets
The volume of each smaller hemisphere-shaped mold = × π × r³ cubic units
So, for 27 molds, the volume = 27 × × π × r³ cubic units
All of the chocolate is then evenly distributed between 27 congruent, smaller hemisphere-shaped molds.
Then,
× π = 27 ×
× π × r³
⇒ r³ = 1/27
⇒ r = 1/3 ft
Therefore, the required radius of each of the smaller molds is 1/3 foot.
Learn more about the volume of a hemisphere here:
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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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