a piggy bank contains $5.60 in nickels and dimes. the number of nickels is 8 less than 3 times the dimes. how many nickels and d
2 answers:
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Let h = height of the box,
x = side length of the base.
Volume of the box is
.
So
Surface area of a box is S = 2(Width • Length + Length • Height + Height • Width).
So surface area of the box is
The surface are is supposed to be the minimum. So we'll need to find the first derivative of the surface area function and set it to zero.
![4x = \frac{460}{ x^{2} } \\ 4x^{3} = 460 \\ x^{3} = 115 \\ x = \sqrt[3]{115} = 4.86](https://tex.z-dn.net/?f=%204x%20%3D%20%5Cfrac%7B460%7D%7B%20x%5E%7B2%7D%20%7D%20%20%5C%5C%20%204x%5E%7B3%7D%20%3D%20460%20%20%5C%5C%20x%5E%7B3%7D%20%3D%20115%20%20%5C%5C%20x%20%3D%20%20%5Csqrt%5B3%5D%7B115%7D%20%3D%204.86%20)
Then
So the box is 4.86 in. wide and 4.87 in. high.
x = side length of the base.
Volume of the box is
So
Surface area of a box is S = 2(Width • Length + Length • Height + Height • Width).
So surface area of the box is
The surface are is supposed to be the minimum. So we'll need to find the first derivative of the surface area function and set it to zero.
Then
So the box is 4.86 in. wide and 4.87 in. high.
The time interval x >0.5 and x > 2.04 will the tennis ball be at least 15 feet above the ground.
Given that,
The height of a tennis ball tossed into the air is modeled by,
Where x is elapsed time in seconds.
We have to determine,
During what time interval will the tennis ball be at least 15 feet above the ground?
According to the question,
The height of a tennis ball tossed into the air is modeled by,
Where x is elapsed time in seconds.
Then,
When the tennis ball be at least 15 feet above the ground,
Substitute the value of h(x) in the equation,
Factorize the equation for finding the time interval will the tennis ball be at least 15 feet above the ground is,
Hence, The time interval x >0.5 and x > 2.04 will the tennis ball be at least 15 feet above the ground.
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