A cube has as side length of 20.5 cm. What is the surface area of the cube?
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This problem can be modeled by the picture shown below. We notice that we are given to side lengths, specifically legs, of the triangle. Therefore, we can use the Pythagorean Theorem, which states that a^2+b^2=c^2, where a and b are legs and c is the hypotenuse. So we can do:
16^2+12^2=c^2
256+144=c^2
400=c^2
The square root of 400 is 20, which is our hypotenuse.
(You might wonder why we used 12, that is because the whole base length is 24, but we only need half of the base to use the Pythagorean Theorem. 24/2 is 12).
:)
16^2+12^2=c^2
256+144=c^2
400=c^2
The square root of 400 is 20, which is our hypotenuse.
(You might wonder why we used 12, that is because the whole base length is 24, but we only need half of the base to use the Pythagorean Theorem. 24/2 is 12).
:)
An equation is formed of two equal expressions. The value of x that maximizes the area of the printed region of the billboard is 9.655 ft.
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given x is the left-right width of the billboard and y is the height of the billboard. Therefore,
The total area of the billboard, A= x·y
The total printed area of the billboard,
Given in problem that the area of the billboard is 3600 ft².
x·y = 3600
y = (3600)/x
Substituting the value of y in the equation of the total printed area of the billboard,
Now, the value of x is needed to be minimum, therefore, differentiating the given function,
Equate the differentiated function with 0,
Hence, the value of x that maximizes the area of the printed region of the billboard is 9.655 ft.
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