Daniela rented a car. She paid a flat rate for the day, plus a cost per mile charge. The expression 0.15x+220.15x+22 represents
2 answers:
Let
x--------> the number of miles driven
y--------> the amount in dollars that Daniela paid
we know that
where
-------> represent the daily flat rate (the y-coordinate of the y-intercept of the linear equation)
-------> represent the cost per mile (the slope of the linear equation)
---------> number of miles driven
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Answer:
26 ft square by 13 ft high
Step-by-step explanation:
The tank will have minimum surface area when opposite sides have the same total area as the square bottom. That is, their height is half their width. This makes the tank half a cube. Said cube would have a volume of ...
2·(8788 ft^3) = (26 ft)^3
The square bottom of the tank is 26 ft square, and its height is 13 ft.
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<em>Solution using derivatives</em>
If x is the side length of the square bottom, the height is 8788/x^2 and the area is ...
x^2 + 4x(8788/x^2) = x^2 +35152/x
The derivative of this is zero when area is minimized:
2x -35152/x^2 = 0
x^3 = 17576 = 26^3 . . . . . multiply by x^2/2, add 17576
x = 26
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As the attached graph shows, a graphing calculator can also provide the solution.
Answer:
Base of the mirror is 12 feet and height of the mirror is 18 feet.
Step-by-step explanation:
Given:
Area of the triangular mirror = 108 sq ft.
Let base (b) of the mirror be x.
Now given:
height is 6 feet less than twice the base of the mirror
So we can say that;
Height (h) =
We need to find the base and height of the mirror.
Solution:
Now we know that mirror is in triangular shape so we will apply area of triangle formula to find base and height.
Now Area of triangle is half times base times height.
framing in equation form we get;
Now we will find the roots of x by factorizing the equation we get;
Now we will solve for 2 values of x we get;
Now we get 2 values of 'x' one positive and one negative.
Since x is base of the triangle which cannot be negative.
so we will discard the negative value.
Hence;
base of triangle = 12 ft
Height of the triangle =
Hence Base of the mirror is 12 feet and height of the mirror is 18 feet.