1. The function f(x) = -0.05(x2 - 26x - 120) represents the path coming out of the cannon. If x is the horizontal distance from the cannon, what does f(x) represent? (1 point)

f(x) represents the vertical height of the cannon

Step-by-step explanation:

The given function is presented as follows;

f(x) = -0.05·(x² - 26·x - 120)

Given that 'x' represent the horizontal path of the cannon and the function describes the path of the cannon, we have that the vertical height reached by the cannon as it moves along the horizontal path is given as the function f(x)

Therefore, we have;

f(0) = -0.05·(0² - 26×0 - 120) = -0.05 × -120 = 6

f(0) = 6

The starting height of the cannon = 6

The maximum height reached by the cannon is given as follows;

f'(x) = d(-0.05·(x² - 26·x - 120))/dx = -0.05·d(x² - 26·x - 120)/dx = -0.05×(2·x - 26)

f'(x) = -0.05×(2·x - 26)

f'(x) = 0 At maximum height, therefore, we have;

-0.05×(2·x - 26) = 0

(2·x - 26) = 0

2·x = 26

x = 26/2 = 13

x = 13

f(13) = -0.05·(13² - 26×13 - 120) = 14.45

The maximum height = 14.45

Therefore;

f(x) = The vertical height of the cannon

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation:

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