For what value of x does 84^3x=512^2x+12
1 answer:
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Imagine right triangle PHF, where P - park, H - home and F - football field, then PH, PF are legs and HF is hypotenuse . Denote point L to be library. You know that point L lies on the segment FH and FL=8, LH=2. Also you know that PL is an altitude to the hypotenuse.
Use the property of altitude drawn from the vertex of right angle to the hypotenuse (the length of the altitude is geometrical mean between legs' projections onto hypotenuse):
mi.
This means that the distance between park and libriry is 4 miles.
Consider right triangle PLF ( angle L is right angle and PF - hypotenuse). By the Pythagorean theorem,
mi. The distance between park and football field is
miles.
Answer: the distance between park and libriry is 4 miles and the distance between park and football field is miles.
Answer:
- a) 3
- b) 6
- c) 9
- d) the outputs are 3 times as far apart as the inputs
Step-by-step explanation:
(a) "x" in considered to be the input to the function f(x). The variable(s) in parentheses as part of the function name are the inputs. The function value itself is the output.
That is, for an input (x-value) of 0, the output (f(0)) is 5. For an input of 1, the output (f(1)) is 8. These input values (0 and 1) are 1 unit apart: 1 - 0 = 1. The corresponding output values are 3 units apart: 8 - 5 = 3.
(b) Inputs -1 and 1 are 2 units apart (1-(-1)=2). The corresponding output values, 2 and 8, are 6 units apart. (8-2=6)
(c) Inputs 0 and 3 are 3 units apart. The corresponding output values, 5 and 14, are 9 units apart.
(d) The ratio of output differences to input differences can be seen to be ...
... 3/1 = 6/2 = 9/3 = 3
Output differences are 3 times input differences.
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<em>Comment on the problem</em>
These ratios are constant everywhere, so the function is considered to be "linear." The ratio is the "slope" of the line you see when the function is graphed.
