Simplify!! Please!!!
2 answers:
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The ladder in figure 2 reaches 3.2 feet further up than the ladder in figure 1.
Step-by-step explanation:
Step 1:
In both the given figures, the ladder, the wall and the floor form a right-angled triangle. The floor is the adjacent side, the wall is the opposite side and the ladder is the hypotenuse.
According to the Pythagorean theorem,
, where c is the length of the hypotenuse while a and b are the lengths of the other two sides.
Step 2:
For the ladder in figure 1, assume the distance from the floor to the ladder's top is x feet. So a = x, b = 8 and c = 10 (hypotenuse).
,
,
.
So the distance between the floor and the ladder's top is 6 feet.
Step 3:
For the ladder in figure 2, assume the distance between the floor and the ladder's top is y feet. So a = y, b = 4 and c = 10 (hypotenuse).
,
,
.
So the distance between the floor and the ladder's top is 9.1651 feet.
Step 4:
The difference in heights = The wall height in figure 2 - the wall height in figure 1.
The difference in heights = 9.1651 feet - 6 feet = 3.1651 feet.
Rounding this off to the nearest tenth of a foot, we get 3.2 feet.
<h2>Answer:</h2>
The conclusion that is true about f(x) and g(x) based on the table of values is:
- The function f(x) and g(x) are reflections over the y-axis.
- We know that the rule that describes the reflection over the y-axis is:
(x,y) → (-x,y)
Hence, if we have a function f(x) as:
Then it's reflection over the y-axis is:
Hence, they are reflection over the y-axis.
- Also, we know that the exponential function of the type:
where a>0 is a increasing function if b>1
and is a decreasing function if: 0<b<1
Hence, f(x) is a increasing function and g(x) is a decreasing function.
- Also, the initial value of a function is the value of function when x=0
when x=0 we see that both f(x)=g(x)=1
i.e. Both f(x) and g(x) have same initial value.
Also,by the graph we may see the relation.