Answer:
Formula is given
Step-by-step explanation:
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Answer: 216 square units
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Explanation:
A common pythagorean triple you may be familiar with is the 3-4-5 right triangle. This has two legs of 3 and 4, and a hypotenuse of 5. The perimeter is 3+4+5 = 7+5 = 12. Note how this is a factor of 72.
If we multiply the perimeter (12) by 6, then 12*6 = 72. So we have scaled the triangle by a factor of 6. Each length is 6 times longer
the side length 3 becomes 3*6 = 18
the side length 4 becomes 4*6 = 24
the side length 5 becomes 5*6 = 30
The new perimeter is 18+24+30 = 42+30 = 72
The last step is to find the area. The two legs of this triangle are the base and height
area = 0.5*base*height
area = 0.5*18*24
area = 9*24
area = 216
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Or you could find the area of the 3-4-5 right triangle to get
area = 0.5*base*height = 0.5*3*4 = 6
then multiply by 36 to get 6*36 = 216. The 36 is the square of the scale factor 6 we applied above. The new lengths are 6 times longer, so the new area is 6^2 = 36 times larger.
Answer:
11
Step-by-step explanation:
The average rate of change of function f on interval [a, b] is ...
m = (f(b) -f(a))/(b -a)
Here, that is ...
m = (f(6) -f(2))/(6 -2)
So, we need to evaluate the function at x=6 and x=2. Writing it in "Horner form" makes this easier.
f(x) = (x +3)x -2
f(6) = (6 +3)6 -2 = 54 -2 = 52
f(2) = (2 +3)2 -2 = 10 -2 = 8
Then the slope is ...
m = (52 -8)/4 = 13 -2 = 11
The average rate of change of f(x) from 2 to 6 is 11.
The slope is -15/0 so the slope is zero
