Answer:
b=4
Step-by-step explanation:
So, we have the function
. We need to find b such that the average rate of change or the slope is -1/8 between the intervel [2, b]. First, let's find f(2).
f(2) = 1/(2) = 1/2
So, we have the point (2, 1/2)
At point b, f(b) = 1/b.
Let's plug this into the slope formula:
![\frac{y_2-y_1}{x_2-x_1}=\frac{.5-\frac{1}{b} }{2-b} =-1/8](https://tex.z-dn.net/?f=%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%3D%5Cfrac%7B.5-%5Cfrac%7B1%7D%7Bb%7D%20%7D%7B2-b%7D%20%20%3D-1%2F8)
Now, we just need to solve for b. First, let's multiply both the numerator and denominator by b (to get rid of the annoying fraction in the numerator).
![\frac{.5b-1}{2b-b^2} =\frac{-1}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B.5b-1%7D%7B2b-b%5E2%7D%20%3D%5Cfrac%7B-1%7D%7B8%7D)
Now, cross multiply.
![4b-8=b^2-2b](https://tex.z-dn.net/?f=4b-8%3Db%5E2-2b)
![b^2-6b+8=0](https://tex.z-dn.net/?f=b%5E2-6b%2B8%3D0)
Solve for b. Factor using the numbers -4 and -2.
![=(b-4)(b-2)=0](https://tex.z-dn.net/?f=%3D%28b-4%29%28b-2%29%3D0)
Thus, b=4 or b=2.
However, b=2 is not a possible solution since the interval [2,2] means nothing. Thus, b=4.
Answer:
show how you know .. :D good rhyme
Step-by-step explanation:
park = 4" x 6" ( inches) small park
but one inch = 30 miles ooh big park
4*30 X 6*30
120 X 180 miles... like a big game range? :? very big
since we only have 6 square inches to fit the map into... then.. what size of map would fit? what size equals 6 inches? 2 x 3 ? hmm yes that's 6
soooo shrink the 4" x 6" to 2"x 3" so the scale needs to double or
1 inch = 60 miles
2"*60 x 3"*60 = 120 x 180 miles.. looks good try that :)
Answer:
10x^{3}[/tex]
Step-by-step explanation:
![10x^{3}](https://tex.z-dn.net/?f=10x%5E%7B3%7D)
=10·10·10
=1000
The decimal multiplier to decrease by 30 is .7