Answer:
196: 9.8
20: 1
x= 9.8 meters in 1 second
Step-by-step explanation:
This can be determined by following writing equal ratios that represent a word problem. Then, the denominator must be divided from the numerator to get the unit rate/ meters per second.
Answer:
h ≈ 39 ft
Step-by-step explanation:
When we draw out a picture, we should see that we have to use cos∅ to solve this:
cos31.66° = x/46
46cos31.66° = x
x = 39.1542
Answer:
9 and -6 multiply to -54 and add to 3
Step-by-step explanation:
when listing the factors of 54, we can find a pair that add to 3
1, 2, 3, 6, 9, 18, 27 and 54
9 and -6 is the pair.
hope this helps! :D
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Answer:
3π square units.
Step-by-step explanation:
We can use the disk method.
Since we are revolving around AB, we have a vertical axis of revolution.
So, our representative rectangle will be horizontal.
R₁ is bounded by y = 9x.
So, x = y/9.
Our radius since our axis is AB will be 1 - x or 1 - y/9.
And we are integrating from y = 0 to y = 9.
By the disk method (for a vertical axis of revolution):
![\displaystyle V=\pi \int_a^b [R(y)]^2\, dy](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cpi%20%5Cint_a%5Eb%20%5BR%28y%29%5D%5E2%5C%2C%20dy)
So:

Simplify:

Integrate:
![\displaystyle V=\pi\Big[y-\frac{1}{9}y^2+\frac{1}{243}y^3\Big|_0^9\Big]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cpi%5CBig%5By-%5Cfrac%7B1%7D%7B9%7Dy%5E2%2B%5Cfrac%7B1%7D%7B243%7Dy%5E3%5CBig%7C_0%5E9%5CBig%5D)
Evaluate (I ignored the 0):
![\displaystyle V=\pi[9-\frac{1}{9}(9)^2+\frac{1}{243}(9^3)]=3\pi](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cpi%5B9-%5Cfrac%7B1%7D%7B9%7D%289%29%5E2%2B%5Cfrac%7B1%7D%7B243%7D%289%5E3%29%5D%3D3%5Cpi)
The volume of the solid is 3π square units.
Note:
You can do this without calculus. Notice that R₁ revolved around AB is simply a right cone with radius 1 and height 9. Then by the volume for a cone formula:

We acquire the exact same answer.
Answer:
Step-by-step explanation:
hello :
h(x) = x² – 5x + 7
h(-2) = (-2)² – 5(-2) + 7 =4+10+7 =21
h(-5) = (-5)² – 5(-5) + 7= 25+25+7 =57
h(-8) = (-8)² – 5(-8) + 7 = 64+40+7=111