Answer:
t = 13.2 s
Step-by-step explanation:
Given that,
An athlete ran the 100 meter sprint in 13.245 seconds. We need to round off the time to the nearest tenth.
Here, t = 13.245 s
In order to round off to the nearest tenth, thousandths place and hundredth place gets eliminated.
So, t = 13.2 s
So, time is 13.2 seconds.
Answer:
A function to represent the height of the ball in terms of its distance from the player's hands is ![y=\frac{-1}{54}(x-18)^2+12](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-1%7D%7B54%7D%28x-18%29%5E2%2B12)
Step-by-step explanation:
General equation of parabola in vertex form ![y= a(x-h)^2+k](https://tex.z-dn.net/?f=y%3D%20a%28x-h%29%5E2%2Bk)
y represents the height
x represents horizontal distance
(h,k) is the coordinates of vertex of parabola
We are given that The ball travels to a maximum height of 12 feet when it is a horizontal distance of 18 feet from the player's hands.
So,(h,k)=(18,12)
Substitute the value in equation
---1
The ball leaves the player's hands at a height of 6 feet above the ground and the distance at this time is 0
So, y = 6
So,![6=a(0-18)^2+12](https://tex.z-dn.net/?f=6%3Da%280-18%29%5E2%2B12)
6=324a+12
-6=324a
![\frac{-6}{324}=a](https://tex.z-dn.net/?f=%5Cfrac%7B-6%7D%7B324%7D%3Da)
![\frac{-1}{54}=a](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B54%7D%3Da)
Substitute the value in 1
So,![y=\frac{-1}{54}(x-18)^2+12](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-1%7D%7B54%7D%28x-18%29%5E2%2B12)
Hence a function to represent the height of the ball in terms of its distance from the player's hands is ![y=\frac{-1}{54}(x-18)^2+12](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-1%7D%7B54%7D%28x-18%29%5E2%2B12)
Answer:
FG=30
Step-by-step explanation:
Since we know that Point G is on the Segment FH, it doesn't really matter where G is, but we can know for certain that:
![FH=FG+GH](https://tex.z-dn.net/?f=FH%3DFG%2BGH)
We are given that FH is 4x, GH is x, and FG is 2x+10. Substitute:
![4x=(2x+10)+x](https://tex.z-dn.net/?f=4x%3D%282x%2B10%29%2Bx)
Solve for x. On the right, combine like terms:
![4x=3x+10](https://tex.z-dn.net/?f=4x%3D3x%2B10)
Subtract 3x from both sides:
![x=10](https://tex.z-dn.net/?f=x%3D10)
So, the value of x is 10.
To find the value of FG, substitute 10 into its x:
![FG=2x+10\\FG=2(10)+10](https://tex.z-dn.net/?f=FG%3D2x%2B10%5C%5CFG%3D2%2810%29%2B10)
Multiply:
![FG=20+10](https://tex.z-dn.net/?f=FG%3D20%2B10)
Add:
![FG=30](https://tex.z-dn.net/?f=FG%3D30)
And we're done!
Answer:
![A_s=179 \ yd](https://tex.z-dn.net/?f=A_s%3D179%20%20%5C%20yd)
Step-by-step explanation:
Area of Circle can be calculated using following formula
![A=\pi r^{2}](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E%7B2%7D)
Where r is radius of circle
<u>Area of outer circle (r=11 yd)</u>
![A_1=\pi (11)^{2}\\A_1=379.94 \ yd](https://tex.z-dn.net/?f=A_1%3D%5Cpi%20%2811%29%5E%7B2%7D%5C%5CA_1%3D379.94%20%5C%20yd)
<u>Area of inner circle (r=8 yd)</u>
![A_2=\pi (8)^{2}\\A_2=200.96 \ yd](https://tex.z-dn.net/?f=A_2%3D%5Cpi%20%288%29%5E%7B2%7D%5C%5CA_2%3D200.96%20%5C%20yd)
Area of shaded region
![A_s=A_1-A_2](https://tex.z-dn.net/?f=A_s%3DA_1-A_2)
![A_s=379.94-200.96\\A_s=179 \ yd](https://tex.z-dn.net/?f=A_s%3D379.94-200.96%5C%5CA_s%3D179%20%20%5C%20yd)
Answer:
8 hours worked, 64 dollars
56 dollars, 7 hours worked
themepark:
5 hours worked, 45 dollars
6 hours worked, 54 dollars
8 hours worked, 72 dollars
working at the themepark earns 5 extra dollars when they work for 5 hours.