Answer:
t is between 0.47 seconds and 4.02 seconds
Step-by-step explanation:
Given
![Inequality: -4.9t^2+22t+0.75>10](https://tex.z-dn.net/?f=Inequality%3A%20-4.9t%5E2%2B22t%2B0.75%3E10)
Required
Determine the values of t
![-4.9t^2+22t+0.75>10](https://tex.z-dn.net/?f=-4.9t%5E2%2B22t%2B0.75%3E10)
Subtract 10 from both sides
![-4.9t^2+22t+0.75 - 10 >10 - 10](https://tex.z-dn.net/?f=-4.9t%5E2%2B22t%2B0.75%20-%2010%20%3E10%20-%2010)
![-4.9t^2+22t-9.25 >0](https://tex.z-dn.net/?f=-4.9t%5E2%2B22t-9.25%20%3E0)
Multiply through y -1
![4.9t^2-22t+9.25](https://tex.z-dn.net/?f=4.9t%5E2-22t%2B9.25%20%3C0)
Solve t using quadratic formula:
![t = \frac{-b \±\sqrt{b^2 - 4ac}}{2a}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B-b%20%5C%C2%B1%5Csqrt%7Bb%5E2%20-%204ac%7D%7D%7B2a%7D)
Where
![a = 4.9](https://tex.z-dn.net/?f=a%20%3D%204.9)
![b = -22](https://tex.z-dn.net/?f=b%20%3D%20-22)
![c = 9.25](https://tex.z-dn.net/?f=c%20%3D%209.25)
So, we have:
![t = \frac{-(-22) \±\sqrt{(-22)^2 - 4*4.9*9.25}}{2 * 4.9}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B-%28-22%29%20%5C%C2%B1%5Csqrt%7B%28-22%29%5E2%20-%204%2A4.9%2A9.25%7D%7D%7B2%20%2A%204.9%7D)
![t = \frac{22 \±\sqrt{484 - 181.3}}{9.8}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B22%20%5C%C2%B1%5Csqrt%7B484%20-%20181.3%7D%7D%7B9.8%7D)
![t = \frac{22 \±\sqrt{302.7}}{9.8}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B22%20%5C%C2%B1%5Csqrt%7B302.7%7D%7D%7B9.8%7D)
![t = \frac{22 \±17.40}{9.8}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B22%20%5C%C2%B117.40%7D%7B9.8%7D)
Split the equation
or ![t = \frac{22 - 17.40}{9.8}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B22%20-%2017.40%7D%7B9.8%7D)
or ![t = \frac{4.6}{9.8}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B4.6%7D%7B9.8%7D)
or ![t = \frac{4.6}{9.8}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B4.6%7D%7B9.8%7D)
or ![t = 0.47](https://tex.z-dn.net/?f=t%20%3D%200.47)
Hence; the range is
![0.47 < t](https://tex.z-dn.net/?f=0.47%20%3C%20t%20%3C4.02)
Answer:
1872 gross should Reggie order for a three month supply.
Step-by-step explanation:
Given:
200 guitar picks each week.
To Find:
How many gross should be ordered for three months period
Solution:
Now the guitar picks corresponds to the order picks by gross as follows;
given that 200 guitar picks corresponds to 144 gross orders
Now 200 are sold for each weeks i.e 7 days
<em>Now for 3 months there are approximately 13 weeks </em>
so Total sell for 3 months=13*200=2600 guitars
Now The ratio of guitar picks to gross orders is ,
144/200
=1/1.39=0.72
So 2600 guitars corresponds to 2600*(1/1.39)
i.e. 2600/1.39
=1872 Gross orders are required to get three month of supply
The volume of a triangular pyramid<span> can be found using the </span>formula<span> V = 1/3AH where A = area of the triangle base, and H = height of the </span>pyramid<span> or the distance from the </span>pyramid's<span> base to the apex.</span>
Answer:
<u>36</u>
Step-by-step explanation:
![7500/75=100](https://tex.z-dn.net/?f=7500%2F75%3D100)
This means that a field of those dimensions would not be the required length of a minimum of 110 feet.