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Answer:</h2>
The graph is shown in the attached image
Answer ran 2 3/4 miles in 1/3 of an hour
2 3/4 miles =11/4 miles in 1/3 of hour
11/4 miles divided by 1/3 hr
11/4 ÷ 1/3
11/4 * 3/1 =33/4 =8 1/4 miles in 1 hr
Answer:
Area of shaded region = 134.13 square feet
Step-by-step explanation:
Area of the shaded region = Area of square - Area of circle
![= ( 25 \times 25) - ( \pi 12.5^2)\\= 625 - 490.87\\= 134.13 ft^2](https://tex.z-dn.net/?f=%3D%20%28%2025%20%5Ctimes%2025%29%20-%20%28%20%5Cpi%2012.5%5E2%29%5C%5C%3D%20625%20-%20490.87%5C%5C%3D%20134.13%20ft%5E2)
So we just need to plug in our values and solve
![v = 20 \sqrt{273 + t}](https://tex.z-dn.net/?f=v%20%3D%2020%20%5Csqrt%7B273%20%2B%20t%7D%20)
we are given v is 369 so we have
![369 = 20 \sqrt{273 + x}](https://tex.z-dn.net/?f=369%20%3D%2020%20%5Csqrt%7B273%20%2B%20x%7D%20)
now we solve for x.
divide both sides by 20
square both sides
subtract 273 from both sides
![369 = 20 \sqrt{273 + x} \\ 18.45 = \sqrt{273 + x} \\ 340.40 = 273 + x \\ x = 67.4](https://tex.z-dn.net/?f=369%20%3D%2020%20%5Csqrt%7B273%20%2B%20x%7D%20%20%5C%5C%2018.45%20%3D%20%20%5Csqrt%7B273%20%2B%20x%7D%20%20%5C%5C%20340.40%20%3D%20273%20%2B%20x%20%5C%5C%20x%20%3D%2067.4)
so a temp of about 67 degrees C
Answer:
sinΘ = ![\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D)
Step-by-step explanation:
using the identity
sin²x + cos²x = 1 ( subtract cos²x from both sides )
sin²x = 1 - cos²x ( take square root of both sides )
sinx = ± ![\sqrt{1-cos^2x}](https://tex.z-dn.net/?f=%5Csqrt%7B1-cos%5E2x%7D)
given
cosΘ = -
, then
sinΘ = ± ![\sqrt{1-(-\frac{\sqrt{5} }{3})^2 }](https://tex.z-dn.net/?f=%5Csqrt%7B1-%28-%5Cfrac%7B%5Csqrt%7B5%7D%20%7D%7B3%7D%29%5E2%20%7D)
= ± ![\sqrt{1-\frac{5}{9} }](https://tex.z-dn.net/?f=%5Csqrt%7B1-%5Cfrac%7B5%7D%7B9%7D%20%7D)
= ± ![\sqrt{\frac{4}{9} }](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B4%7D%7B9%7D%20%7D)
= ± ![\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D)
since Θ is in quadrant II where sinΘ > 0 , then
sinΘ = ![\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D)