Tenth of a second refers to one decimal place. So Ashley swam a 32.8 because the four is rounded down.
Answer:
π/2, 2π/3, 3π/2, 4π/3.
Step-by-step explanation:
8cos^2x+4cosx=0
4cosx(2cosx + 1) = 0
so cosx = 0, -1/2.
Therfore
When cos x = 0:
x = π/2, 3π/2
When cos x = -1/2:
x = 2π/3, 4π/3.
Answer:
2,400
Step-by-step explanation:
2,389 rounded to the nearest hundred is 2,400
We know that the volume of a sphere of radius r is given by
![V=\frac{4}{3}\pi r^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3)
Now, we have been given the initial volume was 4,188.79 cubic centimeters. Let us find the radius at this time.
Substituting the value of volume in the above equation, we get
![4,188.79=\frac{4}{3}\pi r^3\\ \\ 4\pi r^3=4,188.79 \times 3\\ \\ r^3=\frac{4188.79 \times 3}{4\pi}\\ \\ r^3=1000\\ \\ r=10](https://tex.z-dn.net/?f=4%2C188.79%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3%5C%5C%0A%5C%5C%0A4%5Cpi%20r%5E3%3D4%2C188.79%20%5Ctimes%203%5C%5C%0A%5C%5C%0Ar%5E3%3D%5Cfrac%7B4188.79%20%5Ctimes%203%7D%7B4%5Cpi%7D%5C%5C%0A%5C%5C%0Ar%5E3%3D1000%5C%5C%0A%5C%5C%0Ar%3D10)
Now, the final volume is given by 14,137.167 cubic centimeters. Thus, we have
![14137.167 =\frac{4}{3}\pi r^3\\ \\ 4\pi r^3=14137.167 \times 3\\ \\ r^3=\frac{14137.167\times 3}{4\pi}\\ \\ r^3=3375\\ \\ r=15](https://tex.z-dn.net/?f=14137.167%20%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3%5C%5C%0A%5C%5C%0A4%5Cpi%20r%5E3%3D14137.167%20%20%5Ctimes%203%5C%5C%0A%5C%5C%0Ar%5E3%3D%5Cfrac%7B14137.167%5Ctimes%203%7D%7B4%5Cpi%7D%5C%5C%0A%5C%5C%0Ar%5E3%3D3375%5C%5C%0A%5C%5C%0Ar%3D15)
Now, let us find the surface areas for these two radii.
For ![r=10](https://tex.z-dn.net/?f=r%3D10)
Surface area is given by
![S=4\pi r^2\\ \\ S=4\times 3.14 \times (10)^2\\ \\ S=1256 \text{ square centimeters}](https://tex.z-dn.net/?f=S%3D4%5Cpi%20r%5E2%5C%5C%0A%5C%5C%0AS%3D4%5Ctimes%203.14%20%5Ctimes%20%2810%29%5E2%5C%5C%0A%5C%5C%0AS%3D1256%20%5Ctext%7B%20square%20centimeters%7D)
Similarly, for
![r=15\\ \\ S=4\times 3.14\times (15)^2\\ \\ S=2826 \text{ square centimeters}](https://tex.z-dn.net/?f=r%3D15%5C%5C%0A%5C%5C%0AS%3D4%5Ctimes%203.14%5Ctimes%20%2815%29%5E2%5C%5C%0A%5C%5C%0AS%3D2826%20%5Ctext%7B%20square%20centimeters%7D)
Therefore, the increase in the surface area is given by
![\Delta S= 2826-1256= 1570 \text{ square centimeters}](https://tex.z-dn.net/?f=%5CDelta%20S%3D%202826-1256%3D%201570%20%5Ctext%7B%20square%20centimeters%7D)
Hence, the average rate at which the surface area is changing is given by
![\frac{1570}{12}=130.8](https://tex.z-dn.net/?f=%5Cfrac%7B1570%7D%7B12%7D%3D130.8)
Therefore, the average rate at which the surface area is changing is given by 130.8 square centimeters per second.