A(-3,5) to B(8,1)
That makes a right triangle 8 - -3 = 11 in the x direction, 5 - 1 = 4 in the y direction.
d² = (8 - -3)² + (1 - 5)² = 11² + (-4)² = 121 + 25 = 146
d = √146 = 12.083045973594572
Answer: 12.1
ANSWER
A. 22 in
EXPLANATION
The volume of a cone is calculated using the formula:
![Volume = \frac{1}{3} \times \pi {r}^{2} h](https://tex.z-dn.net/?f=Volume%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%5Ctimes%20%5Cpi%20%7Br%7D%5E%7B2%7D%20h)
It was given that: the volume is 2,279.64 in³
The height of the cylinder is also given as: h=18 in.
We substitute, the given values into the formula to get:
![2279.64= \frac{1}{3} \times (3.14) \times {r}^{2} \times 18](https://tex.z-dn.net/?f=2279.64%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%5Ctimes%20%283.14%29%20%5Ctimes%20%7Br%7D%5E%7B2%7D%20%20%5Ctimes%2018)
![2279.64= 18.84 {r}^{2}](https://tex.z-dn.net/?f=2279.64%3D%2018.84%20%7Br%7D%5E%7B2%7D%20)
![{r}^{2} = \frac{2279.64}{18.84}](https://tex.z-dn.net/?f=%20%7Br%7D%5E%7B2%7D%20%20%3D%20%20%5Cfrac%7B2279.64%7D%7B18.84%7D%20)
![{r}^{2} = 121](https://tex.z-dn.net/?f=%20%7Br%7D%5E%7B2%7D%20%20%3D%20121)
We take positive square root to get;
![r = \sqrt{121}](https://tex.z-dn.net/?f=r%20%3D%20%20%5Csqrt%7B121%7D%20)
![r = 11in](https://tex.z-dn.net/?f=r%20%3D%2011in)
Therefore the diameter is 2(11) which is equal to 22 inches.
Answer:
No. The new height of the water is less than the height of the glass(6.33 cm<10 cm)
Step-by-step explanation:
-For the water in the glass to overflow, the volume of the inserted solid must be greater than the volume of the empty space or the ensuing height of water >height of glass.
#Volume of the golf ball:
![V=\frac{4}{3}\pi r^3\\\\=\frac{4}{3}\pi \times 4^3\\\\\approx 268.08\ cm^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3%5C%5C%5C%5C%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20%5Ctimes%204%5E3%5C%5C%5C%5C%5Capprox%20268.08%5C%20cm%5E3)
#The volume of the water in the glass:
![V=\pi r^2 h\\\\=\pi \times 4^2\times 10\\\\\approx 50.27\ cm^2](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E2%20h%5C%5C%5C%5C%3D%5Cpi%20%5Ctimes%204%5E2%5Ctimes%2010%5C%5C%5C%5C%5Capprox%2050.27%5C%20cm%5E2)
We then equate the two volumes to the glass' volume to determine the new height of the water:
![V=\pi r^2h\\\\(206.08+50.27)=\pi r^2 h\\\\h=318.35/(\pi \times 4^2)\\\\=6.33\ cm](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E2h%5C%5C%5C%5C%28206.08%2B50.27%29%3D%5Cpi%20r%5E2%20h%5C%5C%5C%5Ch%3D318.35%2F%28%5Cpi%20%5Ctimes%204%5E2%29%5C%5C%5C%5C%3D6.33%5C%20cm)
Hence, the glass will not overflow since the new height of the water is less than the height of the glass(6.33 cm<10cm).
Answer:
A number line going from 27 to 37, open circle at 32, everything to the right is shaded
Step-by-step explanation:
-1/2p < -16
multiply each side by -2 (don't forget to switch inequality symbol)
p > 32