2 * 22 = 44. Hope this helps.
Triangle ABC is a right triangle, meaning we can use the Pythagorean Theorem to find x.
The formula for the Pythagorean Theorem is:
![a = \sqrt{ {b}^{2} + {c}^{2} }](https://tex.z-dn.net/?f=a%20%3D%20%20%5Csqrt%7B%20%7Bb%7D%5E%7B2%7D%20%20%2B%20%20%7Bc%7D%5E%7B2%7D%20%7D%20)
where a is the hypotenuse, and b and c are the legs.
In this problem, we have the vertical leg as 16, the horizontal leg as x, and the hypotenuse as 20. Therefore, we can say that
![a = 20 \\ b = 16 \\ c = x](https://tex.z-dn.net/?f=a%20%3D%2020%20%5C%5C%20b%20%3D%2016%20%5C%5C%20c%20%3D%20x)
Therefore, we can plug into the formula to find x:
![a = \sqrt{ {b}^{2} + {x}^{2} } \\ {a}^{2} = { \sqrt{ {b}^{2} + {x}^{2} } }^{2} \\ {a}^{2} = {b}^{2} + {x}^{2} \\ {a}^{2} - {b}^{2} = {x}^{2}](https://tex.z-dn.net/?f=a%20%3D%20%20%5Csqrt%7B%20%7Bb%7D%5E%7B2%7D%20%20%2B%20%20%7Bx%7D%5E%7B2%7D%20%7D%20%20%5C%5C%20%20%7Ba%7D%5E%7B2%7D%20%20%3D%20%20%7B%20%5Csqrt%7B%20%7Bb%7D%5E%7B2%7D%20%20%2B%20%20%7Bx%7D%5E%7B2%7D%20%7D%20%7D%5E%7B2%7D%20%20%5C%5C%20%20%7Ba%7D%5E%7B2%7D%20%20%3D%20%20%7Bb%7D%5E%7B2%7D%20%20%2B%20%20%7Bx%7D%5E%7B2%7D%20%20%5C%5C%20%20%7Ba%7D%5E%7B2%7D%20%20-%20%20%7Bb%7D%5E%7B2%7D%20%20%3D%20%20%7Bx%7D%5E%7B2%7D)
We first change the variable c to x and square both sides of the equation. Then we subtract b^2 from both sides.
![{x}^{2} = {a}^{2} - {b}^{2} \\ \sqrt{ {x}^{2} } = \sqrt{ {a}^{2} - {b}^{2} } \\ x = \sqrt{ {a}^{2} - {b}^{2} }](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%3D%20%20%7Ba%7D%5E%7B2%7D%20%20-%20%20%7Bb%7D%5E%7B2%7D%20%20%5C%5C%20%20%5Csqrt%7B%20%7Bx%7D%5E%7B2%7D%20%7D%20%20%3D%20%20%5Csqrt%7B%20%7Ba%7D%5E%7B2%7D%20%20-%20%20%7Bb%7D%5E%7B2%7D%20%7D%20%20%5C%5C%20x%20%3D%20%20%5Csqrt%7B%20%7Ba%7D%5E%7B2%7D%20-%20%20%7Bb%7D%5E%7B2%7D%20%20%7D%20)
We square root each side to find the variable answer for x. Then we plug in the numbers:
![x = \sqrt{ {(20)}^{2} - {(16)}^{2} } \\ x = \sqrt{400 - 256} \\ x = \sqrt{144} \\ x = 12](https://tex.z-dn.net/?f=x%20%3D%20%20%5Csqrt%7B%20%7B%2820%29%7D%5E%7B2%7D%20-%20%20%7B%2816%29%7D%5E%7B2%7D%20%20%7D%20%20%5C%5C%20x%20%3D%20%20%5Csqrt%7B400%20-%20256%7D%20%20%5C%5C%20x%20%3D%20%20%5Csqrt%7B144%7D%20%20%5C%5C%20x%20%3D%2012)
We find that x = 12. The answer is A. 12.
Answer:
10 feet wide and 36 feet long
Step-by-step explanation:
5 x 2= 10 wide
4 x 9= 36 long
Answer:
3i square root 3
Step-by-step explanation:
We assume the composite figure is a cone of radius 10 inches and slant height 15 inches set atop a hemisphere of radius 10 inches.
The formula for the volume of a cone makes use of the height of the apex above the base, so we need to use the Pythagorean theorem to find that.
h = √((15 in)² - (10 in)²) = √115 in
The volume of the conical part of the figure is then
V = (1/3)Bh = (1/3)(π×(10 in)²×(√115 in) = (100π√115)/3 in³ ≈ 1122.994 in³
The volume of the hemispherical part of the figure is given by
V = (2/3)π×r³ = (2/3)π×(10 in)³ = 2000π/3 in³ ≈ 2094.395 in³
Then the total volume of the figure is
V = (volume of conical part) + (volume of hemispherical part)
V = (100π√115)/3 in³ + 2000π/3 in³
V = (100π/3)(20 + √115) in³
V ≈ 3217.39 in³