Answer:
a = 16.733
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2
a^2 + 9^2 = 19^2
a^2 = 19^2 - 9^2
a^2 = 361-81
a^2 =280
Taking the square root of each side
sqrt(a^2) = sqrt(280)
a = 16.73320053
Rounding to the nearest thousandth
a = 16.733
Answer:
![x^2 + ( y + 4)^2 = 52](https://tex.z-dn.net/?f=x%5E2%20%2B%20%28%20y%20%2B%204%29%5E2%20%3D%2052)
Step-by-step explanation:
Equation of circle with center (a , b) and radius, r is :
![(x -a)^2 + ( y -b)^2 = r^2](https://tex.z-dn.net/?f=%28x%20-a%29%5E2%20%2B%20%28%20y%20-b%29%5E2%20%3D%20r%5E2)
Given : a = 0 , b = - 4
Step 1 : Find the radius.
Given ( 6 , 0 ) lies on the circle. Therefore the distance between the center (0 , - 4) of the circle and ( 6 , 0 ) gives the radius of the circle.
![r = \sqrt{( 0 - 6)^2 + ( -4 - 0)^2} \\\\](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B%28%200%20-%206%29%5E2%20%2B%20%28%20-4%20-%200%29%5E2%7D%20%5C%5C%5C%5C)
![= \sqrt{ 36 + 16 } \\\\= \sqrt{52}](https://tex.z-dn.net/?f=%3D%20%5Csqrt%7B%2036%20%2B%2016%20%7D%20%5C%5C%5C%5C%3D%20%5Csqrt%7B52%7D)
Step 2 : Equation of circle.
![(x - 0)^2 + (y -( - 4))^2 = (\sqrt{52})^2\\\\x^2 + ( y+ 4)^2 = 52](https://tex.z-dn.net/?f=%28x%20-%200%29%5E2%20%2B%20%28y%20-%28%20-%204%29%29%5E2%20%3D%20%28%5Csqrt%7B52%7D%29%5E2%5C%5C%5C%5Cx%5E2%20%2B%20%28%20y%2B%204%29%5E2%20%3D%2052)
Answer:
Option C.
Step-by-step explanation:
Given information: In triangle ABC, ST║AC, SB=10 ft, BT=9 ft and CT=2.7 ft.
Triangle proportionality theorem: If a line segment parallel to a side of a triangle then the line segments divides the remaining sides proportionally.
Using triangle proportionality theorem we get
![\dfrac{SA}{SB}=\dfrac{CT}{BT}](https://tex.z-dn.net/?f=%5Cdfrac%7BSA%7D%7BSB%7D%3D%5Cdfrac%7BCT%7D%7BBT%7D)
![\dfrac{SA}{10}=\dfrac{2.7}{9}](https://tex.z-dn.net/?f=%5Cdfrac%7BSA%7D%7B10%7D%3D%5Cdfrac%7B2.7%7D%7B9%7D)
On cross multiplication we get
![9\times SA=2.7\times 10](https://tex.z-dn.net/?f=9%5Ctimes%20SA%3D2.7%5Ctimes%2010)
![9SA=27](https://tex.z-dn.net/?f=9SA%3D27)
Divide both sides by 9.
![SA=3](https://tex.z-dn.net/?f=SA%3D3)
The length of SA is 3ft.
Therefore, the correct option is C.
50+20=70
Have a great day:)
Answer:
144pi
Step-by-step explanation:
The formula for the volume of a cylinder is base*height
The base of a cylinder is a circle, so it's pi*r^2
r = 6, so pi*r^2 is 36pi
height is 4 so 36pi*4 is 144pi