Answer:
Area of the shaded region = 23.33 in²
Step-by-step explanation:
Area of a sector = ![\frac{\theta}{360}(\pi r^{2})](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctheta%7D%7B360%7D%28%5Cpi%20r%5E%7B2%7D%29)
Where θ = Central angle subtended by an arc
r = radius of the circle
Area of the sector BCD = ![\frac{60}{360}(\pi) (10^{2})](https://tex.z-dn.net/?f=%5Cfrac%7B60%7D%7B360%7D%28%5Cpi%29%20%2810%5E%7B2%7D%29)
= 52.36 in²
Area of equilateral triangle BCD = ![\frac{\sqrt{3} }{4}(\text{Side})^2](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B4%7D%28%5Ctext%7BSide%7D%29%5E2)
= ![\frac{\sqrt{3} }{4}(10)^2](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B4%7D%2810%29%5E2)
=
in²
= 43.30 in²
Area of the shaded portion in ΔBCD = 52.36 - 43.3
= 9.06 in²
Area of sector CAD = ![\frac{90}{360}(\pi)(\sqrt{50})^2](https://tex.z-dn.net/?f=%5Cfrac%7B90%7D%7B360%7D%28%5Cpi%29%28%5Csqrt%7B50%7D%29%5E2)
= 39.27 in²
Area of right triangle CAD = ![\frac{1}{2}(\text{Base})(\text{Height})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28%5Ctext%7BBase%7D%29%28%5Ctext%7BHeight%7D%29)
= ![\frac{1}{2}(\text{AC})(\text{AD})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28%5Ctext%7BAC%7D%29%28%5Ctext%7BAD%7D%29)
=
= 25 in²
Area of the shaded part in the ΔACD = 39.27 - 25
= 14.27 in²
Area of the shaded part of the figure = 9.06 + 14.27
= 23.33 in²
The answer is answer choice 3
Answer:
if you are lookng for C it is 17
Step-by-step explanation:
Answer:
![-2x - h - 3](https://tex.z-dn.net/?f=-2x%20-%20h%20-%203)
Step-by-step explanation:
Step 1: Define
Difference Quotient: ![\frac{f(x+h)-f(x)}{h}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%2Bh%29-f%28x%29%7D%7Bh%7D)
f(x) = -x² - 3x + 1
f(x + h) means that x = (x + h)
f(x) is just the normal function
Step 2: Find difference quotient
- <u>Substitute:</u>
![\frac{[-(x+h)^2-3(x+h)+1]-(-x^2-3x+1)}{h}](https://tex.z-dn.net/?f=%5Cfrac%7B%5B-%28x%2Bh%29%5E2-3%28x%2Bh%29%2B1%5D-%28-x%5E2-3x%2B1%29%7D%7Bh%7D)
- <u>Expand and Distribute:</u>
![\frac{[-(x^2+2hx+h^2)-3x-3h+1]+x^2+3x-1}{h}](https://tex.z-dn.net/?f=%5Cfrac%7B%5B-%28x%5E2%2B2hx%2Bh%5E2%29-3x-3h%2B1%5D%2Bx%5E2%2B3x-1%7D%7Bh%7D)
- <u>Distribute:</u>
![\frac{-x^2-2hx-h^2-3x-3h+1+x^2+3x-1}{h}](https://tex.z-dn.net/?f=%5Cfrac%7B-x%5E2-2hx-h%5E2-3x-3h%2B1%2Bx%5E2%2B3x-1%7D%7Bh%7D)
- <u>Combine like terms:</u>
![\frac{-2hx-h^2-3h}{h}](https://tex.z-dn.net/?f=%5Cfrac%7B-2hx-h%5E2-3h%7D%7Bh%7D)
- <u>Factor out </u><em><u>h</u></em><u>:</u>
![\frac{h(-2x-h-3)}{h}](https://tex.z-dn.net/?f=%5Cfrac%7Bh%28-2x-h-3%29%7D%7Bh%7D)
- <u>Simplify:</u>
![-2x - h - 3](https://tex.z-dn.net/?f=-2x%20-%20h%20-%203)
The answer to the question is y=-4x+23