Answer:
6. B) 115
7. B) 180 - (180 - 90 + 30) = x
Step-by-step explanation:
Answer:
B. 30 ft
Step-by-step explanation:
The ladder is 32 ft long
The angle of elevation of the ladder is 70°
The height (h) of the top of the ladder to the ground is what we are to find.
= sin 70°
h = 32 × sin 70° = 30.07016387 or 30 ft (rounded off to nearest feet)
Answer:
36 is the answer of this question
Answer:
![\boxed{\dfrac{f(a+h)-f(a)}{h}=-3a^2-3ah-h^2}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cdfrac%7Bf%28a%2Bh%29-f%28a%29%7D%7Bh%7D%3D-3a%5E2-3ah-h%5E2%7D)
Step-by-step explanation:
![f(x)=-x^3+2\\\\\dfrac{f(a+h)-f(a)}{h}\\\\f(a+h)\to\text{substitute x = a + h}\\f(a)\to\text{substitute x = a}\\\\\dfrac{f(a+h)-f(a)}{h}=\dfrac{-(a+h)^3+2-(-a^3+2)}{h}\\\\\text{use}\ (x+y)^3=x^3+3x^2y+3xy^2+y^3\\\\=\dfrac{-(a^3+3a^2h+3ah^2+h^3)+2-(-a^3)-2}{h}\\\\=\dfrac{-a^3-3a^2h-3ah^2-h^3+2+a^3-2}{h}\\\\\text{combine like terms}](https://tex.z-dn.net/?f=f%28x%29%3D-x%5E3%2B2%5C%5C%5C%5C%5Cdfrac%7Bf%28a%2Bh%29-f%28a%29%7D%7Bh%7D%5C%5C%5C%5Cf%28a%2Bh%29%5Cto%5Ctext%7Bsubstitute%20x%20%3D%20a%20%2B%20h%7D%5C%5Cf%28a%29%5Cto%5Ctext%7Bsubstitute%20x%20%3D%20a%7D%5C%5C%5C%5C%5Cdfrac%7Bf%28a%2Bh%29-f%28a%29%7D%7Bh%7D%3D%5Cdfrac%7B-%28a%2Bh%29%5E3%2B2-%28-a%5E3%2B2%29%7D%7Bh%7D%5C%5C%5C%5C%5Ctext%7Buse%7D%5C%20%28x%2By%29%5E3%3Dx%5E3%2B3x%5E2y%2B3xy%5E2%2By%5E3%5C%5C%5C%5C%3D%5Cdfrac%7B-%28a%5E3%2B3a%5E2h%2B3ah%5E2%2Bh%5E3%29%2B2-%28-a%5E3%29-2%7D%7Bh%7D%5C%5C%5C%5C%3D%5Cdfrac%7B-a%5E3-3a%5E2h-3ah%5E2-h%5E3%2B2%2Ba%5E3-2%7D%7Bh%7D%5C%5C%5C%5C%5Ctext%7Bcombine%20like%20terms%7D)
![=\dfrac{(-a^3+a^3)-3a^2h-3ah^2-h^3+(2-2)}{h}\\\\=\dfrac{-3a^2h-3ah^2-h^3}{h}\\\\=\dfrac{h(-3a^2-3ah-h^2)}{h}\\\\=-3a^2-3ah-h^2](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B%28-a%5E3%2Ba%5E3%29-3a%5E2h-3ah%5E2-h%5E3%2B%282-2%29%7D%7Bh%7D%5C%5C%5C%5C%3D%5Cdfrac%7B-3a%5E2h-3ah%5E2-h%5E3%7D%7Bh%7D%5C%5C%5C%5C%3D%5Cdfrac%7Bh%28-3a%5E2-3ah-h%5E2%29%7D%7Bh%7D%5C%5C%5C%5C%3D-3a%5E2-3ah-h%5E2)
8 is x-intercept and 9 is y-intercept