height of ladder = 12 feet
let x be the distance from the wall to the base of the ladder then
height = 2x + 2
Using Pythagoras' identity
(2x + 2)² + x² = 13² ( expand bracket and simplify left side )
4x² + 8x + 4 + x² = 169 ( rearrange into standard form )
5x² + 8x - 165 = 0 ← in standard form
consider the factors of the product 5 × - 165 = - 825
which sum to the coefficient of the x- term + 8
These are + 33 and - 25
split the middle term using these factors
5x² - 25x + 33x - 165 = 0 ( factor by grouping )
5x(x - 5) + 33(x - 5) = 0 ( take out the common factor (x - 5) )
(x - 5)(5x + 33) = 0
equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
5x + 33 = 0 ⇒ x = - ![\frac{33}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B33%7D%7B5%7D)
but x > 0 ⇒ x = 5
Hence height of ladder = (2 × 5 ) + 2 = 12 feet
M is less than or equal to 22!
hope this helps
Answer:
Step-by-step explanation:
This is what I got
The volume of the cylinder is ![1539 cm^3](https://tex.z-dn.net/?f=1539%20cm%5E3)
Step-by-step explanation:
The volume of a cylinder is given by the equation
![V=\pi r^2 h](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E2%20h)
where
is the area of the base, with r being the radius
h is the height
For the cylinder in this problem we know:
h = 10 cm (height)
c = 44 cm (circumference of the base)
The circumference is given by
![c=2\pi r](https://tex.z-dn.net/?f=c%3D2%5Cpi%20r)
So the radius is
![r=\frac{c}{2\pi}=\frac{44}{2\pi}=7 cm](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bc%7D%7B2%5Cpi%7D%3D%5Cfrac%7B44%7D%7B2%5Cpi%7D%3D7%20cm)
Therefore, the volume of the cylinder is:
![V=\pi (7)^2 (10)=1539 cm^3](https://tex.z-dn.net/?f=V%3D%5Cpi%20%287%29%5E2%20%2810%29%3D1539%20cm%5E3)
Learn more about volume of a solid:
brainly.com/question/12497249
#LearnwithBrainly
Answer:
y=5
Step-by-step explanation:
y = 0,1 × 10 × 5 = 5
I hope I answered correctly