Answer:
A=a+b
2h
Step-by-step explanation:
ANSWER
The slant height is 40cm.
EXPLANATION
The lateral area of a cone is given by:
![Area= \pi \: r \: l](https://tex.z-dn.net/?f=Area%3D%20%5Cpi%20%5C%3A%20r%20%5C%3A%20l)
where r=10cm is the radius of the circle and l is the slant height.
It was also given that, the lateral area is 400π cm²
We substitute the values to get,
![400\pi = \pi \times \: 10 \times \: l](https://tex.z-dn.net/?f=400%5Cpi%20%3D%20%5Cpi%20%20%5Ctimes%20%5C%3A%2010%20%5Ctimes%20%20%5C%3A%20l)
We now divide both sides by 10π.
This implies that,
![\frac{400 \pi}{10\pi} = l](https://tex.z-dn.net/?f=%20%5Cfrac%7B400%20%5Cpi%7D%7B10%5Cpi%7D%20%20%3D%20l)
![40 = l](https://tex.z-dn.net/?f=40%20%3D%20l)
Hence the slant height is 40cm.
The point P(–4, 4) that is
of the way from A to B on the directed line segment AB.
Solution:
The points of the line segment are A(–8, –2) and B(6, 19).
P is the point that bisect the line segment in
.
So, m = 2 and n = 5.
![x_1=-8, y_1=-2, x_2=6, y_2=19](https://tex.z-dn.net/?f=x_1%3D-8%2C%20y_1%3D-2%2C%20x_2%3D6%2C%20y_2%3D19)
By section formula:
![$P(x, y)=\left(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n}\right)](https://tex.z-dn.net/?f=%24P%28x%2C%20y%29%3D%5Cleft%28%5Cfrac%7Bmx_2%2Bnx_1%7D%7Bm%2Bn%7D%2C%20%5Cfrac%7Bmy_2%2Bny_1%7D%7Bm%2Bn%7D%5Cright%29)
![$P(x, y)=\left(\frac{2\times 6+5\times (-8)}{2+5}, \frac{2\times 19+5\times (-2)}{2+5}\right)](https://tex.z-dn.net/?f=%24P%28x%2C%20y%29%3D%5Cleft%28%5Cfrac%7B2%5Ctimes%206%2B5%5Ctimes%20%28-8%29%7D%7B2%2B5%7D%2C%20%5Cfrac%7B2%5Ctimes%2019%2B5%5Ctimes%20%28-2%29%7D%7B2%2B5%7D%5Cright%29)
![$P(x, y)=\left(\frac{12-40}{7}, \frac{38-10}{7}\right)](https://tex.z-dn.net/?f=%24P%28x%2C%20y%29%3D%5Cleft%28%5Cfrac%7B12-40%7D%7B7%7D%2C%20%5Cfrac%7B38-10%7D%7B7%7D%5Cright%29)
![$P(x, y)=\left(\frac{-28}{7}, \frac{28}{7}\right)](https://tex.z-dn.net/?f=%24P%28x%2C%20y%29%3D%5Cleft%28%5Cfrac%7B-28%7D%7B7%7D%2C%20%5Cfrac%7B28%7D%7B7%7D%5Cright%29)
P(x, y) = (–4, 4)
Hence the point P(–4, 4) that is
of the way from A to B on the directed line segment AB.
Answer:
see explanation
Step-by-step explanation:
To find the roots factor the left side
x³ + 7x² + 12x = 0 ← factor out x from each term
x(x² + 7x + 12) = 0
x(x + 3)(x + 4) = 0
Equate each factor to zero and solve for x
x = 0
x + 3 = 0 ⇒ x = - 3
x + 4 = 0 ⇒ x = - 4
Roots are x = - 4, x = - 3, x = 0