Volume of the cone = 1/3 pi r^2 h = 1005.31 cm^3
Volume of the sphere = 4/3 pi r^3 = 463.25 cm^3
Volume of remaining portion of the cone = 1005.31 - 463.25
= 542.1 cm^3 to nearest tenth
The solutions are
.
Solution:
Given equation:
![-2 x^{2}+y=-5](https://tex.z-dn.net/?f=-2%20x%5E%7B2%7D%2By%3D-5)
Add
on both sides.
![-2 x^{2}+y+2 x^{2}=-5+2 x^{2}](https://tex.z-dn.net/?f=-2%20x%5E%7B2%7D%2By%2B2%20x%5E%7B2%7D%3D-5%2B2%20x%5E%7B2%7D)
-------- (1)
(given) -------- (2)
Equate (1) and (2).
![-5+2 x^{2}=-3 x^{2}+5](https://tex.z-dn.net/?f=-5%2B2%20x%5E%7B2%7D%3D-3%20x%5E%7B2%7D%2B5)
Add
on both sides.
![-5+2 x^{2}+3 x^{2}=-3 x^{2}+5 +3 x^{2}](https://tex.z-dn.net/?f=-5%2B2%20x%5E%7B2%7D%2B3%20x%5E%7B2%7D%3D-3%20x%5E%7B2%7D%2B5%20%2B3%20x%5E%7B2%7D)
![-5+5x^{2}=5](https://tex.z-dn.net/?f=-5%2B5x%5E%7B2%7D%3D5)
Add 5 on both sides.
![-5+5x^{2}+5=5+5](https://tex.z-dn.net/?f=-5%2B5x%5E%7B2%7D%2B5%3D5%2B5)
![5x^{2}=10](https://tex.z-dn.net/?f=5x%5E%7B2%7D%3D10)
Divide by 5 on both sides, we get
![x^{2}=2](https://tex.z-dn.net/?f=x%5E%7B2%7D%3D2)
Taking square root on both sides, we get
![x=\sqrt{2}, x=-\sqrt{2}](https://tex.z-dn.net/?f=x%3D%5Csqrt%7B2%7D%2C%20x%3D-%5Csqrt%7B2%7D)
Substitute
in (1).
![y=-5+2(\sqrt{2})^2](https://tex.z-dn.net/?f=y%3D-5%2B2%28%5Csqrt%7B2%7D%29%5E2)
![y=-5+4](https://tex.z-dn.net/?f=y%3D-5%2B4)
![y=-1](https://tex.z-dn.net/?f=y%3D-1)
Substitute
in (1).
![y=-5+2(-\sqrt{2})^2](https://tex.z-dn.net/?f=y%3D-5%2B2%28-%5Csqrt%7B2%7D%29%5E2)
![y=-5+4](https://tex.z-dn.net/?f=y%3D-5%2B4)
![y=-1](https://tex.z-dn.net/?f=y%3D-1)
Therefore the solutions are
.
Option C is the correct answer.
Answer:
1. 7 to the square root of 3
2. negative square root of 3
Step-by-step explanation:
1. simplify 0.7 x 10 square of 3
2. Calculate: you get 7 to the square root of 3
1. simplify -0.125 x 8 to the square root of 3
2. Calcaute: you get negative square root of 3
Answer:
Math:The Union of A and B is the set of all those elements which belong either to A or to B or both A and B. use the notation A U B (which is read as 'A union B') to denote the union of set A and set B.
Algebra: n(A U B) = n(A) + n(B) - n(A n B) so 20 = n(A) + 10 - 5 OR n(A) = 15.
I found these as a match for what they stand for, not sure if any of them are exactly what you need, but i hope this helps ^_^
Hi there!
![2x + 6 {x}^{2} - 1 = 3 {x}^{2}](https://tex.z-dn.net/?f=2x%20%2B%206%20%7Bx%7D%5E%7B2%7D%20%20-%201%20%3D%203%20%7Bx%7D%5E%7B2%7D%20)
First subtract 3x^2 from both sides.
![2x + 3 {x}^{2} - 1 = 0](https://tex.z-dn.net/?f=2x%20%2B%203%20%7Bx%7D%5E%7B2%7D%20%20-%201%20%3D%200)
Now rearrange the equation.
![3 {x}^{2} + 2x - 1 = 0](https://tex.z-dn.net/?f=3%20%7Bx%7D%5E%7B2%7D%20%20%2B%202x%20-%201%20%3D%200)
Finally we can see our answer.
![a = 3](https://tex.z-dn.net/?f=a%20%3D%203)
![b = 2](https://tex.z-dn.net/?f=b%20%3D%202)