Answer:
For a sphere, the height is equal to the diameter, or two times the radius.
and because both objects have the same base area, then we can take the radius of the sphere equal to R and the radius of the base of the cylinder also equal to R.
The volume of the cylinder is:
Vc = pi*r^2*h
and here we have r = R and h = 2R
V = pi*(R^3)*2
the volume of a sphere of radius R is:
Vs = (4/3)*pi*R^3
The quotient between them is:
Vc/Vs = 2/(4/3) = 6/4 = 3/2.
This means that the volume of the cylinder is 3/2 times the volume of the sphere, always, for any value of R.
Answer :
The value of q for, the given quadratic equation is 40
Step-by-step explanation :
Given quadratic equation as :
x² - 14 x + q = 0
And , Difference between the roots of equation is 6
Let A , B be the roots of the equation
So, A - B = 6
The roots of the quadratic equation ax² + bx + c = 0 as can be find as :
x = ![\frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E%7B2%7D-4%5Ctimes%20a%5Ctimes%20c%7D%7D%7B2%5Ctimes%20a%7D)
x = ![\frac{14\pm \sqrt{(-14)^{2}-4\times 1\times q}}{2\times 1}](https://tex.z-dn.net/?f=%5Cfrac%7B14%5Cpm%20%5Csqrt%7B%28-14%29%5E%7B2%7D-4%5Ctimes%201%5Ctimes%20q%7D%7D%7B2%5Ctimes%201%7D)
or, x = ![\frac{-14\pm \sqrt{196-4 q}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B-14%5Cpm%20%5Csqrt%7B196-4%20q%7D%7D%7B2%7D)
Or, x = ![\frac{-14\pm \sqrt{196-4 q}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B-14%5Cpm%20%5Csqrt%7B196-4%20q%7D%7D%7B2%7D)
So , The roots are
A = ![-7 + \frac{\sqrt{196-4q}}{2}](https://tex.z-dn.net/?f=-7%20%2B%20%5Cfrac%7B%5Csqrt%7B196-4q%7D%7D%7B2%7D)
And B = ![-7 - \frac{\sqrt{196-4q}}{2}](https://tex.z-dn.net/?f=-7%20-%20%5Cfrac%7B%5Csqrt%7B196-4q%7D%7D%7B2%7D)
∵ The difference between the roots is 6
So, A - B = 6
Or, (
) - (
) = 6
Or, ( - 7 + 7 ) + 2 (
= 6
Or, 0 + 2 (
= 6
∴ 196 - 4 q = 36
or, 4 q = 196 - 36
or 4 q = 160
∴ q =
I.e q = 40
S0, The value of q = 40
Hence The value of q for, the given quadratic equation is 40 . Answer
Step-by-step explanation:
solution:
here,
x/2+4
= 6/2+4 ( x = 6 )
= 3+4
= 7
X is 19.96588 (25sin(53)) and Y is 15.04537 (25sin(37))