The next year one day tomorrow
Option 3! x is one and y is 6
Answer:
You're looking for 14x + 2.
Answer:
Center of sphere = (0, 1, 2)
Radius of sphere = ![\dfrac{5}{\sqrt3}\text{ units}](https://tex.z-dn.net/?f=%5Cdfrac%7B5%7D%7B%5Csqrt3%7D%5Ctext%7B%20units%7D)
Step-by-step explanation:
We are given the following in the question:
Equation of sphere:
![3x^2+3y^2+3z^2=10+6y+12z](https://tex.z-dn.net/?f=3x%5E2%2B3y%5E2%2B3z%5E2%3D10%2B6y%2B12z)
Formula:
The equation of sphere is of the form
![(x-a)^2 + (y-b)^2 + (z-c)^2 = r^2\\\text{where (a,b,c) is the centre of sphere and r is the radius of sphere.}](https://tex.z-dn.net/?f=%28x-a%29%5E2%20%2B%20%28y-b%29%5E2%20%2B%20%28z-c%29%5E2%20%3D%20r%5E2%5C%5C%5Ctext%7Bwhere%20%28a%2Cb%2Cc%29%20is%20the%20centre%20of%20sphere%20and%20r%20is%20the%20radius%20of%20sphere.%7D)
Simplifying the given equation we get,
![3x^2+3y^2+3z^2=10+6y+12z\\\text{Dividing by 3}\\x^2 + y^2 + z^2 = \dfrac{10}{3} + 2y + 4z\\\\x^2 + y^2 -2y + z^2-4z = \dfrac{10}{3}\\\\\text{Adding 1 and 4 on both sides, we get,}\\\\x^2 + y^2 -2y +1 + z^2-4z + 4 = \dfrac{10}{3} + 1+ 4\\\\(x-0)^2 + (y-1)^2 + (z-2)^2 = \dfrac{25}{3}\\\\\text{Comparing with the equation of sphere}\\a = 0\\b = 1\\c = 2\\\\r^2 = \dfrac{25}{3}\\\\r = \sqrt{\dfrac{25}{3}}= \dfrac{5}{\sqrt3}](https://tex.z-dn.net/?f=3x%5E2%2B3y%5E2%2B3z%5E2%3D10%2B6y%2B12z%5C%5C%5Ctext%7BDividing%20by%203%7D%5C%5Cx%5E2%20%2B%20y%5E2%20%2B%20z%5E2%20%3D%20%5Cdfrac%7B10%7D%7B3%7D%20%2B%202y%20%2B%204z%5C%5C%5C%5Cx%5E2%20%2B%20y%5E2%20-2y%20%2B%20z%5E2-4z%20%3D%20%5Cdfrac%7B10%7D%7B3%7D%5C%5C%5C%5C%5Ctext%7BAdding%201%20and%204%20on%20both%20sides%2C%20we%20get%2C%7D%5C%5C%5C%5Cx%5E2%20%2B%20y%5E2%20-2y%20%2B1%20%2B%20z%5E2-4z%20%2B%204%20%3D%20%5Cdfrac%7B10%7D%7B3%7D%20%2B%201%2B%204%5C%5C%5C%5C%28x-0%29%5E2%20%2B%20%28y-1%29%5E2%20%2B%20%28z-2%29%5E2%20%3D%20%5Cdfrac%7B25%7D%7B3%7D%5C%5C%5C%5C%5Ctext%7BComparing%20with%20the%20equation%20of%20sphere%7D%5C%5Ca%20%3D%200%5C%5Cb%20%3D%201%5C%5Cc%20%3D%202%5C%5C%5C%5Cr%5E2%20%3D%20%5Cdfrac%7B25%7D%7B3%7D%5C%5C%5C%5Cr%20%3D%20%5Csqrt%7B%5Cdfrac%7B25%7D%7B3%7D%7D%3D%20%5Cdfrac%7B5%7D%7B%5Csqrt3%7D)
Center of sphere = (0, 1, 2)
Radius of sphere = ![\dfrac{5}{\sqrt3}\text{ units}](https://tex.z-dn.net/?f=%5Cdfrac%7B5%7D%7B%5Csqrt3%7D%5Ctext%7B%20units%7D)
Answer: see below
Step-by-step explanation:
(i)
200/2 = 100
Find 100 on cumulative frequency and the correspinding time: 14 minutes. So the answer is 14 minutes.
(ii)
First, find the lower quartile —> 200/4 = 50
Upper quartile —> 200/(3/4) = 150
Find the difference: 150 - 50 = 100
So the interquartile range is 100
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