Answer:
Step-by-step explanation:
Given
Hoop, Uniform Solid Cylinder, Spherical shell and a uniform Solid sphere released from Rest from same height
Suppose they have same mass and radius
time Period is given by
,where h=height of release
a=acceleration

Where I=moment of inertia
a for hoop


a for Uniform solid cylinder


a for spherical shell


a for Uniform Solid


time taken will be inversely proportional to the square root of acceleration




thus first one to reach is Solid Sphere
second is Uniform solid cylinder
third is Spherical Shell
Fourth is hoop
Answer:
A) 99.7% of people have an IQ between 64 and 136.
B) 5% of people have an IQ score less than 76 or greater than 124.
C) 16% of people have an IQ score greater than 112.
Step-by-step explanation:
The Empirical Rule tells us that, in a normal or 'bell-shaped' distribution, 68% of the data is one standard deviation from the mean, 95% of the data is two standard deviations from the mean, and 99.7% of the data is three standard deviations from the mean.
A) 64 and 136 are 3 standard deviations away from the mean, so 99.7% of people have an IQ between 64 and 136.
B) 76 and 124 are 2 standard devations away from the mean, but the answer is asking what percentage is not between them. 100% - 95% gives us 5%.
C) 112 is one standard deviation away from the mean. If we want to find the percentage greater, then we can do 100% - 50% (as 112 is to the left of the mean), then we can take half of 68 to get 34%, and after subtracting 50% and 34% from the 100%, we get 16%.
so, we have two 54x18 rectangles, so their perimeter is simply all those units added together, 54+54+54+54+18+18+18+18 = 288.
we know the circle's diameter is 1.5 times the width, well, the width is 18, so the diameter of the circle must be 1.5*18 = 27.
![\bf \stackrel{\textit{circumference of a circle}}{C=d\pi }~~ \begin{cases} d=diameter\\[-0.5em] \hrulefill\\ d=27 \end{cases}\implies C=27\pi \implies C=\stackrel{\pi =3.14}{84.78} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{perimeter of the rectangles}}{288}~~~~+~~~~\stackrel{\textit{perimeter of the circle}}{84.78}~~~~=~~~~372.78](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Bcircumference%20of%20a%20circle%7D%7D%7BC%3Dd%5Cpi%20%7D~~%20%5Cbegin%7Bcases%7D%20d%3Ddiameter%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20d%3D27%20%5Cend%7Bcases%7D%5Cimplies%20C%3D27%5Cpi%20%5Cimplies%20C%3D%5Cstackrel%7B%5Cpi%20%3D3.14%7D%7B84.78%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bperimeter%20of%20the%20rectangles%7D%7D%7B288%7D~~~~%2B~~~~%5Cstackrel%7B%5Ctextit%7Bperimeter%20of%20the%20circle%7D%7D%7B84.78%7D~~~~%3D~~~~372.78)
The vertex form of the equation is:
y = a ( x - h )² + k
- 81 = a ( 0 - 6 )² + 27
- 81 = 36 a + 27
- 108 = 36 a
a = - 108 : 36
a = - 3
y = - 3 ( x - 6 )² + 27
y = - 3 ( x² - 12 x + 36 ) + 27
y = - 3 x² + 36 x - 108 + 27
y = - 3 x² + 36 x - 81
y = - 3 ( x² - 12 x + 27 )
x² - 12 x + 27 = 0
x² - 9 x - 3 x + 27 = 0
x ( x - 9 ) - 3 ( x - 9 ) = 0
( x - 9 ) ( x - 3 ) = 0
x 1 = 3, x 2 = 9
Answer:
The x-intercepts are ( 3, 0 ) and ( 9, 0 ).
Answer:

Step-by-step explanation:
Given


See attachment
Required
Find 
First, calculate 
--- angle on a straight line
So, we have:

Collect like terms


Next, calculate PQR

So, we have:

Collect like terms


So, PRO is calculated as:
--- angles in a triangle
So, we have:


Collect like terms

