ElectricPavlov

Sin(x) = .2588     Given

ARCSin (x) = x = ARCSin(.2588)        using the calculator   = 14.9988 degrees  ( ~ 15 degrees)   

COMPLIMENTARY angle is the angle which added to 'x' will equal 90      so the COMPLIMENTARY Angle is 75 degrees

Using the calculator again    cos (75) = .2588   The same as the complimentary angle's SIN !!!

It looks like there are THREE  very similar qiestions related to potential energy and work posted this morning.  I'll show you how to do this one...you should be able to multiply hte others w/out much difficulty.  When an object has a CHANGE in potential energy and equivalent amount of work ahs to be done to change this potential energy.....so for THIS problem there is a CHANGE in potential energy as the man is raised from 2.3 to 7.6 meters:

Potential Energy (in joules) = U = mgh      m = mass in kg  g = gravitational constant 9.8 m/sec^2   h = change in height in meters

92.5 kg man     h = 7.6-2.3 = 5.3 meters        92.5 (9.8) (5.3) = potential enrgy change (work done) = 4804.45 j

to solve for t    first divide both sides by 100000

2=e^.0475t   take ln of both sides

ln 2 = .0475t

14.59=t

Just multiply all of the numerators together and all of the denominators to gether    to get    40/504   = 5/63  (using the calculator!)

First you need to make sure you are working in consistent (the same) units

1.1 liter = 1100 cm^3 (cubic cm)

Volume of a cylinder   Vc = pi r^2 h   1100 = pi r^2 (27)

1100/(pi 27) = r^2    r=    3.601    Diameter = 2 x r  = 7.202 cm

6*8/12 +5 + 1 = 10  is another way

Before you can add or subtrac numbers with fractions involved you have to have a COMMON DENOMINATOR.

The denoms in this problem are   21   and 7          21  is an easy common denom for these tww.....right?

22  2/21  =   ((22 x 21) + 2 )  / 21 = 464/21          8 1/7  = ( (8x21) + (3x1) ) / 21  =  171/21

Now we can do the math:     464/21  - 171/21  =   (464-171)/21 = 293/21         you can simplify this to    13  20/21

Probabiltiy say 1 out of 10 tryout.....if 22 tryout then there is    10 x 22 in class = 220  

If t is in years and 315000 is the (in question) population in the present day, then t = 2020-2016 = 4 yrs from now

315000 (1.02)^4 = 340,966