ElectricPavlov

First find the area of the trapezium    get the average of the bases  (10 and 16)   and multiply by the height

   (10+16)/2  *  7.6 =  98.8 m²

How many liters of paint are required?    98.8 m² / 1.9 m²/l = 52 liters

The cans of paint are 5 liters each      How many cans ?     52 liters / 5 liters/can = 10.4 cans        round up to 11 cans

11 cans   *   L16.99/can =   L  186.89    to buy all of the paint necessary

NOT CPhil here...

Remember  TAN function in a RIGHT triangle = opposite side / adjacent side ?

The opposite side is the height of the pole.....the adjacent side is given as 12 ft

SOOOO   tan 70 = 2.747 (from calculator)   and this = opposite/ adjacent   =   height /12

2.747 = height /12       Multiply both sides of this equation by 12

2.747 (12)  = height in feet      You can punch the numbers in your calculator           Ta Da !    

Just read across the rows to find where the value under the f(x) heading is the same as the value as under the g(x) heading.......then scan back to the left to find the value of 'x'     HINT:   There are two values of x   where f(x) = g(x) 

Yikes !!

According to The Hitchikers Guide to the Galaxy , the answer is 42.   

20 revolutions is 20 circumferences

circumference = pi * d          twenty of them is        20 pi d   = 136 ft

                                                                                         d = 136/(20 pi) = 2.165 ft diameter

Make sure your calculator is set in the same mode as 37      radians or degrees or whatever !

Whoa !  Not so fast.... 

csc = 1/sin x           1/ sin(2x)    =   1/ (2sinx cos x)       and this is not merely doubling the value !

ANyway   csc (10) = -1.838          (where 10 is in radians)  

The volume of a cylinder =  pi r^2 h

                           432 pi = pi r^2 h    divide both sides by pi

                           432 = r^2 h            Now since the ball touches the bottom and top    and the sides

                                                               h must be equal to diameter    and thus r = h/2   put this into the equation

                            432 = (h/2)^2 h   and solve for h = 12

Now you know the diameter of the sphere = 12    and the radius of the sphere = 6

sub this in to the volume of a sphere = 4/3  pi  r^3       and you will have your answer !

There isn't any graphs to choose from in your Q submission....

     However the graph should be a slanted line getting higher to the right.....

the first three terms are found by substituting   n = 1      n= 2     and n = 3 into the equation

n² + 20    put in  n = 1     1^2 + 20 = 21

   I think you can do the  n=2  and n=3 versions

How many terms are less than 50?

n^2 + 20  < 50

n^2  <   30

n   <  5.47   ( taking the positive root only)  

                         the answer would be 5                  5^2 + 20 = 45                but 6 would not work  6^2 + 20 = 56