CPhill

The 210th term is given by :

210 (210 - 1) =

210 (209)  = 43890

BTW....this is just the sum of the first 209 positive/even integers....

Note.....7/12 is the slope of the line relating P and Q.........this means that, everytime P changes by 7, Q changes by 12

So....using a proportion.....change in P / change in Q = 

7/12  =  35/ change in Q             cross-multiply

7 * change in Q  = 35 * 12          divide by 7

change in Q =  35* 12 / 7

change in Q = [35/7] * 12

change in Q  = 5 * 12

change in Q = 60  →  (B)

10 ft = 120 inches  .....

N * 8  <= 120       where N is the number of shelves.......divide both sides by

N <= 15

However.....this assumes that the first shelf is at floor level and the last shelf will have an 8 inch clearance with the ceiling......

9.12/s=2.4      rearrange as

s  = 9.12 / 2.4   = 3.8

Angle that the base of the ladder makes with the ground can be found with the sine inverse [arcsin].....so we have....

arcsin (7/8)  = about 61.04°

Distance from  base of wall to ladder base,  (d) =

cos(61.04)  = d/8    multiply both sides by 8

8cos(61.04)  = d  = about 3.87 ft

We could have also used the Pythagorean Theorem to find this last measurement

sqrt(8^2  - 7^2)  =  sqrt (64 - 49)   = sqrt(15)  = about 3.87 ft

The total tower height  = 32.6 + the remaining tower height

32.6 + 50.3*tan(13)   = 44.21 ft

We can use the sine for this......the ramp length is the hypotenuse of a right triangle and the opposite side from the angle of elevation is the ramp height, h

sin(25)  = h/ 140          .....multiply both sides by 140

140*sin(25)  = h  =  about 59.17 ft

We can use the tangent to find this........

tangent 68  = d/75     where d is the distance the boat is from the light house      multiply both sides by 75

75* tangent  68 = d = about 185.63 m

Here's a rough sketch....DAB is the angle of depression.....CA is the lighthouse height....and CB is the distance from the boat to the lighthouse

3,3,6   means that 180°   is divided into 12 parts

So  3/12 * 180   =  1/6 * 180   = 30°

And 6/12 * 180  = 1/2 * 180  = 90°

So  x, y   = 30°

And z  = 90°

If you saw my earlier answer, here.......http://web2.0calc.com/questions/creating-a-polynomial-equation-in-a-word-problem#r1

Notice that the price of a ticket was represented by (20 +P)  where P is the price increase...or, in this case, decrease

So.........look at the graph, here......https://www.desmos.com/calculator/teadcoca0a

P ranges from  -7.52  to 14.19......thus....the price per ticket  would be from

(20 + -7.52)  to  (20 + 14.19)   =   (12.48)  to (34.19)

Thus .....b) is the correct answer.......between these two prices we make at least the minimum....