CPhill

tan45 - 7.cot45 + 5csc30 =

(1) - 7(1) + 5(2/1) =

1 - 7 + 10=

4

Nice one, geno...!!!!

Think of it this way....

Total amount =  Amount per day  x  number of days......

Geno....thanks for all those great answers to those geometry questions...!!!

Let me expand on Melody's answer just a bit....

The median of a trapezoid is just (1/2) the sum of the lengths of the bases. So....calling the length of the unknown base, "x," we have

(5 + x ) / 2   = 8

5 + x = 16

x = 11

And that's just as Melody found.....

Yeah, Melody, using "x" for the length probably would have made it easier.....I just didn't think to do it that way.....!!!

Using 4h + k = 16....we have that k = 16 - 4h.....and equating distances, we have

(h-4)^2 +  ( 16 - 4h -1)^2  = (h-6)^2 + (16 - 4h - 5)^2 ....... simplify

(h-4)^2 + (15 - 4h)^2  = (h-6)^2 + (11-4h)^2

h^2 - 8h + 16 + 16h^2 - 120h + 225 = h^2 - 12h + 36 + 16h^2 - 88h + 121

-8h + 16 -120h + 225  =  -12h + 36 -88h + 121

-128h + 241 = -100h + 157

84 = 28h

h = 3

So...using k = 16 - 4h....then k = 16 - 4(3)  = 16 - 12 = 4

Then (h,k)  = (3, 4)  and the circle has a radius of  √10

Nice job, Melody......I couldn't think how to get this one started...!!!!...I might work through it myself, just to see if I can do it....!!!

Wow, Melody....!!!..that was a lot of work just to arrive at "4"......but I'll give you credit.....you even managed to keep rosala's attention....!!!  LOL!!!

I'm assuming that you're saying that one side of the quadrilateral is the same as the circle's diameter, and we have two adjacent sides to this that are 8 and 12m, respectively. Then the circle's radius = 10 m

To find the remaining side, we need to first find the central angles intercepting the 8 and 12 m sides.....

We can use the Law of Cosines in both cases....for the 12m side, we have

12^2 = 10^2 + 10^2 - 2(10)(10)cosΘ   ......simplifying, we have

cosΘ= 7/25  = cos^-1(7/25) = about 73.739795291688°

For the 8m side, we have

8^2 = 10^2 + 10^2 - 2(10(10)cosΘ   ...simplifying again, we have

cosΘ = 17/25 = cos^-1(17/25) = about 47.156356956404°

So, since the diameter would span 180° of arc, the remaing side must span (180 - 73.739795291688 - 47.156356956404)° = 59.103847751908° of arc

So...the remaining side... (s).... is given by

s^2  = 10^2 + 10^2 - 2(10)(10)cos(59.103847751908)

s = √[10^2 + 10^2 - 2(10)(10)cos(59.103847751908)] = about 9.86 m

This makes sense....the greater side intercepts the greatest arc, the next greatest side intercepts the next greatest arc, etc.