CPhill

Ah....Mathcad......you did very well but you gave up a little too quickly, here........!!!!......notice the following factorization....

15sec^2(x)-32sec(x)+17=0

(15sec(x) - 17) (sec(x) -1)  = 0

So either......

sec(x) = 1  which happens at 0 and 360.....but, both of these are out of the requested interval....or....

sec(x)  = 17/15   which happens at about 28.072°  and about 331.928°

3x+y=1 and 5x-y=15

Using the first equation, y = 1 - 3x    ....and substituting this into the second, we have

5x - (1 - 3x) = 15

5x -1 + 3x = 15

8x - 1  = 15

8x = 16

x = 2     and y = (1 - 3x) = (1 - 3(2))  = (1 - 6)  = -5

So the solution point is (2, -5)

And the equation of the circle would be.....

(x - 2)^2 + (y + 5)^2  = 4

Sorry, Mathcad, but.....

sin(70) ≠ sin(40)cos(30) +cos(30)sin(40)

sin(70) = sin(40)cos(30) + sin(30)cos(40)

And .... 8sin(40)/sin (70) = Melody's answer  ...... which is not =   8/√3  = 4.6188021535170061

A new McDonald's offering.......advertised as follows :

"Three McSquare Meals A Day = All You Need...."

1/F  = 1/20  + 1/9 

1/F  = [29 / 180]     .....so......taking the reciprocals of both sides, we have

F  = [180/29]

y=2(3^x)  

y = 5x + 4 

Look at the graph, here.......

The solutiion points occur at about (-0.591, 1.045) and (1.65, 12.25)

So.....the first positive integer where the exponential function > the linear function is  x = 2

It's between these two integers..... 28 and 29

28^2 < 800 < 29^2

784 < 800 <  841

S_area = ( pi * r) (r + √[r^2 + h^2] )     where r is the radius and h is the height  ..... so we have.....

S_area  = ( pi * 10 ) (10 + √[10^2 + 10^2] )  = (10*pi) *(10 + 10√2) = 758.48 sq units

Are you sure that "red"  isn't something in that glass you're drinking????

Huh????