CPhill

Is the line at the bottom supposed to be tangent to the circle or  parallel  to the other tangent??

When two chords intersect in a circle, the products of their segments are equal.

Thus we have   ....  20 * 15 = 26 * x      ....    so we have

300 = 26 * x         divide both sides by 26

300/26 = x  = 150/13 =  about 11.538

We are trying to find an angle whose cosine = 2/3. Using the cosine inverse, we have

arcos(2/3) = about 48.19 degrees

Please realize that because the cosine is also positive in the 4th quadrant, this also might be -48.19 degrees = 360-48.19 = 311.81 degrees

When we have an angle formed by a tangent to a circle and a secant cutting the circle, the angle formed = (1/2)(measure of the of the difference of the intercepted arcs)

So...we have  x = (1/2) (160 -68) = (1/2)(92) = 46 degrees.....

I'll see if I remember how to prove this..........If I do, I'll include it a little later.......unless someone else beats me to it !!!

I'm assuming you want to find an angle with the same value as -cos(300)

cos(300) = 1/2   ....so ...-cos(300) = -1/2

So, you're looking for an angle with a cosine value of -1/2

This occurs at 120 degrees and at 240 degrees

The general answers would be

120 + n360   and   240 + n360          where n is an integer

Rearranging 5x -10y =1, we have  10y = 5x -1....dividing by 10 on both sides, we get

y = (5/10)x - 1/10

Since we want to write an euation of a line perpendicular to this one, the slope of our line has the negative reciprocal slope of  (5/10) = -(10/5) = -2

So, using point - slope form, we have

y - (-2/7) = -2(x - 1/2)

y + 2/7 = -2x +1         subtract 2/7 from both sides

y = -2x + 5/7             I actually like this form because I can see the slope and y intercept right away, but putting it into Ax + By = C form, we have   (by multiplying both sides by 7)

7y = -14x + 5        

14x + 7y = 5

And there you go.......

That looks more like a right angle, to me....but it IS acute one !!!!

It's the first time that a right angle ever had four "legs" instead of the normal two..........

Simplifying, we have

(1.043^n - 1)  >  65000 (1.043-1)/(5000*1.043)

1.043^n - 1 > 65000(.043) / (5215)

1.043^n >  2795/5215 +1

1.043^n > 1.535953978906999    take the log of both sides

log 1.043^n > log 1.535953978906999          and by a property of logs, we can write

(n)log 1.043 > log 1.535953978906999          divide both sides by log 1.043

n > log 1.535953978906999 / log 1.043

n > 10.193341688070085987

We have

96 = ab⁵        and  384 = ab⁷    Using the first, we have 96/b⁵  = a

Substituting into the second, we have

384 = (96/b⁵ ) b⁷    simplifying, we have

384 = 96b²      divide both sides by 96

384/96 =  b²

4 = b²

2 = b     and using  ..... 96/b⁵  = a     ... we have     96/(2)⁵ = a    96/32 = a  = 3

So....our function is .... f(x) =  3(2^x)

Call the number "N"   ... and if it decreased by 20%, it must just be 80% of what it was = 112

So  ...  80% of N = 112      ..  or....  in equation form

.80*N = 112          divide both sides by .80

N = 112/.80 = 140