geno3141

g(x)  =  6 - x         h(x)  =  x³

h(-3)   --->   place -3 in for x into the h(x) formula:  h(-3)  =  (-3)³  =  -27

hg(2)   --->   h( g(2) )

     first, calculate g(2):  g(2)  =  6 - 2  =  4

     then, place this result into the h formula:

     --->   h( g(2) )  =  h(4)  =  4³  =  64

gh(2)   --->   g( h(2) )

     first, calculate h(2):  h(2)  =  2³  =  8

     then, place this result into the g formula:

     --->   g( h(2) )  =  g( 8 )  =  6 - 8  =  2

You need to work the functions from right to left:  hg(x)  =  h( g(x) )     and     gh(x)  =  g( h(x) )

Bearing is measured clockwise from north.

However, trig is measured counterclockwise from east.

So a bearing of 65° translates to a trig angle of 25°.     (90° - 65° = 25°)      (Everything is in Quadrant I.)

Picture a right triangle that has an endpoint at the origin, a 25° angle going to the upper right, a hypotenuse of 200, and a base along the x-axis. You want to find the length along the x-axis.

East is along the x-axis, so use cos:  cos(25°)  =  x/200   --->   x  =  200cos(25°)   --->   x  =  181 km

The symbol always points to the smaller number:  10 > 2     and     3 < 7.

'>' means 'greater than'     and     '<' means 'less than'

Is this meant to be a quadratic equation that you are supposed to solve by using the quadratic formula?

If so:  4x¹ - 24 x - 35 = 0

Quadratic Formula:  x  =  [ -b ±√( b² - 4·a·c ) ] / ( 2·a )

In this problem,  a = 4,   b = -24,   and  c = -35.

--->    x  =  [ --24 ± √( (-24)² - 4·4·(-35) ) ] / ( 2·4 )

--->   x  =  [ 24 ± √( 576 + 560 ) ] / ( 8 )

--->   x  =  [ 24 ± √( 1136 ) ] / ( 8 )

--->   x  =  [ 24 ± 4√(71) ] / ( 8 )

--->   x  =  3 ± √(71)/2

This is a major unsolved problem -- your chance to be both rich and famous!

Absolute value bars guarantee that the answer is positive; if the number inside the absolute value bars is already positive, the answer remains positive. --->  |10|  =  10

28 - (-x) - |10|

--->   28 - (-15) - |10|

--->   28 + 15 - 10

--->   43 - 10

--->   33

∑_{i=1 to 5} (-1)^i-1(i/3)ⁱ

Euler's constant:

=  0.57721566490...

Euler's number:

=  2.71828182846...

If you write them with the same number of decimal places, then you are comparing:

0.0008

0.0040

Written this way, it is easy to see that 40 > 8, so 0.004 > 0.0008.

Let  x  be the average amount that each person raises.

Since there are  50  students, the total amount that they raise will be the average amount for each times the number of students.    This becomes:  50x

Take this amount and add to it the amount that they have already earned:  50x + 1250.

Since you want to raise at least 12500, you have this equation:  50x + 1250  ≥  12500

50x + 1250  ≥  12500

Subtract 1250 from both sides:

--->   50x  ≥  11250

Divide both sides by 50:

--->   x  ≥  225

So, the average amount left to earn is at least $225.00.