geno3141

Since the formula for R'(c)  =  5000 - 200c:

To find where R'(x) > 0:      5000 - 200c > 0     --->   -200c > -5000   --->   c < 25

To find where R'(c) < 0:      5000 - 200c < 0     --->   -200c < -5000   --->   c > 25

The maximum occurs where R'(c) = 0:     5000 - 200c = 0   --->   -200c = -5000   --->   c = 25

When  c = 25,  the revenue will be R(25)  =  5000(25) - 100(25)²  =  62,500

tan^-1(x) represents the angle that has x for a tangent.

For example, tan^-1(1.732...) = 60^o or any addition (or subtraction) of 180^o of that angle; so, answers of 240^o, 360^o, etc; also, answers of -120^o, -300^o, etc. are also correct.

If there is no difference between looking at the picture in a clockwise manner or an anti-clockwise manner, there are 5 persons who can be the individual placed between B and P. Of the four remaining, any of four can be placed next to B, any of three can be placed next to that person, any of two can be placed next to that person, and there is one person remaining to be placed next to P. (There is no difference if you start with P instead of B.)To find the total number of ways, multiply these choices together:  5 x 4 x 3 x 2 x 1  =  120 ways. If there is a difference beween listing them clockwise and anticlockwise, multiply that answer by 2.

This can be a kite ...

(a + 5)²   =  (a + 5)(a + 5)  =  a(a) + (a)(5) + (5)(a) + (5)(5)  =  a² + 5a + 5a + 25  =  a² + 10a + 25

(a - 5)²   =  (a - 5)(a - 5)  =  a(a) + (a)(-5) + (-5)(a) + (-5)(-5)  =  a² - 5a - 5a + 25  =  a² - 10a + 25

(a +5)² - (a - 5)²  = [a² + 10a + 25] - [a² - 10a + 25]  =  a² + 10a + 25 - a² + 10a - 25  =  20a

Yes; it's correct!

(g o f)(x)  can be rewritten as  g( f(x) ).

This means that you replace the  x  inside  g(x)  with the expression of  f(x).

Since  f(x)  =  x - 5,  g( f(x) )  =  g( x - 5)  =  2(x - 5) - 8

Simplifying:  g( f(x) )  =  2x - 10 - 8  or  g( f(x) )  =  2x - 18

To find the unit cost divide the total cost by the number of items:

$150.95 / 5  =  $30.19   <--  the unit cost

-x³ - x² + x  can be factored as  x(-x² - x + 1)  or as  -x(x² + x - 1)

So, either  -x  or  x  is the greatest common factor, depending upon which one is positive.

There is a right triangle formed from Kate, along the ground to the base of the screen, a right angle that the ground forms with the screen, and up the screen to the top of the screen.

Label the point where Kate sits as A, the point where the ground hits the screen as C, and the point at the top of the screen as B.

From corner A, the side AC is the adjacent side and the side CB is the opposite side. Corner C is a right angle.

The trig formula using adjacent and opposite is tangent.

Tangent = Opposite / Adjacent

Tangent (A)  =  CB / AC.

tan(24)  =  CB / 36.

CB  =  36 x tan(24)  =  36 x 0.4452 = 16 feet

4 x 9  =  36

4 + 9  =  13