CPhill

To find the rate, we just divide the distance by the time....so we have.....

480 miles / 7.5 hours   =  64 miles per hour

r=3cos(Theta)  ...... and to convert to Cartesian form, we have

√(x^2 + y^2)  = 3 (x)/√(x^2 + y^2)    simplify

(x^2 + y^2)  = 3x  subtract 3x from both sides

x^2 - 3x + y^2 = 0  complete the square on x

x^2 - 3x + 9/4 + y^2  = 9/4      factor

(x - 3/2)^2 + y^2  = 9/4

We have

  d = -1.5 t ² + 120    and when d = 10, we have

10 = -1.5t^2 + 120   rearrange

1.5t^2 -110  = 0

Add 110  to both sides

1.5t^2 = 110     divide both sides by 1.5

t^2  = 110/1.5      take the positive root of both sides

t = √(110/1.5)  =  about 8.56 seconds

Take (1/2) of the coefficient on "x," i.e., (-8/3)....so ....(1/2)(-8/3)  = -8/6

To find  "c," square this =  (64/36) = (16/9)  = c

So, the polynomial is  x² - (8/3)x + 16/9

And to factor this, we have

[x - 4/3 ] ²

The correct answer is "c"

y = (2)3^x    where x in an integer > 0

3x-4y=-15 and 5x+y=-2

We can write the second equation as y = -2-5x   ......and substituting this into the first equation for y, we have

3x -4(-2-5x)  = -15   simplify

3x + 8 + 20x   = -15

23x + 8  = -15     subtract 8 from both sides

23x  = - 23          divide both sides by 23

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

So (x, y)  = (-1, 3)

Yep....nice job !!!

It can be shown that the curve traced out by a point on this wheel  is known as a cycloid. It's arc length through one rotation can be found by using Calculus and is equal to 8r, where "r" is the radius of the wheel....!!! Also, the area under one arc is just .... 3*pi*r^2......

y+3<-2/3(x-9)  subtract 3 from both sides

y < -2/3(x-9) - 3   simplify

y < (-2/3)x + 6 - 3

y < (-2/3)x + 3