Answer:
= 9.2 cm
Step-by-step explanation:
D = C ÷ π
= 29cm ÷ 3.14
= 9.2356
= 9.2 cm
First let's assume that the table contains points on a straight line. Then all we have to do is to determine the slope of that line.
Suppose we go from (0,3) to (7,-28.5).
-28.5-3 -31.5
Then the slope, m, is m = ------------- = ---------- = - 9/2, or - 4.5.
7-0 7
Let's check this result!
Suppose that y = mx + b governs the relationship between x and y.
Then y = -4.5x + b
suppose we find b by substituting the coordinates from the point (0,3):
3 = -4.5(0) + b
Then b = 3, and y = -4.5x + 3. Does the point (-2,12) satisfy this equation?
Does 12 = -4.5(-2) + 3? Does 12 = 9 + 3? YES.
So y = -4.5x + 3 is the equation from which these points came, and the rate of change of y with respect to x is the slope m = -4.5, or m = -9/2.
Answer:
.
Step-by-step explanation:
Let the 
-coordinate of 
be 
. For 
to be on the graph of the function 
, the 
-coordinate of 
would need to be 
. Therefore, the coordinate of 
would be 
.
The Euclidean Distance between and 
is:
.
The goal is to find the a that minimizes this distance. However, 
is non-negative for all real 
. Hence, the 
that minimizes the square of this expression, 
, would also minimize 
.
Differentiate with respect to :
![\displaystyle \frac{d}{dt}\left[t^2 - 17 \, t + 81\right] = 2\, t - 17](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%5Bt%5E2%20-%2017%20%5C%2C%20t%20%2B%2081%5Cright%5D%20%3D%202%5C%2C%20t%20-%2017)
.
![\displaystyle \frac{d^{2}}{dt^{2}}\left[t^2 - 17 \, t + 81\right] = 2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%5E%7B2%7D%7D%7Bdt%5E%7B2%7D%7D%5Cleft%5Bt%5E2%20-%2017%20%5C%2C%20t%20%2B%2081%5Cright%5D%20%3D%202)
.
Set the first derivative, 
, to 
and solve for :
.
.
Notice that the second derivative is greater than for this . Hence, would indeed minimize . This value would also minimize , the distance between and .
Therefore, the point would be closest to when the -coordinate of is .
Answer to your question be $750 will be the total charge on her account
You have to figure this out my adding 9 points to how many points Mary has, to get how many points Alice has, with an answer of 30 points. <span />
