Answer:

Step-by-step explanation:
The standard form of a quadratic is 
We will use the x and y values from each of our 3 points to find a, b, and c. Filling in the x and y values from each point:
First point (-5, 0):
and
0 = 25a - 5b + c
Second point (9, 0):
and
0 = 81a + 9b + c
Third point (8, -39):
and
-39 = 64a + 8b + c
Use the elimination method of solving systems on the first 2 equations to eliminate the c. Multiply the first equation by -1 to get:
-25a + 5b - c = 0
81a + 9b + c = 0
When the c's cancel out you're left with
56a + 14b = 0
Now use the second and third equations and elimination to get rid of the c's. Multiply the second equation by -1 to get:
-81a - 9b - c = 0
64a + 8b + c = -39
When the c's cancel out you're left with
-17a - 1b = -39
Between those 2 bolded equations, eliminate the b's. Do this by multiplying the second of the 2 by 14 to get:
56a + 14b = 0
-238a - 14b = -546
When the b's cancel out you're left with
-182a = -546 and
a = 3
Use this value of a to back substitute to find b:
56a + 14b = 0 so 56(3) + 14b = 0 gives you
168 + 14b = 0 and 14b = -168 so
b = -12
Now back sub in a and b to find c:
0 = 25a - 5b + c gives you
0 = 75+ 60 + c so
0 = 135 + c and
c = -135
Put that all together into the standard form equation to get

First we gather all the information we have about the amount of miles that Carolyn runs:
Monday, Wednesday, Friday: 4 1/2 miles
Tuesday, Saturday: 2 3/4 miles
And the question is the amount of miles that she runs in 4 weeks.
So lets begin by calculating the amount of miles she runs in one week, then we just multiply by 4 and we'll have the final answer.
So, we have to add 4 1/2 three times (Monday, Wed, Friday), and 2 3/4 two times (Tuesday, Sat):
1 week Miles = 4 1/2 + 4 1/2 + 4 1/2 + 2 3/4 + 2 3/4
lets add the whole parts and the fraction parts apart:
1 week Miles = (4 + 4 + 4 + 2 + 2) + (1/2 + 1/2 + 1/2 + 3/4 + 3/4)
1 week <span>Miles = (16) + (3/2 + 6/4)
</span>we can reduce the last fraction:
1 week <span>Miles = (16) + (3/2 + 3/2)
</span>1 week <span>Miles = (16) + (6/2)
</span>1 week <span>Miles = (16) + (3)
</span>1 week <span>Miles = 19
</span>therefore Carolyn runs 19 miles each week, so for 4 weeks we have to add 19 four times or multiply it by 4, is the same:
4 weeks <span>Miles = 4*19
</span>4 weeks <span>Miles = 76
hence Carolyn runs 76 miles in 4 weeks.</span>
The unit tangent vector is T(u) and the unit normal vector is N(t) if the vector function. R(t) is equal to 9 2 t, e9t, e−9t.
<h3>What is vector?</h3>
It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.
We have vectored function:

Find its derivative:

Now its magnitude:

After simplifying:

Now the unit tangent is:

After dividing and simplifying, we get:

Now, finding the derivative of T(u), we get:

Now finding its magnitude:

After simplifying, we get:

Now for the normal vector:
Divide T'(u) and |T'(u)|
We get:

Thus, the unit tangent vector is T(u) and the unit normal vector is N(t) if the vector function. R(t) is equal to 9 2 t, e9t, e−9t.
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Examining the table the functional notation is in the second option which is f ( x ) = x^2
<h3>How to determine the functional notations of the table</h3>
The table represents functions of input variables and the output variables.
The functional notation represents the relationship between the input and out variables
comparing the values and the function
f ( x ) = x^2
at x = -3 ⇒ f ( -3 ) = (-3)^2 = 9
at x = 0 ⇒ f ( 0 ) = (0)^2 = 0
at x = 1 ⇒ f ( 1 ) = (1)^2 = 1
This shows that f ( x ) = x^2 is the correct option
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It would be 0 because as you go along it doesn't go up but keeps moving. An undefined slope is up and down/vertical.