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valentinak56 [21]
3 years ago
8

A car starts a journey with a full tank of gas. The equation y=16 - 0.05x relates the number of gallons of gas, y, left in the t

ank to the number of miles the car has traveled, x.
A. What are the x- and y-intercepts of the graph of this equation?

B. What does x-intercept represent in the context of this problem?

C. What does y-intercept represent in the context of this problem?
Mathematics
1 answer:
mr_godi [17]3 years ago
4 0

A.  The y-intercept is y = −0.05 x + 16 and the x-intercept is x = −20y + 320

B. The x-intercept represents the number of miles the car has traveled.

C. The y-intercept represents the number of gas in gallons.

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Solve the following recurrence relation: <br> <img src="https://tex.z-dn.net/?f=A_%7Bn%7D%3Da_%7Bn-1%7D%2Bn%3B%20a_%7B1%7D%20%3D
-Dominant- [34]

By iteratively substituting, we have

a_n = a_{n-1} + n

a_{n-1} = a_{n-2} + (n - 1) \implies a_n = a_{n-2} + n + (n - 1)

a_{n-2} = a_{n-3} + (n - 2) \implies a_n = a_{n-3} + n + (n - 1) + (n - 2)

and the pattern continues down to the first term a_1=0,

a_n = a_{n - (n - 1)} + n + (n - 1) + (n - 2) + \cdots + (n - (n - 2))

\implies a_n = a_1 + \displaystyle \sum_{k=0}^{n-2} (n - k)

\implies a_n = \displaystyle n \sum_{k=0}^{n-2} 1 - \sum_{k=0}^{n-2} k

Recall the formulas

\displaystyle \sum_{n=1}^N 1 = N

\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2

It follows that

a_n = n (n - 2) - \dfrac{(n-2)(n-1)}2

\implies a_n = \dfrac12 n^2 + \dfrac12 n - 1

\implies \boxed{a_n = \dfrac{(n+2)(n-1)}2}

4 0
2 years ago
Find the relative rate of change fro each of the following functions. f(x)=x^3 -3x^2
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3 years ago
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Answer:

Step-by-step explanation:

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8 0
3 years ago
What is 2 = 8 − 6/4x solved?
KengaRu [80]

Answer:

x=4

General Formulas and Concepts:

  • Order of Operations: BPEMDAS
  • Equality Properties

Step-by-step explanation:

<u>Step 1: Define equation</u>

<u />2=8-\frac{6}{4} x<u />

<u />

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Subtract 8 on both sides:                    -6=-\frac{6}{4} x
  2. Divide both sides by -6/4:                   4=x
  3. Rewrite:                                                x=4

<u>Step 3: Check</u>

<em>Plug in x to verify it's a solution.</em>

  1. Substitute:                    2=8-\frac{6}{4}(4)
  2. Multiply:                        2=8-6
  3. Subtract:                       2=2
7 0
3 years ago
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