If the position at time <em>t</em> is
<em>s(t)</em> = (1 m/s³) <em>t</em> ³
then the average velocity over <em>t</em> = 2 s and <em>t</em> = 2.001 s is
<em>v</em> (ave) = (<em>s</em> (2.001 s) - <em>s</em> (2 s)) / (2.001 s - 2 s)
<em>v</em> (ave) = ((1 m/s³) (2.001 s)³ - (1 m/s³) (2 s)³) / (2.001 s - 2 s)
<em>v</em> (ave) ≈ (8.01201 m - 8 m) / (0.001 s)
<em>v</em> (ave) ≈ 12.006 m/s
Answer:
18. y = -5
19. y = 4x-10
Step-by-step explanation:
Parallel lines have the same slope. You can find the slope from the equation y=mx+b. It is the m value.
For 19, the slope is 4 since y=4x has m = 4. To find a line parallel to it that crosses through the point (3,2), substitute m = 4 and (3,2) into the point slope formula.

It simplifies to y = 4x - 10.
For equations like 18 where y = 8 there is no m value. There is no slope. This is a horizontal line through 8 on the y-axis. A parallel line is another horizontal line through the y value of (-6,-5). The line is written he same way as y = -5.
let's firstly convert the mixed fractions to improper fractions.
![\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{1\frac{3}{4}}\implies \cfrac{1\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{7}{4}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} \stackrel{size}{actual~miles}&\stackrel{size}{map~inches}\\ \cline{1-2} 210&\frac{7}{2}\\\\ x&\frac{7}{4} \end{array} \implies \cfrac{210}{x}=\cfrac{~~\frac{7}{2}~~}{\frac{7}{4}}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B3%5Cfrac%7B1%7D%7B2%7D%7D%5Cimplies%20%5Ccfrac%7B3%5Ccdot%202%2B1%7D%7B2%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B7%7D%7B2%7D%7D~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B1%5Cfrac%7B3%7D%7B4%7D%7D%5Cimplies%20%5Ccfrac%7B1%5Ccdot%204%2B3%7D%7B4%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B7%7D%7B4%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Bccll%7D%20%5Cstackrel%7Bsize%7D%7Bactual~miles%7D%26%5Cstackrel%7Bsize%7D%7Bmap~inches%7D%5C%5C%20%5Ccline%7B1-2%7D%20210%26%5Cfrac%7B7%7D%7B2%7D%5C%5C%5C%5C%20x%26%5Cfrac%7B7%7D%7B4%7D%20%5Cend%7Barray%7D%20%5Cimplies%20%5Ccfrac%7B210%7D%7Bx%7D%3D%5Ccfrac%7B~~%5Cfrac%7B7%7D%7B2%7D~~%7D%7B%5Cfrac%7B7%7D%7B4%7D%7D)
![\bf \cfrac{210}{x}=\cfrac{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{2}{~~\begin{matrix} 4\\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \implies \cfrac{210}{x}=2\implies 210=2x\implies \cfrac{210}{2}=x\implies 105=x](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B210%7D%7Bx%7D%3D%5Ccfrac%7B~~%5Cbegin%7Bmatrix%7D%207%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%7D%7B~~%5Cbegin%7Bmatrix%7D%202%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%7D%5Ccdot%20%5Ccfrac%7B%5Cstackrel%7B2%7D%7B~~%5Cbegin%7Bmatrix%7D%204%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%7D%7D%7B~~%5Cbegin%7Bmatrix%7D%207%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%7D%20%5Cimplies%20%5Ccfrac%7B210%7D%7Bx%7D%3D2%5Cimplies%20210%3D2x%5Cimplies%20%5Ccfrac%7B210%7D%7B2%7D%3Dx%5Cimplies%20105%3Dx)