130+31.67x=500
31.67x=370
x≈ 11 days. As a result, the maximum number of days that I can rent a car if i have a $500 budget is 11 days. Hope it help!
Answer:
a) See attachment 1.
b) t² and D
c) See attachment 2.
d) g = 9.8 m/s² (1 d.p.)
Step-by-step explanation:
<h3><u>Part (a)</u></h3>
See attachment 1. The line of best fit is shown in red.
<h3><u>Part (b)</u></h3>
The quantities the student should graph in order to produce a <u>linear relationship</u> between the two quantities are t² and D.
<h3><u>Part (c)</u></h3>
Make a table of values of t² and D:
![\begin{array}{|l|l|l|l|l|l|}\cline{1-6} \rm t^2& 0.0196& 0.1024& 0.2116 & 0.3481& 0.3969\\\cline{1-6} \rm D & 0.10 & 0.50& 1.00 & 1.70 & 2.00\\\cline{1-6}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7B%7Cl%7Cl%7Cl%7Cl%7Cl%7Cl%7C%7D%5Ccline%7B1-6%7D%20%5Crm%20t%5E2%26%200.0196%26%200.1024%26%200.2116%20%26%200.3481%26%200.3969%5C%5C%5Ccline%7B1-6%7D%20%5Crm%20D%20%26%200.10%20%26%200.50%26%201.00%20%26%201.70%20%26%202.00%5C%5C%5Ccline%7B1-6%7D%5Cend%7Barray%7D)
<u>Plot</u> a graph of D against t² and draw a line of best fit (see attachment 2).
<h3><u>Part (d)</u></h3>
From inspection of the graph, the line of best fit passes through the origin (0, 0) and (0.1024, 5.0). Therefore, use these two points to find the slope of the line:
![\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0.5-0}{0.1024-0}=4.8828125...\:\rm m/s^2](https://tex.z-dn.net/?f=%5Ctextsf%7Bslope%7D%5C%3A%28m%29%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%3D%5Cdfrac%7B0.5-0%7D%7B0.1024-0%7D%3D4.8828125...%5C%3A%5Crm%20m%2Fs%5E2)
Therefore:
![\rm \implies \dfrac{1}{2}g=4.8828125...\:\rm m/s^2](https://tex.z-dn.net/?f=%5Crm%20%5Cimplies%20%5Cdfrac%7B1%7D%7B2%7Dg%3D4.8828125...%5C%3A%5Crm%20m%2Fs%5E2)
![\rm \implies g=2 \cdot 4.8828125...\:\rm m/s^2](https://tex.z-dn.net/?f=%5Crm%20%5Cimplies%20g%3D2%20%5Ccdot%204.8828125...%5C%3A%5Crm%20m%2Fs%5E2)
![\rm \implies g=9.8\:\rm m/s^2\:(1\:d.p.)](https://tex.z-dn.net/?f=%5Crm%20%5Cimplies%20g%3D9.8%5C%3A%5Crm%20m%2Fs%5E2%5C%3A%281%5C%3Ad.p.%29)
I believe you haven't included the system of equations for us to solve.
However, I will tell you that you need to solve for one variable in an equation and substitute that into the other equation.
For example:
x = yz; z = x/y
a = zb; a = (x/y)b
Hope this helps!
Answer: 21
Step-by-step explanation: