Answer: a. [tex]v=\dfrac{2}{3}t[/tex] and b. [tex]t=\dfrac{3}{2}v[/tex].
Step-by-step explanation:
Let as consider,
Volume (in gallons) of water in the container = v
The number of minutes = t
(a)
From the given graph it is clear that the line passing through the points (0,0) and (3,2). So, the equation of line is
[tex]v-v_1=\dfrac{v_2-v_1}{t_2-t_1}(t-t_1)[/tex]
[tex]v-0=\dfrac{2-0}{3-0}(t-0)[/tex]
[tex]v=\dfrac{2}{3}t[/tex]
Therefore, the required formula is [tex]v=\dfrac{2}{3}t[/tex].
(b)
We have,
[tex]v=\dfrac{2}{3}t[/tex]
Multiply both sides by 3/2.
[tex]v\times \dfrac{3}{2}=\dfrac{2}{3}t\times \dfrac{3}{2}[/tex]
[tex]\dfrac{3}{2}v=t[/tex]
[tex]t=\dfrac{3}{2}v[/tex]
Therefore, the required formula is [tex]t=\dfrac{3}{2}v[/tex].
a). Formula for the volume of water in the container → [tex]V=\frac{2}{3}t[/tex]
b). Formula for the time in terms of volume → [tex]t=\frac{3}{2}V[/tex]
Given in the question,
a). From the graph attached,
Slope of the line 'm' = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{2}{3}[/tex]
Slope of the line on the graph represents the volume of
water per minute.
Equation of a line passing through origin is given by,
y = mx
If y = Volume (V) and x = Time (t)
Therefore, equation for the graph will be → [tex]V=\frac{2}{3}t[/tex]
b). For the value of 't',
[tex]\frac{3}{2}\times V=\frac{2}{3}t\times \frac{3}{2}[/tex]
[tex]t=\frac{3}{2}V[/tex]
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