Mathematics, 06.04.2020 18:29 repirce9141

The distance a car can travel on a certain amount of fuel varies inversely with its speed. If a car traveling 50 mph can travel 300 miles on 10 gallons of fuel, how far could the car travel on 10 gallons of fuel at 60 mph?

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Answer from: abigailstolp

2500 miles

Step-by-step explanation:

Since the distance of the car varies inversely with its speed, the distance can be expressed as follows:

$d = \frac{g*a}{s}$ (1)

Where:

d: is the distance

s: is the speed of the car

g: is the gallons of fuel

a: is a constant of proportionality

With the first values, we can find the constant a.

We have:

d = 300 milles

s = 50 mph

g = 10 gallons

Hence, a is:

$a = \frac{d*s}{g} = \frac{300 m*500 m/h}{10 g} = 15000 m^{2}g^{-1}h^{-1}$

Now, we can find the distance that the car can travel on 10 gallons of fuel at 60 mph:

$d = \frac{g*a}{s} = \frac{10 g*15000 m^{2}g^{-1}h^{-1}}{60 m/h} = 2500 m$

Therefore, the car can travel 2500 miles on 10 gallons of fuel at 60 mph.

I hope it helps you!

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

Answer from: Quest

answer: 1 box of pens at the store ? ? pens in the box

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