Advertisements
Advertisements
Question
A family is using Liquefied petroleum gas (LPG) of weight 14.2 kg for consumption. (Full weight 29.5kg includes the empty cylinders tare weight of 15.3kg.). If it is used with constant rate then it lasts for 24 days. Then the new cylinder is replaced. Find the equation relating the quantity of gas in the cylinder to the days
Solution
Find the equation relating the quantity of gas in the cylinder to the days.
Given Total weight of cylinder = 29.5 kg
Weight of the gas inside the cylinder = 14.2 kg
Let x denote the number of days of consumption of the gas, y denote the quantity of gas inside a cylinder.
Initially x = 0 then y = 14.2
The corresponding point is (0, 14.2)
The gas inside the cylinder lasts for 24 days
∴ When x = 24
We have y = 0
The corresponding point is (24, 0)
∴ The linear relation between the quantity of gas in the cylinder to the number of days of consumption is the equation of the line joining the points (0, 14.2) and (24, 0).
`(x - 0)/(24 - 0) = (y - 14.2)/(0 - 14.2)`
`x/24 = (y - 14.2)/(- 14.2)`
y – 14.2 = `- 14.2 xx x/24`
y = `(- 14.2)/24 x + 14.2`
y = `- 142/240 x + 14.2`
y = `- 71/120 x + 14.2`
0 ≤ x ≤ 24
which is the required relation
APPEARS IN
RELATED QUESTIONS
Find the slope of the following line which passes through the points:
G(7, 1), H(−3, 1)
Find the acute angle between the X-axis and the line joining points A(3, −1) and B(4, −2).
Answer the following question:
Find the value of k the point P(1, k) lies on the line passing through the points A(2, 2) and B(3, 3)
Answer the following question:
Find the equation of the line containing the point T(7, 3) and having inclination 90°.
Answer the following question:
Line through A(h, 3) and B(4, 1) intersect the line 7x − 9y − 19 = 0 at right angle Find the value of h
Find the equation of the lines passing through the point (1, 1) and the perpendicular from the origin makes an angle 60° with x-axis
The normal boiling point of water is 100°C or 212°F and the freezing point of water is 0°C or 32°F. Find the value of F for 38°C
An object was launched from a place P in constant speed to hit a target. At the 15th second, it was 1400 m from the target, and at the 18th second 800 m away. Find the distance between the place and the target
Find the equation of the line, if the perpendicular drawn from the origin makes an angle 30° with x-axis and its length is 12
Find the equation of the straight lines passing through (8, 3) and having intercepts whose sum is 1
Show that the points (1, 3), (2, 1) and `(1/2, 4)` are collinear, by using concept of slope
A straight line is passing through the point A(1, 2) with slope `5/12`. Find points on the line which are 13 units away from A
In a shopping mall there is a hall of cuboid shape with dimension 800 × 800 × 720 units, which needs to be added the facility of an escalator in the path as shown by the dotted line in the figure. Find the heights at which the escalator changes its direction
Choose the correct alternative:
Straight line joining the points (2, 3) and (−1, 4) passes through the point (α, β) if
The distance of the origin from the centroid of the triangle whose two sides have the equations. x – 2y + 1 = 0 and 2x – y – 1 = 0 and whose orthocenter is `(7/3. 7/3)` is ______.
A point on the straight line, 3x + 5y = 15 which is equidistant from the coordinate, axes will lie only in ______.
