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A step-by-step solution to translating joint variation statements into equations and finding the unknown variable. It includes examples and activities in various contexts, such as physics and chemistry. Students will learn how to determine the constant of proportionality and use it to find the unknown variable.
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Presented by: Paul Jorel R. Santos
Republic of the Philippines Department of Education Region IV โ A (CALABARZON) City Schools Division of Dasmariรฑas DASMARIรAS NATIONAL HIGH SCHOOL Congressional South Ave. Burol I, Dasmariรฑas City
Translate a joint variation statement into an equation and solve it.
a varies jointly as b and c. If ๐ = 18 when ๐ = 2 and ๐ = 3 , what is b if ๐ = 24 when ๐ = 6?
Joint variation is a type of variation that describes two direct variations in one statement. The variation statement ' y varies jointly as x and z ' is written in equation form as ๐ฆ = ๐๐ฅ๐ง.
a varies jointly as b and c. If ๐ = 18 when ๐ = 2 and ๐ = 3 , what is b if ๐ = 24 when ๐ = 6? Step 2: Find the constant of proportionality. Since ๐ = 18 , when ๐ = 2 and ๐ = 3. 18 = ๐( 2 )( 3 ) 18 = 6๐ ๐ = 3
a varies jointly as b and c. If ๐ = 18 when ๐ = 2 and ๐ = 3 , what is b if ๐ = 24 when ๐ = 6? Step 3: Rewrite the equation in Step 1 by substituting the value of k. Since ๐ = 3 and ๐ = ๐๐๐, hence ๐ = 3๐๐
In chemistry, the absolute temperature T of a perfect gas varies jointly as its pressure P and its volume V. At 400K, the pressure of the gas is 40 pounds per square inch (psi) and the volume is 100 cubic inches. Find the volume of the gas at 700 K when its pressure is 50 psi. Step 1: Write the correct equation. ๐ = ๐๐๐
Step 2: Find the constant of proportionality. Since ๐ = 400๐พ, when ๐ = 40๐๐ ๐ and ๐ = 100๐๐ข. ๐๐ ๐ = ๐๐๐ 400 = ๐( 40 )( 100 ) 400 = 4000๐ ๐ =
Step 4: Find the unknown by substituting to the equation in Step 3. ๐ =
The volume of the gas is 140 cubic inches.
Solve for the indicated variable in each of the following.
Solve the following:
