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Translate a combined variation statement into an equation and solve it
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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 combined variation statement into an equation and solve it.
It is given that ๐ varies directly as ๐ and inversely as ๐. If ๐ = 16 when ๐ = 4 and ๐ = 3 , what is c when ๐ = 24 and ๐ = 6?
Combined variation is a type of variation that describes direct and inverse variations in the same statement. Combined variation commonly stated as ' y varies directly as x and inversely as z '. It is written in equation form as ๐ฆ = ๐๐ฅ ๐ง , where k is the constant of proportionality.
Step 2: Find the constant of proportionality ๐. Since ๐ = 16 , when ๐ = 4 and ๐ = 3. ๐ =
Step 3: Rewrite the equation in Step 1 by substituting the value of k. Since ๐ = 12 and ๐ = ๐๐ ๐ , hence ๐ =
The volume V of wood in a tree varies directly as its height h and inversely as the square of its girth g. If the volume of a tree is 140 cubic meters if its height is 20 meters and its girth is 2 meters, what is the height of a tree with a volume of 500 cubic meters and a girth of 3 meters? Step 1: ๐ = ๐โ ๐ 2
Step 2: What is the value of k? If the volume of a tree is 140 cubic meters if its height is 20 meters and its girth is 2 meters. ๐ =
2 140 =
2
Step 3: From step 1 we have ๐ = ๐โ ๐ 2 and from step 2 we have ๐ = 28. Combining this we have ๐ =
2
What is the height of a tree with a volume of 500 cubic meters and a girth of 3 meters? Step 4: Find the unknown by substituting to the equation in Step 3. ๐ =
2 500 =
2
Solve the ff.
Solve the following:
