The variable A varies jointly with b and the square of c, and A = 9 when b and c are both 3. Find c when A = 48 and b =4

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ANJILYNPARANIN ANJILYNPARANIN

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The variable A varies jointly with b and the square of c, and A = 9 when b and c are both 3. Find c when A = 48 and b =4

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QUINZENIN QUINZENIN · Answer 1

JOINT VARIATION

Direction: The variable A varies jointly with b and the square of c, and A = 9 when b and c are both 3. Find c when A = 48 and b = 4.

Answer:

[tex]\Large \blue{\bold{c = 36.000000004}}[/tex]

Step-by-step explanation:

Step 1: Write the correct equation. Joint variation problems are solved using the equation z=kxy if z varies jointly as x and y.

[tex]\large \bold{A = kbc^{2}}[/tex]

Step 2: Use the information given in the problem to find the value of k. In this case, you need to find k if A = 9 when b and c are both 3.

[tex]A = kbc² \\ 9 = k(3)(3²) \\ 9=27k \\ \frac{9}{27} = \frac{ \cancel{27}k}{ \cancel{27}} \\ \bold{\frac{1}{3} = k}[/tex]

Therefore, the constant of variation k is ⅓.

Step 3: Rewrite the equation from step 1 substituting in the value of k found in step 2.

[tex]\large \bold{A = bc²}[/tex]

Step 4: Use the equation found in step 3 and the remaining information given in the problem to answer; in this case, you need to find c when A = 48 and b = 4

[tex]A = \frac{1}{3}bc² \\ 48 = (\frac{1}{3})(4)c² \\ 48=1.3333333332c² \\ \frac{48}{1.3333333332} = \frac{\cancel{1.3333333332}c²}{\cancel{1.3333333332}} \\ \bold{36.000000004 = c²}[/tex]

Thus, the value of c is equal to 36.000000004.

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