a varies directly as b as the square of c and 4-?

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ScanSolve AI Tutor · Accepted Answer

Here's the solution to your variation problem. The problem states that a varies directly as b and as the square of c. This can be written as an equation: a = kbc² where k is the constant of variation. We are given that a=30 when b=0.5 and c=2. a) Find the value of k, the constant of variation. Step 1: Substitute the given values into the variation equation. 30 = k(0.5)(2)² Step 2: Simplify and solve for k. 30 = k(0.5)(4); 30 = k(2); k = 30/2; k = 15 The constant of variation is 15. b) Find the value of a when b=2 and c=3. Step 1: Use the constant of variation k=15 found in part (a) and the new values for b and c. a = 15(2)(3)² Step 2: Calculate the value of a. a = 15(2)(9); a = 30(9); a = 270 The value of a is 270. c) Find the values of c when a=300 and b=4. Step 1: Use the constant of variation k=15 and the given values for a and b. 300 = 15(4)c² Step 2: Simplify and solve for c². 300 = 60c²; c² = 300/60; c² = 5 Step 3: Take the square root of both sides to find c. Remember to include both positive and negative roots. c = ±√(5) The values of c are √(5) or −√(5).

A varies directly as b as the square of c and 4-?

Answers

Step-by-step solution

Part a· 2 steps

Substitute the given values into the variation equation.

Simplify and solve for $k$ .

Part b· 2 steps270

Use the constant of variation $k=15$ found in part (a) and the new values for $b$ and $c$ .

Calculate the value of $a$ .

Part c· 3 steps
$\sqrt{5} \text{ or } -\sqrt{5}$

Use the constant of variation $k=15$ and the given values for $a$ and $b$ .

Simplify and solve for $c^2$ .

Take the square root of both sides to find $c$ .

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A varies directly as b as the square of c and 4-?

Answers

Step-by-step solution

Part a· 2 steps

Substitute the given values into the variation equation.

Simplify and solve for kkk.

Part b· 2 steps270

Use the constant of variation k=15k=15k=15 found in part (a) and the new values for bbb and ccc.

Calculate the value of aaa.

Part c· 3 steps5 or −5\sqrt{5} \text{ or } -\sqrt{5}5​ or −5​

Use the constant of variation k=15k=15k=15 and the given values for aaa and bbb.

Simplify and solve for c2c^2c2.

Take the square root of both sides to find ccc.