Question

y is directly proportional to (x + 2)2.
When x = 8, y = 250.
Find y when x = 4.

Answer 1

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GIVEN THAT:-

$&#10144$ y is directly proportional to (x + 2)2. When x = 8, y = 250.

We have to find the value of y when x = 4

SOLUTIONS:-

• Given y is directly proportional to (x+2)2

$&#10144$ y = K (x+2)2

where K = propertional constant

Now when x = 8 , y = 250

$&#10230 \: \: y = K(x + 2)2 \: \: \: \: \\ \\ &#10230 \: \: 250 = K(8 + 2)2 \\ \\ &#10230 \: \: 250 = K \times 20 \: \: \: \: \: \: \\ \\ &#10230 \: \: K = \frac{\cancel{250}}{\cancel{20}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ &#10230 \: \: K = 12.5 \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Now the value of propertional constant K = 12.5

• Now the value of y when x = 4

$&#10230 \: \: y = K(x + 2)2 \: \: \: \\ \\ &#10230 \: \: y = 12.5(4 + 2)2 \\ \\ &#10230 \: \: y = 25 \times 6 \: \: \: \: \: \: \: \: \: \: \\ \\ &#10230 \: \: y = 150 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$&#10144$ The value of y = 150