Question

P varies directly as the square of q and p=12 when q=3, find the value of p when q=5

Answer 1

Answer: - The value of P is = 100/3, when Q is =5.

Detailed solution: -

Given: -

P varies directly as square of Q.

Therefore,

P is proportional to Q².

So,

P = KQ², where K is constant in the place of the proportionality.

So,

Now,

Given is P = 12 when Q = 3.

Then,

That means,

$P = KQ^2\\\\12=K*3^2\\\\12=K*9\\\\\frac{12}{9} =K\\\\\frac{4}{3} =K$

Therefore,

K = 4/3

If Q = 5 then, P =?

$P=KQ^2\\\\P=\frac{4}{3} *5^2\\\\P=\frac{4}{3}*25\\\\ P= \frac{100}{3}$

Therefore,

When Q = 5, then P = 100/3

To know more about the topic, go to the given links: -

https://brainly.in/question/35445641

https://brainly.in/question/32081935

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Answer 2

When q = 5, the value of p is 100/3.

Given:

p varies directly with q²

When p = 12, q = 3

To find:

The value of p when q = 5

Solution:

Two quantities are said to be directly proportional to one another if they are at a constant ratio called the proportionality constant.

According to the given data,

p ∝ q²

=> p = kq² where k is the proportionality constant

=> p / q² = k ...(i)

When p = 12, q = 3.

Substituting the value of p and q in equation (i), we get:

12 / 3² = k

=> k = 12/9

=> k = 4/3

When q = 5 and k = 4/3,

p / 5² = 4/3

=> p = 4/3 x 25

=> p = 100/3

Hence, when q = 5, the value of p is 100/3.

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