Question

if y varies directly as the square root of x, find the percentage change in y when x is increased by 21%

Answer 1

Answer:

10%

Step-by-step explanation:

y =k √x

here k is proportional constant

y = k √(1.21x )

y = 1.1k √x

increase = 0.1 k√x

increase% = 0.1k√x/ k√x *100 = 10%

% change = 10%

Answer 2

Answer:

y is increased by 10%.

Step-by-step explanation:

Given,

y varies directly as the square root of x,

i.e. y ∝ √x

y = k√x

Where, k is the constant of proportionality,

If x increased by 21%,

Its new value = x + 21% of x = x + 0.21x = 1.21x,

So, new value of y = k√1.21x = 1.1k√x,

$\because \frac{\text{New value of y-Original value of y}}{\text{Original value of y}}\times 100$

$=\frac{1.1k\sqrt{x}-k\sqrt{x}}{k\sqrt{x}}\times 100$

$=\frac{(1.1-1)k\sqrt{x}}{k\sqrt{x}}\times 100$

$=\frac{0.1}{1}\times 100$

= 10%

Hence, y is increased by 10%.

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