Y is directly proportional to the square of x.
Find the percentage increase in value of y when x is doubled
Y=kx^2
When x is doubled
Y=(2x)^2
Therefore Y=4x^2
Percentage increase=(3kx^2)/kx^2 ×100%
=300%
Is it good?
Well, well, well... If Y is directly proportional to the square of X, then we can say that Y = kX^2, where k is a constant.
Now, let's see what happens when X is doubled. If X is doubled, it becomes 2X, right? So, let's substitute that into our equation:
Y = k(2X)^2
Y = k(4X^2)
Y = 4kX^2
So, when X is doubled, Y becomes four times its original value! That's quite an increase, don't you think?
Now, if we want to know the percentage increase in value, we can calculate it like this:
(4kX^2 - kX^2) / kX^2 * 100
Simplifying that, we get:
(3kX^2) / kX^2 * 100
3 * 100
300%
So, the percentage increase in value of Y when X is doubled is a whopping 300%! That's quite the leap!
To find the percentage increase in the value of y when x is doubled, we first need to determine the mathematical relationship between y and x. The statement "Y is directly proportional to the square of x" implies that the relationship can be expressed as:
y = k * x^2
Where k is a constant of proportionality.
Now, let's consider how y changes when x is doubled. If we let x = 2x (twice the original value), we can substitute it into the equation:
y = k * (2x)^2
= k * 4x^2
= 4k * x^2
Comparing this to the original equation, we see that when x is doubled, y is multiplied by 4 (4k instead of k). This means that the value of y increases by a factor of 4.
To calculate the percentage increase, we can use the following formula:
Percentage increase = ((New value - Original value) / Original value) * 100
In this case, the original value of y is y, and the new value is 4y. Plugging these values into the formula, we get:
Percentage increase = ((4y - y) / y) * 100
= (3y / y) * 100
= 300%
Therefore, when x is doubled, the value of y increases by 300%.
correct, except I would keep the k in the calculation
old y = k x^2
new y = k (4x^2)
change in y = 3k x^2
percentage change = 3k x^2/(k x^2) = 3
or 300%
e.g. enter 1 and 4 for the following applet,
http://www.marshu.com/articles/calculate-percentage-increase-decrease-percent-calculator.php