when y varies directly at the square of X, the variation equation is written y= kx square, where K is constitution
(a) given that y=50 when x=10,find the value of K.
(b) calculate the value of y when X= 30
mmmh, they gave you the equation
y = kx^2
when y = 50, x = 10 , so....
50 = k(100)
k = 1/2
your equation is y = (1/2)x^2
now just plug in x = 30
in your head you can do y = 900/2 or 450
To find the value of K, we can use the given information in the equation y = kx^2.
(a) Given that y = 50 when x = 10, we can substitute these values into the equation and solve for K.
50 = k * (10)^2
50 = k * 100
Dividing both sides of the equation by 100, we get:
k = 50/100
k = 0.5
Therefore, the value of K is 0.5.
(b) To calculate the value of y when x = 30, we can use the value of K obtained in part (a) and substitute it into the equation.
y = k * x^2
y = 0.5 * (30)^2
y = 0.5 * 900
y = 450
Therefore, when x = 30, the value of y is 450.
To find the value of k in the variation equation y = kx^2, we can substitute the given values of y and x and solve for k.
(a) Given y = 50 when x = 10, we can substitute these values into the equation:
50 = k * 10^2
To solve for k, divide both sides of the equation by 10^2:
50 / 100 = k
Simplifying further:
0.5 = k
So, the value of k is 0.5.
(b) Now that we have the value of k, we can use it to find the value of y when x = 30. Substituting these values into the equation:
y = k * x^2
y = 0.5 * 30^2
Calculating this expression:
y = 0.5 * 900
y = 450
Therefore, when x = 30, the value of y is 450.