the path of the rocket is represented by the equation y= root under(25-x)^2. the path of a missile designed to intrersect the path of the rocket is represented by the equation x = 3/2 root under (y). the value of x at the point of intersection is 3. what is the corresponding value of y?
sorry but i didn't find the key for root under so just wrote it down.... i hope that makes sense..... please it's due tomorrow. please help!
It does not make sense to me
the parabola opening to the left
y^2 = (25-x)^2
does not hit the parabola
x^2 = (9/4) y or y = (4/9) x^2
at x = 3
Oh no, you're in a root situation! Don't worry, I'm here to help. Let's simplify the equations and find the point of intersection.
Starting with the equation for the rocket's path, we have y = √(25 - x)^2.
Now, let's substitute the value of x = 3 into the equation for the missile's path:
3 = 3/2 √y.
To simplify this, let's get rid of the fraction:
2 * 3 = 3 * √y,
6 = 3√y.
Dividing both sides by 3, we have:
2 = √y.
To square both sides and eliminate the square root, we get:
4 = y.
So, the corresponding value of y at the point of intersection is 4.
Therefore, the rocket and missile paths intersect at the coordinates (3, 4).
I hope that helps, and good luck with your assignment!
To find the corresponding value of y at the point of intersection, we can substitute the given value of x = 3 into the equation x = (3/2) * √y. Let's solve for y step by step:
1. Start with the equation: x = (3/2) * √y
2. Substitute x = 3 into the equation: 3 = (3/2) * √y
3. Multiply both sides of the equation by 2/3 to isolate √y: (2/3) * 3 = √y
4. Simplify: 2 = √y
5. Square both sides of the equation to eliminate the square root: (2)^2 = (√y)^2
6. Simplify: 4 = y
Therefore, the corresponding value of y at the point of intersection is 4.
To find the corresponding value of y at the point of intersection, we can substitute the given value of x into the equation for the rocket's path.
Given:
Rocket's path equation: y = √[(25-x)^2]
Missile's path equation: x = (3/2)√y
Value of x at the point of intersection: x = 3
Substituting x = 3 into the missile's path equation:
3 = (3/2)√y
To solve for y, we need to isolate it on one side of the equation. Multiply both sides of the equation by 2/3:
2/3 * 3 = √y
2 = √y
To solve for y, we need to square both sides of the equation:
(2)^2 = (√y)^2
4 = y
Therefore, the corresponding value of y at the point of intersection is y = 4.