Find a set of parametric equations for y= -4x + 9 given the parameter t= Sqrt x-1.
Answer choices:
A) x(t) =t^2 + 1
y(t) =-4t^2 + 5
B) x(t)= t^2 - 1
y(t) =-4t^2 + 5
C) x(t) =t^2 + 1
y(t) =-4t^2 + 13
D) x(t) =t^2 -1
y(t) =-4t^2 + 13
Thanks!
If
t = √ ( x -1 )
then
t² = [ √ ( x -1 ) ]²
t² = x - 1
Add 1 to both sides
t² + 1 = x
x = t² +1
Put this value in equation:
y = - 4 x + 9
y = - 4 ( t² +1 ) + 9
y = - 4 t² - 4 + 9
y = - 4 t² + 5
Answer A
Well, well, well, let's solve this math puzzle with a touch of clownishness! We're given the equation y = -4x + 9, and we need to find its parametric equations using the parameter t = sqrt(x - 1).
To accomplish that, we can isolate x in the equation t = sqrt(x - 1):
t^2 = x - 1
Now, let's plug this back into the original equation for y:
y = -4x + 9
Substituting x with t^2 + 1, we get:
y = -4(t^2 + 1) + 9
Expanding this out a bit, we have:
y = -4t^2 - 4 + 9
Simplifying further, we find:
y = -4t^2 + 5
So, matching this to the answer choices, we can see that:
x(t) = t^2 + 1
y(t) = -4t^2 + 5
Thus, the correct answer is A) x(t) = t^2 + 1, y(t) = -4t^2 + 5. You did it, clown-genius!
To find the parametric equations for y = -4x + 9 given the parameter t = √(x - 1), we can start by solving for x in terms of t and then substituting that into the equation for y.
Given t = √(x - 1), we can solve for x as follows:
Square both sides of the equation:
t^2 = x - 1
Add 1 to both sides:
t^2 + 1 = x
Now that we have x in terms of t, we can substitute this expression into the equation for y = -4x + 9:
y = -4(t^2 + 1) + 9
Simplify the expression for y:
y = -4t^2 - 4 + 9
y = -4t^2 + 5
Therefore, the correct set of parametric equations is:
x(t) = t^2 + 1
y(t) = -4t^2 + 5
Hence, the answer choice is A) x(t) = t^2 + 1, y(t) = -4t^2 + 5.
To find the set of parametric equations for y = -4x + 9 given the parameter t = sqrt(x - 1), we need to eliminate x and express y in terms of t.
First, let's solve the given equation for x:
y = -4x + 9
Rearranging the equation, we get:
4x = -y + 9
x = (-y + 9)/4
Now substitute t = sqrt(x - 1) into the expression for x:
t = sqrt((-y + 9)/4 - 1)
Simplify the expression inside the square root:
t = sqrt((-y - 7)/4)
Square both sides of the equation to eliminate the square root:
t^2 = (-y - 7)/4
Multiply both sides by 4:
4t^2 = -y - 7
Rearrange the equation to express y in terms of t:
y = -4t^2 - 7
So the set of parametric equations is:
x(t) = t^2 - 1
y(t) = -4t^2 + 7
Comparing these equations with the given answer choices, we can see that the correct answer is B) x(t) = t^2 - 1 and y(t) = -4t^2 + 7.