x and y intercept
y=2x^3√9-x^2
y intercept, when x is zero...
x interctpt, when y is zero.
Solve each case.
i no but from there im lost
To find the x-intercept of a function, set y equal to zero and solve for x. Similarly, to find the y-intercept, set x equal to zero and solve for y.
Let's find the x-intercept first:
y = 2x^(3√(9-x^2))
To find the x-intercept, set y equal to zero:
0 = 2x^(3√(9-x^2))
Next, divide both sides of the equation by 2:
0/2 = x^(3√(9-x^2))/2
Simplifying further:
0 = x^(3√(9-x^2))/2
Since anything raised to the power of zero is equal to 1, we are left with:
1 = x^(3√(9-x^2))
To solve for x, we need to eliminate the exponent. Taking the cube root of both sides, we get:
∛1 = ∛x^(3√(9-x^2))
Simplifying further:
1 = x^(√(9-x^2))
Now, let's solve for the y-intercept:
Setting x equal to zero, we have:
y = 2(0)^(3√(9-0^2))
Simplifying:
y = 2(0)^(3√9)
Any number (except zero) raised to the power of zero is equal to 1. Therefore:
y = 2(1)
So the y-intercept is y = 2.
To summarize, the x-intercept is given by the solution to the equation x^(√(9-x^2)) = 1, while the y-intercept is y = 2.