Troubleshooting an Equation of the Curve with y Intercept 4

Thread starter beanryu
Start date Apr 25, 2006
Tags

Curve Troubleshooting

In summary, the y-intercept of 4 in an equation of a curve represents the point where the curve intersects with the y-axis. To find the y-intercept, you can set x to 0 and solve for y or graph the equation. If the y-intercept is negative, it means the curve intersects below the origin. The y-intercept can also be 0, in which case the equation is in the form of y = mx. The y-intercept can give an idea of the overall shape of the curve, but other factors like slope and degree of the polynomial also play a role.

Apr 25, 2006

beanryu

Find an equation of the curve that satisfies

dy/dx = 88yx^(10)
and whose y intercept is 4

dy/y = 88x^(10)dx

integral both sides

ln(y) = 8x^(11)
y = e^(8x^(11))+C

put x = 0 into the equation
I got C = 3.

Why am I wrong?

Physics news on Phys.org

Apr 25, 2006

AKG

Science Advisor

Homework Helper

Because you're supposed to add the constant of integration C right after you integrate, and THEN exponentiate both sides.

Apr 25, 2006

beanryu

THanx dude!

FAQ: Troubleshooting an Equation of the Curve with y Intercept 4

What does the y-intercept of 4 represent in an equation of a curve?

The y-intercept of 4 represents the point where the curve intersects with the y-axis, or where the value of y is equal to 4. This point is important because it gives us a reference point for the curve and can help us determine the general shape and direction of the curve.

How do I find the y-intercept of an equation of a curve?

To find the y-intercept of an equation of a curve, set the value of x to 0 and solve for y. This will give you the y-coordinate of the point where the curve intersects with the y-axis. Alternatively, you can also graph the equation and visually determine the y-intercept.

What if the y-intercept is a negative value?

If the y-intercept is a negative value, it simply means that the curve intersects with the y-axis below the origin. This does not change the method for finding the y-intercept, and you can still set x to 0 and solve for y to find the y-coordinate of the point of intersection.

Can the y-intercept of an equation of a curve be 0?

Yes, the y-intercept of an equation of a curve can be 0. This would mean that the curve intersects with the y-axis at the origin, or the point (0,0). In this case, the equation of the curve would be in the form of y = mx, where m is the slope of the line.

How does the y-intercept affect the overall shape of the curve?

The y-intercept can give us an idea of the general shape and direction of the curve. For example, if the y-intercept is a positive value, the curve will likely have a positive slope and increase as x increases. If the y-intercept is a negative value, the curve will likely have a negative slope and decrease as x increases. However, the y-intercept alone cannot determine the shape of the entire curve, as other factors such as the slope and degree of the polynomial may also play a role.