Identify the polar form of the linear equation 4x+3y=10.
x=rcos(theta),y=rsin(theta)
4x+3y=4rcos(theta)+3rsin(theta)=10
r=10/(4cos(theta)+3sin(theta)
I got it wrong
4cos(theta)+3sin(theta)=(10/r)
The only problem I can see is that you forgot a closing parentheses in your final answer. Without knowing how your answer was graded, I cannot say whether that caused you to get it wrong; but the rest of your math looks correct.
4x + 3y = 10
4rcos(theta) + 3rsin(theta) = 10
r = 10/(4cos(theta) + 3sin(theta))
To convert a linear equation into polar form, you need to first express the variables x and y in terms of r and theta.
Given the equation 4x + 3y = 10, let's rearrange it by isolating y:
3y = 10 - 4x
Now, we'll express y in terms of r and theta:
y = (10 - 4x) / 3
Since x is equal to r * cos(theta), we can substitute it in the equation:
y = (10 - 4(r * cos(theta))) / 3
Now, we simplify:
y = (10 - 4rcos(theta)) / 3
Therefore, the polar form of the linear equation 4x + 3y = 10 is:
r(3sin(theta)) + 4rcos(theta) = 10