+ y = -1 ⇒ y = 
- 1
To graph this line, plot a point at the y-intercept (0, -1), than plot the next point using the rise over run from the slope 
by counting up 1 and to the right 3 of the y-intercept. This gives you a second point of (3. 0). Draw a line through those two coordinates.
Answer: Plot (0, -1) and (3, 0) and draw a line through them.
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y = 4 + ⇒ y = + 4
Same as above. Plot the y-intercept (0, 4) and then use rise over run from the slope to plot (3, 5).
Answer: Plot (0, 4) and (3, 5) and draw a line through them.
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You should end up with two PARALLEL lines. Since the lines never intersect, there are no solutions to this system of equations.
Answer: No Solution
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dy
Find —— for an implicit function:
dx
cos(xy) = 3x + 1.
First, differentiate implicitly both sides with respect to x. Keep in mind that y is not just a variable, but it is also a function of x, so you have to use the chain rule there:
![\mathsf{\dfrac{d}{dx}\big[cos(xy)\big]=\dfrac{d}{dx}(3x+1)}\\\\\\ \mathsf{-\,sin(xy)\cdot \dfrac{d}{dx}(xy)=\dfrac{d}{dx}(3x)+\dfrac{d}{dx}(1)}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cdfrac%7Bd%7D%7Bdx%7D%5Cbig%5Bcos%28xy%29%5Cbig%5D%3D%5Cdfrac%7Bd%7D%7Bdx%7D%283x%2B1%29%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7B-%5C%2Csin%28xy%29%5Ccdot%20%5Cdfrac%7Bd%7D%7Bdx%7D%28xy%29%3D%5Cdfrac%7Bd%7D%7Bdx%7D%283x%29%2B%5Cdfrac%7Bd%7D%7Bdx%7D%281%29%7D)
Apply the product rule to differentiate that term at the left-hand side:
![\mathsf{-\,sin(xy)\cdot \left[\dfrac{d}{dx}(x)\cdot y+x\cdot \dfrac{dy}{dx}\right]=3+0}\\\\\\ \mathsf{-\,sin(xy)\cdot \left[1\cdot y+x\cdot \dfrac{dy}{dx}\right]=3}\\\\\\ \mathsf{-\,sin(xy)\cdot \left[y+x\cdot \dfrac{dy}{dx}\right]=3}](https://tex.z-dn.net/?f=%5Cmathsf%7B-%5C%2Csin%28xy%29%5Ccdot%20%5Cleft%5B%5Cdfrac%7Bd%7D%7Bdx%7D%28x%29%5Ccdot%20y%2Bx%5Ccdot%20%5Cdfrac%7Bdy%7D%7Bdx%7D%5Cright%5D%3D3%2B0%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7B-%5C%2Csin%28xy%29%5Ccdot%20%5Cleft%5B1%5Ccdot%20y%2Bx%5Ccdot%20%5Cdfrac%7Bdy%7D%7Bdx%7D%5Cright%5D%3D3%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7B-%5C%2Csin%28xy%29%5Ccdot%20%5Cleft%5By%2Bx%5Ccdot%20%5Cdfrac%7Bdy%7D%7Bdx%7D%5Cright%5D%3D3%7D)
Now, multiply out the terms to get rid of the brackets at the left-hand
dy
side, and then isolate —— :
dx
and there it is.
I hope this helps. =)
Tags: <span><em>implicit function derivative implicit differentiation chain product rule differential integral calculus</em>
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Answer:
b.) distance north or south of the equator
Step-by-step explanation:
Lines of latitude are horizontal lines parallel with the equator.
The equator is the central line of latitude, and latitude is measured north or south of the equator.
Answer: b.) distance north or south of the equator
1. She earns 300 dollars an hour
2. He will be paid 180 dollars
3. She pays 26,150 dollars
