Answer:
a. dy/dx = -2/3
b. dy/dx = -28
Step-by-step explanation:
One way to do this is to assume that x and y are functions of something else, say "t", then differentiate with respect to that. If we write dx/dt = x' and dy/dt = y', then the required derivative is y'/x' = dy/dx.
a. x'·y^3 +x·(3y^2·y') = 0
y'/x' = -y^3/(3xy^2) = -y/(3x)
For the given point, this is ...
dy/dx = -2/3
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b. 2x·x' +x^2·y' -2x'·y^3 -2x·(3y^2·y') + 0 = 2x' + 2y'
y'(x^2 -6xy^2 -2) = x'(2 -2x +2y^3)
y'/x' = 2(1 -x +y^3)/(x^2 +6xy^2 -2)
For the given point, this is ...
dy/dx = 2(1 -0 +27)/(0 +0 -2)
dy/dx = -28
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The attached graphs show these to be plausible values for the derivatives at the given points.
The volume of the prism is 144 ft^3. If we use the letter V to represent volume, the formula for the volume of a rectangular prism is V=length*width*height. When you plug in the numbers, the equation is V=12*6*2. When you multiply these three numbers together, you get 144. Because you are finding the volume, your units are cubed, so your answer is 144 ft^3. I have attached an image of this problem written out (I’m sorry if the image is bad, I drew it on my phone). If you need any more help or any clarification, please let me know and I will be happy to help!
Answer:
A. LCM of 6,9, and 15 is 90.
B. LCM of 3,12, and 16 is 48.
C. LCM of 8,9, and 12 is 72.
D. LCM of 24 and 18 is 72.
E. LCM of 21 and 28 is 84.
F. LCM of 19 and 42 is 798.
Step-by-step explanation:
Hope this helps! :)
300 milliliters would be more appropriate for a soup bowl :)
180°=triangle
360°=quadrangle
180°*34+180=6300°