Answer:
Step-by-step explanation:
y = csc x
y' = -cot x csc x
![y' = \dfrac{d}{dx} [\csc \sqrt{x}]](https://tex.z-dn.net/?f=%20y%27%20%3D%20%5Cdfrac%7Bd%7D%7Bdx%7D%20%5B%5Ccsc%20%5Csqrt%7Bx%7D%5D%20)
Answer:
Step-by-step explanation:
Given a curve defined by the function 2x²+3y²−4xy=36
The total differential of this function with respect to a variable x makes the function an implicit function because it contains two variables.
Differentiating both sides of the equation with respect to x we have:
4x+6ydy/dx-(4xd(y)/dx+{d(4x)/dx(y))} = 0
4x + 6ydy/dx -(4xdy/dx +4y) = 0
4x + 6ydy/dx - 4xdy/dx -4y = 0
Collecting like terms
4x-4y+6ydy/dx - 4xdy/dx = 0
4x-4y+(6y-4x)dy/dx = 0
4x-4y = -(6y-4x)dy/dx
4y-4x = (6y-4x)dy/dx
dy/dx = (4y-4x)/6y-4x
dy/dx = 2(2y-2x)/2(3y-2x)
dy/dx = 2y-2x/3y-2x proved!
Answer:
Length = 27.2
Width = 6.8
Step-by-step explanation:
P = L+L+W+W
68 = 4(L+L)+W+W
68 = 4(x+x)+x+x
68 = 4x+4x+x+x
68 = 10x
x = 6.8
L = 4x
L = 27.2
W = x
W = 6.8
68 = 27.2+27.2+6.8+6.8
68 = 68
(-1,1.5) because you add both ys and both xs then divide by two to find the middle
9514 1404 393
Answer:
179/495
Step-by-step explanation:
When the repeating decimal starts at the decimal point, the repeating digits can be turned into a fraction by putting them over the same number of 9s. That is, 0.61616161... is equivalent to 61/99.
Here, the repeating part is 1/10 that value, so is 61/990. This is added to the non-repeating part, which is 0.3 = 3/10.
Then the entire decimal is ...
0.361_61 = 3/10 + 61/990 = (297 +61)/990 = 358/990 = 179/495
