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!
Lets write an equation for each guy's shots and score:
4A + 2B = 18
3A + 3B = 21
To solve we multiply the first equation by -3 and the second by 2:
-12A - 6B = -54
6A + 6B = 42
--------------------
-12A + 0 = -12
A = 1
to find B we substitute in the first equation:
<span>4A + 2B = 18
</span><span>4(1) + 2B = 18
</span><span>4 + 2B = 18
</span>2B = 14
B = 7
therefore there were given 7 points in an arrow in B
Answer: 
Step-by-step explanation:
DIAMETER length = 6
radius length = 3
Area of the circle = 
The other number is -3.
Step-by-step explanation:
Step 1; First we develop formulae for the given information. A number is added with 3 and the resulting sum is multiplied by 4. This number is then divided by 2 and the quotient is 0. Assume the unknown number is x, then the given information is as follows
The quotient of 
is 0. So = 0.
Step 2; Now we solve the above equation. The denominator is taken to the RHS and the RHS remains zero.
= 0, 4(x+3)= 0, 4x+ 12 = 0, 4x = -12, x = 
= -3.
So the other number is -3.
