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:
y= 5x + 3
Step-by-step explanation:
This is because you solve for slope, which is 5, then plug that into point slope form to get:
y - 8 = 5(x - 1)
y - 8 = 5x - 5
y = 5x + 3.
Answer:
a x a x a x a x a x a x a
Step-by-step explanation:
a^3 is three a's being multiplied by each other. a^4 is four a's being multiplied by each other
Answer:
There are 165 ways to distribute the blackboards between the schools. If at least 1 blackboard goes to each school, then we only have 35 ways.
Step-by-step explanation:
Essentially, this is a problem of balls and sticks. The 8 identical blackboards can be represented as 8 balls, and you assign them to each school by using 3 sticks. Basically each school receives an amount of blackboards equivalent to the amount of balls between 2 sticks: The first school gets all the balls before the first stick, the second school gets all the balls between stick 1 and stick 2, the third school gets the balls between sticks 2 and 3 and the last school gets all remaining balls.
The problem reduces to take 11 consecutive spots which we will use to localize the balls and the sticks and select 3 places to put the sticks. The amount of ways to do this is
As a result, we have 165 ways to distribute the blackboards.
If each school needs at least 1 blackboard you can give 1 blackbooard to each of them first and distribute the remaining 4 the same way we did before. This time there will be 4 balls and 3 sticks, so we have to put 3 sticks in 7 spaces (if a school takes what it is between 2 sticks that doesnt have balls between, then that school only gets the first blackboard we assigned to it previously). The amount of ways to localize the sticks is
. Thus, there are only 35 ways to distribute the blackboards in this case.
Answer:
14
Step-by-step explanation:
-2x^3 - 2x^2 - 4x-2
Let x = -2
-2 (-2)^3 - 2 (-2)^2 -4(-2) -2
Exponents first
-2 (-8) -2 (4) -4(-2) -2
Then multiply
16 -8 +8 -2
Then add and subtract
14