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:
$15
Step-by-step explanation:
Let's start by figuring out how much 1 cup of oil costs.
12 cups of oil is 36$
Let's set up a proportion.
12/36=1/x
Cross Multiply
12x=36
Divide both sides by 12.
x=3
1 cup of oil is $3.
Dinesh makes 5 batches of hummus, and each batch requires 1 cup of oil.
5*1=5
This means he needs 5 cups of oil.
5*3=15
He used $15 worth of oil in the 5 batches of his recipe.
However, since it is impossible to buy 5/12 bottles of oil, he would have needed to spend $36.
When you divide by 100 you are essentially moving the decimal of the number two places to the left. In undoing this you would have to move the decimal of the number two places to the right.
28.003 would then turn into 2,800.3
Unfortunately I cannot draw a chart on here but that is the best I can do.
5. You have correctly shown the decimal equivalents of the numbers in selection C. Those are in order. The decimal equivalents for selection D would be
... -1.33, -2.00, -1.00, -0.08, -0.07
The first of these is greater than the second of these, so this list is not in order. The correct choice is D.
6. √169 = 13, the only rational number in the lot. The correct choice is C.
8. All the numbers except the ones with radicals are rational numbers, so the appropriate choice is the one that lists the radicals only: G.
9. You have correctly plotted the points. When you connect them to make a geometric figure, you get a triangle that is 6 units high and 6 units wide. Its area will be half that of a square that is 6×6, so is 18 square units.
_____
The formula for the area of a triangle is
... A = (1/2)bh
where b is the base length of the triangle (6 units), and h is the height (6 units). Filling in the numbers you have, this is
... A = (1/2)·6·6 = 18 . . . . square units.
When you have a plot like this on a graph, it is usually pretty easy to see that the triangle area is half the area of a rectangle (or square) with the same height and width.
5+7-4=6
6-4=2
I’ve created two equations with no solution
