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3 years ago

Consider the curve defined by 2x2+3y2−4xy=36 2 x 2 + 3 y 2 − 4 x y = 36 .

Mathematics

1 answer:

8_murik_8 [283]3 years ago

5 0

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!

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The volume of the oblique cylinder is 24 ft3.

Assoli18 [71]

Answer:

A: The height of the cylinder is 3.4 ft.

C: The diameter of the cylinder is about 3 ft.

E: A right cylinder with the same height and radius as this oblique cylinder would also have a volume of 24 ft3.

Step-by-step explanation:

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3.<br> The perimeter of a square garden is 12 km. Find its area.

7nadin3 [17]

Answer:

the area of the garden is 9 square kilometers

Step-by-step explanation:

4s=12

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3 years ago

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Give an example of each of the following, or argue that such a request is impossible.

Masteriza [31]

Answer and Step-by-step explanation:

Solution:

(a) Let (bn) be a bounded sequence of (an) then, Bolzano- Weierstrass theorem,

(bn) contains a subsequence that is converges.

(b) The sequence :

Xn = 1 + (-1) n / 2 + 1/n

Clearly, (xn) does not contain 1 or 0.

If we take sequence (x2n), then it converges to 1 and when we take sequence (x2n+1),

Then it converges to 0.

1,1/2

1, 1/2, 1/3

1, 1/2, 1/3, 1/4

i.e

(xn) = (1,1/2, 1, 1/2, 1/3, …)

Then, the subsequence (xn) that is identically ½ in second column and 1/3 is third column and so on.

It has sub sequence that converges to every point in infinite set {1, 1/2, 1/3, 1/4, 1/5…}.

(d) The sequence

{1, 1/2, 1/3, 1/4, 1/5…}

if we take sequence of given set, then, this set converges to zero. This is not contained in it.

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3 years ago

The football team has a total of 350 jerseys. There are 154 medium-sized jerseys. What percent of the jerseys are medium-sized

KonstantinChe [14]

Answer:

Step-by-step explanation:

Given : The total number of jerseys = 350

The number of medium-sized jerseys = 154

Then, the percent of the jerseys are medium-sized jerseys will be :-

\begin{gathered}\dfrac{\text{Number of medium-sized jerseys }}{\text{Total jerseys}}\times100\\\\=\dfrac{154}{350}\times100\\\\=0.44\times100=44\%\end{gathered}

Total jerseys

Number of medium-sized jerseys

×100

350

154

×100

=0.44×100=44%

<h3>Therefore , the percent of the jerseys are medium-sized jerseys = 44%</h3>

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2 years ago

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Part 2 of me forgetting everything

Lunna [17]

Answer:

x = 15

Step-by-step explanation:

There are 2 triangles. The small triangle CDE has sides that are 8 and 20.

The big triangle CAB has sides 6+8 and 20 + x. Add the 6 and 8 which is 14. Create a proportion and cross multiply, divide, then solve for x.

$\frac{8}{20}=\frac{14}{20+x\\}\\\\8(20 + x) = 20(14)\\160 + 8x = 280\\160-160+8x=280-160\\8x= 120\\8x/8=120/8\\x=15$

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2 years ago