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3 years ago

Which of the following does not represent a function? PLEASE HELP

Mathematics

1 answer:

svlad2 [7]3 years ago

8 0

Answer: The last one.

Step-by-step explanation: Using the vertical line test, if you place a vertical line at any point of a function it should only cross the line of the function once. since it would cross it twice on the last one, it is not a function.

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In this problem we consider an equation in differential form Mdx+Ndy=0. (4x+2y)dx+(2x+8y)dy=0 Find My= 2 Nx= 2 If the problem is

zheka24 [161]

Answer:

$f(x,y)=2x^2+4y^2+2xy=C_1\\\\Where\\\\y(x)=\frac{1}{4} (-x\pm \sqrt{-7x^2+C_1} )$

Step-by-step explanation:

Let:

$M(x,y)=4x+2y\\\\and\\\\N(x,y)=2x+8y$

This is and exact equation, because:

$\frac{\partial M(x,y)}{\partial y} =2=\frac{\partial N}{\partial x}$

So, define f(x,y) such that:

$\frac{\partial f(x,y)}{\partial x} =M(x,y)\\\\and\\\\\frac{\partial f(x,y)}{\partial y} =N(x,y)$

The solution will be given by:

$f(x,y)=C_1$

Where C1 is an arbitrary constant

Integrate $\frac{\partial f(x,y)}{\partial x}$ with respect to x in order to find f(x,y):

$f(x,y)=\int\ {4x+2y} \, dx =2x^2+2xy+g(y)$

Where g(y) is an arbitrary function of y.

Differentiate f(x,y) with respect to y in order to find g(y):

$\frac{\partial f(x,y)}{\partial y} =2x+\frac{d g(y)}{dy}$

Substitute into $\frac{\partial f(x,y)}{\partial y} =N(x,y)$

$2x+\frac{dg(y)}{dy} =2x+8y\\\\Solve\hspace{3}for\hspace{3}\frac{dg(y)}{dy}\\\\\frac{dg(y)}{dy}=8y$

Integrate $\frac{dg(y)}{dy}$ with respect to y:

$g(y)=\int\ {8y} \, dy =4y^2$

Substitute g(y) into f(x,y):

$f(x,y)=2x^2+4y^2+2xy$

The solution is f(x,y)=C1

$f(x,y)=2x^2+4y^2+2xy=C_1$

Solving y using quadratic formula:

$y(x)=\frac{1}{4} (-x\pm \sqrt{-7x^2+C_1} )$

4 0

3 years ago

Pythagorean Theorem with Known Legs

stepan [7]

you're given the pythagorean theorem, which is a^2 + b^2 = c^2.

what you're trying to find is ?, which is the number under the radical.

let's pretend one leg is a and the other is b.

a = 9

b = 10

so let's plug it into the equation. we get 9^2 + 10^2 = c^2

so that equals 81 + 100 = c^2

181 = c^2

so c will equal the square root of 181. therefore, ? = 181.

hope i helped! good luck.

5 0

2 years ago

Read 2 more answers

What is the equation of the line that passes through the points given in the table

Zepler [3.9K]

Answer:

B: y = -2x + 5

Step-by-step explanation:

-2 - 1 = -3

9 - 3 = 6

$\frac{6}{-3}$ = -2

gradient = -2

3 = 1 x -2 + c

3 = -2 + c

5 = c

y intercept = 5

equation = y = -2x + 5

so the answer is option b

7 0

3 years ago

E. Solve the Inequality

olganol [36]

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$\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}$

Solve the Inequality.

$\blue{\textsf{\textbf{\underline{\underline{Answer:-}}}}$

x<-4

$\blue{\textsf{\textbf{\underline{\underline{How\:to\:Solve:-}}}}$

First, add 6x on both sides:

-2x+3+6x<-13

Add the x's:

4x+3<-13

Now, subtract 3 on both sides:

4x<-13-3

4x<-16

Divide by 4 on both sides:

x<-4

So the values of x that are less than -4 will make the given inequality true.

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7 0

2 years ago

Chứng minh rằng A/(B/C)=(A/B) hợp ( A giao C)

n200080 [17]

Answer:

I like ya cut g

Step-by-step explanation:

hehehhehehhee

5 0

2 years ago