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Novosadov [1.4K]

3 years ago

6

An election ballot asks voters to select four city commissioners from a group of eight candidates. In how many ways can this be

done?

1 answer:

saul85 [17]3 years ago

6 0

The number of combinations of the 8 candidates taken 4 at a time is:
$8C4=\frac{8!}{4!4!}=70\ ways$

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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

Evaluate-2+7x^2-2x^3-8x+7x^4 at x=5

Murljashka [212]

Answer:

4262

Step-by-step explanation:

2 + 7x^2- 2x^3-8x +7x^4 at x = 5

= 2 + 7*(5)^2 - 2*(5)^3-8*5 +7*(5)^4

=2+175-250-40+4375

=4552-290

=4262

4 0

3 years ago

I will give brainliest

garri49 [273]

4(100)=400
400/1=400
You will need 400 stakes

7 0

2 years ago

Write the quadratic function f(x) = (3-x)2 in standard form.

Nitella [24]

Answer:

$y = - 2x + 6$

Step-by-step explanation:

$since \: f(x) = y \\$

then the equation reads:

$y = (3 - x)2 \\ y = 6 - 2x \\$

The standard form of an quadratic function is:

$y = mx + c \\$

So the answer is:

$y = mx + c \\ y = - 2x + 6$

6 0

2 years ago

In the United States, it is possible for someone to give a gift up to how much money per year to another person without that mon

Zielflug [23.3K]

Answer:

I believe the correct answer is $10,000. I'm not positive, though.

3 0

2 years ago

Read 2 more answers