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marshall27 [118]
2 years ago
14

Find two numbers who have a sum of 21 and a product of 104.

Mathematics
1 answer:
sergeinik [125]2 years ago
8 0

The  two numbers are 8 and 13 and the system of equations are x + y = 21 and xy = 104

<h3>System of equations</h3>

Let the two unknown numbers be x and y

If the sum of the numbers is 21, hence;

x + y = 21

x = 21 - y

If the product is 104, then;

xy = 104
(21-y)y = 104

21y - y^2 = 104
y^2-21y + 104 = 0

Factorize the result

y^2-8y - 13y+ 104 = 0
y(y-8) - 13()y-8) = 0
y = 13 and 8

Hence the two numbers are 8 and 13 and the system of equations are x + y = 21 and xy = 104

Learn more on system of equation here:  brainly.com/question/847634

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Step-by-step explanation:

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Apply green’s theorem to evaluate the integral 3ydx 2xdy
Ne4ueva [31]

The value of the integral 3ydx+2xdy using Green's theorem be - xy

The value of    \int\limits_c 3ydx+2xdy  be -xy

<h3>What is Green's theorem?</h3>

Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D bounded by C.

If M and N are functions of (x, y) defined on an open region containing D and having continuous partial derivatives there, then

\int\limits_c Mdx+Ndy = \int\int\〖(N_{x}-M_{y}) \;dxdy

Using green's theorem, we have

\int\limits_c Mdx+Ndy = \int\int\〖(N_{x}-M_{y}) \;dxdy ............................... (1)

Here N_{x} = differentiation of function N w.r.t. x

          M_{y}= differentiation of function M w.r.t. y

Given function is: 3ydx + 2xdy

On comparing with equation (1), we get

M = 3y, N = 2x

Now, N_{x} = \Luge\frac{dN}{dx}

               = \frac{d}{dx} (2x)

              = 2

and, M_{y} = \Huge\frac{dM}{dy}

             = \frac{d}{dy} (3y)

             = 3

Now using Green's theorem

= \int\int\〖(2 -3) dx dy

= \int\int\ -dxdy

= -\int\ x dy

=-xy

The value of  \int\limits_c 3ydx+2xdy  be -xy.

Learn more about Green's theorem here:

brainly.com/question/14125421

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