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2 years ago

14

on average 1 1/3 bushels od seed are needed to plant 1 arce of wheat. how many bushels of seed would be required to pay it arces

?

1 answer:

xenn [34]2 years ago

5 0

Answer:

4/3 x 30/1=120/3

120/3=40

40 bushels of seed would be needed to plant 30 acres of wheat.

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Consider the following differential equation. x^2y' + xy = 3 (a) Show that every member of the family of functions y = (3ln(x) +

Veronika [31]

Answer:

Verified

$y(x) = \frac{3Ln(x) + 3}{x}$

$y(x) = \frac{3Ln(x) + 3 - 3Ln(3)}{x}$

Step-by-step explanation:

Question:-

- We are given the following non-homogeneous ODE as follows:

$x^2y' +xy = 3$

- A general solution to the above ODE is also given as:

$y = \frac{3Ln(x) + C }{x}$

- We are to prove that every member of the family of curves defined by the above given function ( y ) is indeed a solution to the given ODE.

Solution:-

- To determine the validity of the solution we will first compute the first derivative of the given function ( y ) as follows. Apply the quotient rule.

$y' = \frac{\frac{d}{dx}( 3Ln(x) + C ) . x - ( 3Ln(x) + C ) . \frac{d}{dx} (x) }{x^2} \\\\y' = \frac{\frac{3}{x}.x - ( 3Ln(x) + C ).(1)}{x^2} \\\\y' = - \frac{3Ln(x) + C - 3}{x^2}$

- Now we will plug in the evaluated first derivative ( y' ) and function ( y ) into the given ODE and prove that right hand side is equal to the left hand side of the equality as follows:

$-\frac{3Ln(x) + C - 3}{x^2}.x^2 + \frac{3Ln(x) + C}{x}.x = 3\\\\-3Ln(x) - C + 3 + 3Ln(x) + C= 3\\\\3 = 3$

- The equality holds true for all values of " C "; hence, the function ( y ) is the general solution to the given ODE.

- To determine the complete solution subjected to the initial conditions y (1) = 3. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

$y( 1 ) = \frac{3Ln(1) + C }{1} = 3\\\\0 + C = 3, C = 3$

- Therefore, the complete solution to the given ODE can be expressed as:

$y ( x ) = \frac{3Ln(x) + 3 }{x}$

- To determine the complete solution subjected to the initial conditions y (3) = 1. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

$y(3) = \frac{3Ln(3) + C}{3} = 1\\\\y(3) = 3Ln(3) + C = 3\\\\C = 3 - 3Ln(3)$

- Therefore, the complete solution to the given ODE can be expressed as:

$y(x) = \frac{3Ln(x) + 3 - 3Ln(3)}{y}$

6 0

3 years ago

Find the slope of every line that is parallel to the graph of the equation. Y= 1/2x+4

Ostrovityanka [42]

For a line to be parallel it has to have the same slope as the original line. so the slope is 1/2

5 0

3 years ago

Find the domain of the function.

timurjin [86]

When taking square roots, you can't take square roots of negative roots of negative numbers. So, what will work for the domain of u(x) is what makes u(x) zero or more. We can make an inequality for that.

u(x) ≥ 0.

$\sqrt{9x+27} \geq 0$

9x + 27 ≥ 0 by squaring both sides

9x ≥ -27

x ≥ -3

So the domain of the function is when x ≥ -3 is true.

5 0

3 years ago

Division expression for fraction 5/4

Ede4ka [16]

Division expression for fraction 5/4 for is 4 divided by 4 which is .8

8 0

3 years ago

Trent's salary used to be $143,020. After changing the amount of time he works, he has begun earning $78,661. By what percent di

svlad2 [7]

Answer:

The salary decreased by 45%

Step-by-step explanation:

Given,

The previous salary of Trent is $143,020

The current salary of Trent is $78,661

The decrease in salary is ($143,020 - $78,661) = $64,359

When he used to get $143,020, the decrease in salary is = $64,359

When he used to get $1, the decrease in salary is = $64,359/$143,020

When he used to get $100, the decrease in salary is = $(64,359/143,020)*100

= 45%

Therefore, there is a decrease in salary by 45%.

6 0

3 years ago