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konstantin123 [22]

2 years ago

11

What property is shown by the equation? Column A Column B 1. 0 ÷ (–6) = 0 2. (–1) • (–9) = 9 3. 1 • (–18) = –18 4. A. Reciprocal

Property of Multiplication B. Identity Property of Division C. Division into Zero Property D. Identity Property of Multiplication E. Negative One Property of Multiplication

1 answer:

Ivanshal [37]2 years ago

5 0

I think it's E. The negative one property of multiplication. Each function is basically showing that multiplying/dividing two pluses makes a plus and multiplying/dividing one plus and one minus makes a minus etc!

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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

2 years ago

One mile is equal to 5,280 feet. What is the sum of the lengths of all 18 holes on the golf course in miles?

soldi70 [24.7K]

Answer:

the answer would be 4 Miles.

explanation:

We already know that 5,280 feet equals 1 Mile, and so we divide-

21,120 divided by 5,280, and that equals 4.

hope that made sense! I’m not very good with wording things! :)

8 0

2 years ago

A rabbit population doubles every 4 weeks. There are currently five rabbits in a restricted area. If t represents the time, in w

My name is Ann [436]

First, you have to find how many weeks are in 98 and to do so, you would divide it by 7. which turns out to be 14. If you divide 14 by 4 you'll find that their population will double 3 times, but not 3.5 because it is every 4 full weeks.
The equation will look like this, however, I'm not completely certain about the format. I'm using the formula for exponential growth
P(t)=r(2)^t
I did use t as weeks, but for every 4 weeks. R is the number of rabbits. If we were to input our information, we'd get:
P(3)=5(2)^3
If you work it out, you get 40 rabbits. In 14 weeks, the rabbits will double 3 times, so if we were to just figure it out without using the formula, we could double 5 which is 10, double it again, which is 20, and then double it a third time. which is 40.

6 0

2 years ago

The lunch lady has 12 pounds of lasagna left over.

bogdanovich [222]

Answer:

12

Step-by-step explanation: if she has 12 pounds lasagna and make 1 pounds she can make 12 pounds for 12 people? hope this help you ;]

5 0

2 years ago

At the beginning of the week, Josh had 323232 computer games, 133\33, percent as many computer games as Peter had. By the end of

Ronch [10]

Answer:

$Josh =24$

$Peter = 32$

Step-by-step explanation:

Given

Beginning of Week

$Josh = 32$

$Josh = 133\% * Peter$

First, we calculate the amount Peter has at the beginning of the week

$Josh = 133\% * Peter$

Make Peter the subject

$Peter = \frac{Josh}{133\%}$

$Peter = \frac{32}{133\%}$

$Peter = \frac{32}{1.33}$

$Peter = 24$

When Josh gave out 25%.

The number (n) of computers is:

$n = Josh * 25\%$

$n = 32 * 25\%$

$n = 8$

This means that Josh gave out 8 computers.

So, the amount they both have is:

$Josh =32 - 8$

$Josh =24$

$Peter = 24+8$

$Peter = 32$

7 0

1 year ago