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2 years ago

I need help with number 12

Mathematics

1 answer:

fomenos2 years ago

7 0

Ok so when the divisor get larger, the quotient gets smaller.
For example, 15 ÷ 3 = 5. If we make the divisor larger, you can see the quotient get smaller. 15 ÷ 5 = 3.
The same thing goes for the other way around. If the divisor gets smaller, the quotient gets larger. Hope I helped!

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Chris is behind in 9 classes of school he has a total time of 25 days to make up 75 hours and 4 minutes worth of late work how m

Vlad1618 [11]

Answer:

Step-by-step explanation:

First, convert the 4 mins into hours by dividing by 60;

4/60 =0.067

Add 0.067 to 75 hrs to get the total = 75+0.067 = 75.067

Therefore the total time Chris needs to make up for is 75.067 hrs

Total number of days Chris has = 25

Next,

IF in 25 days = he can cover 75.067hrs

then in 1 day he will cover = (1 * 75.067)/ 25

= 3.002

Therefore, Chris needs to do 3hrs each day to be able to complete the deadline

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3 years ago

Zach has a basic cell phone plan that does not include texting. He is going to add a multimedia texting package to his

attashe74 [19]

Package A is less expensive for Zach to send 250 multimedia texts each month.

Step-by-step explanation:

Given that,

Zach plans to send 250 multimedia texts each month.

Package A charges $0.25 per multimedia text with no monthly fees.

Package B charges $0.20 per multimedia text, but has a $15 monthly fee.

We need to find out which package is less expensive for Zach to add the plan.

The cost of 250 multimedia texts by package A :

⇒ Number of texts × cost per text

⇒ 250 × 0.25

⇒ 62.5

∴ The package A charges $62.5 for 250 multimedia texts.

The cost of 250 multimedia texts by package B :

⇒ (Number of texts × cost per text) + monthly fee

⇒ (250 × 0.20) + 15

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The Package A charges $62.5 which is less than package B charge of $65.

Hence, package A is less expensive.

6 0

2 years ago

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:

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