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2 years ago

Tom has saved $390. He plans to spend $30 each month for music lessons. The function

Mathematics

1 answer:

Lena [83]2 years ago

5 0

Answer:

x is the months because that is the amount of time he has before he runs out of savings and y Is the savings because that is what he is calculating

Step-by-step explanation:

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Find the particular solution of the differential equation dy + 7y = 6 satisfying the initial condition y(0) = 0. Answer: y= Your

Aleonysh [2.5K]

Answer:

Step-by-step explanation:

We have the equation $y'+7y=6$ with the initial condition $y(0)=0$ . It is not difficult to notice that this is a linear equation, which has the general expression

$y'+P(x)y=Q(x)$ .

The solution of this equation is expressed by a general formula:

$y(x) = \exp\left(-\int P(x)dx\right)\left(\int Q(x)\exp\left(-\int P(x)dx\right) +C\right)$ .

In the particular case of our equation, we have

$P(x)=7$

$Q(x)=6$ .

Then, we must calculate the integrals

$\int 7dx = 7x$ that implies

$\exp\left(-\int P(x)dx\right) = e^{-7x}$ ,

and

$\int 6e^{7x}dx = \frac{6}{7}e^{7x}$

Then,

$y(x) = e^{-7x}\left(\frac{6}{7}e^{7x} +C\right) = \frac{6}{7} + Ce^{-7x}$ .

In order to obtain the value of the constant we substitute the initial condition

$0=y(0) = \frac{6}{7} + C$ that implies $C=-\frac{6}{7}$

Therefore,

$y(x) = \frac{6}{7}-\frac{6}{7}e^{-7x}$ .

8 0

2 years ago

Two numbers whose sum is -1 and product is -20

enyata [817]

Answer:

Let the two numbers be x and y.

Then x + y = 20, and y = 20 - x.

Their product is what you get when you multiply the two numbers together, in other words xy, or x(20 - x). You can expand this out to get 20x - x².

The product of the two numbers will be maximum at the value

Step-by-step explanation:

sorry if this didn't help

3 0

2 years ago

Congratulatiohs! You just got your first job. The manager says your starting yearly salary will be $20,800. The

Jobisdone [24]

Answer:

120,640

Step-by-step explanation:

3 0

2 years ago

If Jimmy has 5 apples and Sandra gives him 2 more how much does he have?

viktelen [127]

Answer:

He has 7

Step-by-step explanation:

5 plus 2 equals 7

6 0

2 years ago

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The set of all even whole numbers greater than 4 and less than 12 can be written as

Scrat [10]

4,6,8,10,12

Hope this helps!

5 0

3 years ago

Read 2 more answers