Help help help math math

Olive reads 4 books every month for school. How many books does she read in 8 months?

Novosadov [1.4K]

Answer:

32 books.

Step-by-step explanation:

What do we know?

As Olive continues this pattern, this will involve multiplication.

4 books per month and 8 months.

4*8=32 books.

So, Olive will read 32 books within 8 months.

6 0

3 years ago

Solve the following initial-value problem, showing all work, including a clear general solution as well as the particular soluti

Vikki [24]

Answer:

General Solution is $y=x^{3}+cx^{2}$ and the particular solution is $y=x^{3}-\frac{1}{2}x^{2}$

Step-by-step explanation:

$x\frac{\mathrm{dy} }{\mathrm{d} x}=x^{3}+3y\\\\Rearranging \\\\x\frac{\mathrm{dy} }{\mathrm{d} x}-3y=x^{3}\\\\\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{3y}{x}=x^{2}$

This is a linear diffrential equation of type

$\frac{\mathrm{d} y}{\mathrm{d} x}+p(x)y=q(x)$ ..................(i)

here $p(x)=\frac{-2}{x}$

$q(x)=x^{2}$

The solution of equation i is given by

$y\times e^{\int p(x)dx}=\int e^{\int p(x)dx}\times q(x)dx$

we have $e^{\int p(x)dx}=e^{\int \frac{-2}{x}dx}\\\\e^{\int \frac{-2}{x}dx}=e^{-2ln(x)}\\\\=e^{ln(x^{-2})}\\\\=\frac{1}{x^{2} } \\\\\because e^{ln(f(x))}=f(x)]\\\\Thus\\\\e^{\int p(x)dx}=\frac{1}{x^{2}}$

Thus the solution becomes

$\tfrac{y}{x^{2}}=\int \frac{1}{x^{2}}\times x^{2}dx\\\\\tfrac{y}{x^{2}}=\int 1dx\\\\\tfrac{y}{x^{2}}=x+c$ $y=x^{3}+cx^{2$

This is the general solution now to find the particular solution we put value of x=2 for which y=6

we have $6=8+4c$

Thus solving for c we get c = -1/2

Thus particular solution becomes

$y=x^{3}-\frac{1}{2}x^{2}$

5 0

3 years ago

Which of the following numbers is NOT a solution of the equation |x + 5| = x + 5?

Nata [24]

Answer:

-10 is not a solution to the equation

Step-by-step explanation:

I don't really have an explanation

7 0

3 years ago

estimate 0.037854921 to the nearest hundredth express your answer as a single digit times a power of 10

Vilka [71]

To solve this problem you must apply the proccedure shown below:

1. Let's round the value to the nearest hundredth. As you can see, the digit 8 is in the thousandths place and is greater than 5, therefore, you must round up to 0.038.

2. Now express the value as a single digit times a power of 10, as following:

$38$ x $10^{-3}$

Therefore, the answer is: $38$ x $10^{-3}$

6 0

3 years ago

Read 2 more answers

Which of the pairs of events below is mutually exclusive?

Nady [450]

Answer:

Drawing an ace of spades and then drawing another ace of spades without replacement from a standard deck of cards.

Step-by-step explanation:

Given four pair of events:

1. Drawing an ace of spades and then drawing another ace of spades without replacement from a standard deck of cards

2. Drawing a 2 and drawing a 4 with replacement from a standard deck of cards

3. Drawing a heart and then drawing a spade without replacement from a standard deck of cards

4. Drawing a jack and then drawing a 7 without replacement from a standard deck of cards

To find:

Which of the pairs is mutually exclusive?

Solution:

First of all, let us have a look at the definition of mutually exclusive events.

Mutually exclusive events do not have any case in common.

In other words, two events are known as mutually exclusive when both the events can not occur at the same time.

Now, let us have a look at the given options one by one:

1. Drawing an ace of spades and then drawing another ace of spades without replacement from a standard deck of cards.

We know that there is only one ace of spades in a standard deck.

Therefore, the two events can not occur one after the other, so these are mutually exclusive events.

2. Drawing a 2 and drawing a 4 with replacement from a standard deck of cards.

The two events can occur one after the other, so these are not mutually exclusive.

3. Drawing a heart and then drawing a spade without replacement from a standard deck of cards.

Separate cards are drawn one after the other, so not mutually exclusive.

4. Drawing a jack and then drawing a 7 without replacement from a standard deck of cards.

Separate cards are drawn one after the other, so not mutually exclusive.

3 0

3 years ago