Help me with algebra

dalvyx [7]

<h3>Answer: B) real number</h3>

Explanation:

Something like 3.5 = 7/2 is a rational number because its a fraction of two integers.

While on the other hand, the constant pi = 3.14159... is irrational because we cannot write pi as a fraction of two integers. We can get approximations like 22/7, but not a perfect exact match.

Both types of numbers, rational and irrational, are under the umbrella of the real number system. Any real number is a string of decimal digits. Sometimes it might be a whole number, but fractional values can be included as well. The decimal number may terminate, or it may repeat, or it may go on forever without a pattern.

In short, any number you can think of is a real number assuming your teacher hasn't covered complex numbers (or imaginary numbers) just yet.

5 0

2 years ago

Read 2 more answers

x = c1 cos(t) + c2 sin(t) is a two-parameter family of solutions of the second-order DE x'' + x = 0. Find a solution of the seco

igomit [66]

Answer:

$x=-cos(t)+2sin(t)$

Step-by-step explanation:

The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:

A differential equation of the form:

$a_n y^n +a_n_-_1y^{n-1}+...+a_1y'+a_oy=0$

Will have a characteristic equation of the form:

$a_n r^n +a_n_-_1r^{n-1}+...+a_1r+a_o=0$

Where solutions $r_1,r_2...,r_n$ are the roots from which the general solution can be found.

For real roots the solution is given by:

$y(t)=c_1e^{r_1t} +c_2e^{r_2t}$

For real repeated roots the solution is given by:

$y(t)=c_1e^{rt} +c_2te^{rt}$

For complex roots the solution is given by:

$y(t)=c_1e^{\lambda t} cos(\mu t)+c_2e^{\lambda t} sin(\mu t)$

Where:

$r_1_,_2=\lambda \pm \mu i$

Let's find the solution for $x''+x=0$ using the previous information:

The characteristic equation is:

$r^{2} +1=0$

So, the roots are given by:

$r_1_,_2=0\pm \sqrt{-1} =\pm i$

Therefore, the solution is:

$x(t)=c_1cos(t)+c_2sin(t)$

As you can see, is the same solution provided by the problem.

Moving on, let's find the derivative of $x(t)$ in order to find the constants $c_1$ and $c_2$ :

$x'(t)=-c_1sin(t)+c_2cos(t)$

Evaluating the initial conditions:

$x(0)=-1\\\\-1=c_1cos(0)+c_2sin(0)\\\\-1=c_1$

And

$x'(0)=2\\\\2=-c_1sin(0)+c_2cos(0)\\\\2=c_2$

Now we have found the value of the constants, the solution of the second-order IVP is:

$x=-cos(t)+2sin(t)$

3 0

3 years ago

The new balance of a charge account is $145.00. The minimum payment is $20.00. If the interest rate is 1.5%, how much will the n

juin [17]

The balance is $145 but after one makes he minimum payment of $20, there is $125 left to pay. However interest is added before the next month’s bill is generated.

Remember that percent means out of 100. 1.5% means 1.5/100 = .015

To find 1.5% of 125 we multiply (.015)(125) = 1.875 But as this is money the interest is rounded to two decimal places and so is $1.88

We add this to 125 to get next month’s balance which is 125 + 1.88 = $126.88

3 0

3 years ago

4. The cost of a new house is being reduced 22%

olganol [36]

1. Ok so first I would find 22% of 212,000 to do that you do: 22 divide 100 = 0.22

2. Now that you’ve turned 22% into a decimal as 0.22 you find what 22% of 212,000 is like so: 0.22x212,000 =46,640

3. Now that you have to reduce 212,000 but 22% to do this you just subtract: 212,000-46,640= 165,360

They would purchase the house for $165,360

3 0

3 years ago

How much more intense is an earthquake that measures 7.5 on the Richter scale than one that measures 6.2?

PolarNik [594]

It would be 1.3 less than the other.

7 0

3 years ago