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2 years ago

Write an equation in point-slope form of the line (-7,2); m=2

Mathematics

1 answer:

AfilCa [17]2 years ago

5 0

Answer: y - 2 = 2(x + 7)

Step-by-step explanation:

Point-slope form is written as y - $y_{1}$ = m(x - $x_{1}$ ) where m is the slope and ( $x_{1}$ , $y_{1}$ ) are points on the line.

y - $y_{1}$ = m(x - $x_{1}$ )

y - 2 = 2(x + 7)

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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

How much work is done by a man who uses a force of 7 Newtons to push a box 3 meters across the room?

ElenaW [278]

The formula to calculate work done is -

Work done ( in joule, J) = Force (in Newton) X Distance (in meters)

So, we will use the formula to calculate work done,

Here, force is given as = 7 newtons

Distance is given as = 3 meters

So, work done will be -

Work done ( in joule, J) = 7 Newtons X 3 Meters

<u>Work done ( in joule, J) = 21 J (in joule)</u>

7 0

4 years ago

Read 2 more answers

When Ms. Lawrence goes to the doctor’s office, they have patients wait 30 minutes. She found a new doctor that has 15% less wait

baherus [9]

Answer:

25.5 minutes

Step-by-step explanation:

3 0

3 years ago

Which geometric series diverges? Three-fifths three-tenths three-twentieths StartFraction 3 Over 40 EndFraction ellipsis Negativ

Sholpan [36]

The geometric series which diverges is shown in the option number c as the absolute value of the common ratio of this series 4.

$\sum_{n=1 }^{\infty} \dfrac{2}{3}(-4)^{n-1}$

<h3>What is geometric series diverges? </h3>

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

It can be given as,

$a+ar+ ar^2+ ar^3+...$

Here,

is the (<em>a</em>) first term of the sequence, and (<em>r</em>) is the common ratio.

To be a series as geometric series diverges, it should follow,

$|r| > 1$

First option given as,

3/5+3/10+3/20+3/40+ ...

Here, the common ratio is,

$r=\dfrac{\dfrac{3}{10}}{\dfrac{3}{5}}\\r=\dfrac{1}{2}$

The common ratio is less than one. Thus option a is not correct.

First option given as,

-10+4-8/4+18/25- ...

Here, the common ratio is,

$r=\dfrac{4}{-10}\\r=\dfrac{-2}{5}$

For the option number two the common ratio is (-2/5) which is less than 1. This option is also not correct.

In the option number c, the value of common ratio is -4. The absolute value of common ratio is,

$|r|=|-4|\\|r|=4$

The absolute value of this common ratio is more than one. Thus, this is the correct option.

The geometric series which diverges is shown in the option number c as the absolute value of the common ratio of this series 4.

$\sum_{n=1 }^{\infty} \dfrac{2}{3}(-4)^{n-1}$

Learn more about the geometric sequence here;

brainly.com/question/1509142

7 0

2 years ago

Purchased a vase and flowers at her local flower shop. At home, she wants to fill the cylindrical vase and at the

Paraphin [41]

Step-by-step explanation:

We know that

Radius = Diameter/2

=> Radius = 2/2

=> Radius = 1 in

Now,

Volume of cylinder = πr²h

=> π × (1)² × 9

=> 9π in³

Since it is filled ⅔ of the volume

So,

Water to be putted = ⅔ × 9π = 6π in³

3 0

2 years ago