Find the distance between the given points. Round to the nearest tenth.

Slope-intercept from two points<br> Complete the equation of the line through (-8.8) and (1,-10).

Andrei [34K]

Answer:

y=− 2x−8 is the equation

Step-by-step explanation:

equation for slope is y=mx+b the y intercept is -8 and the slope is -2

5 0

2 years ago

PLS EXPLAIN IN FULL DETAIL

elena-14-01-66 [18.8K]

Answer:

1.50x=18

x=12

Step-by-step explanation:

You have to divide 1.50 on both sides and 1.50x/1.50= x and 18/1.50=12 so x=12

3 0

2 years ago

Read 2 more answers

For every 2 miles Joan runs, Stacy runs 3 miles. How far will Stacy have run if Joan runs 24 miles?

oee [108]

Stacy will run 72 miles.

6 0

2 years ago

Read 2 more answers

Find a particular solution to <img src="https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%20%5Cfrac%7B%20d%5E%7B2%7Dy%20%7D%7Bd%20x%5E%7

Digiron [165]

$y=x^r$
$\implies r(r-1)x^r+6rx^r+4x^r=0$
$\implies r^2+5r+4=(r+1)(r+4)=0$
$\implies r=-1,r=-4$

so the characteristic solution is

$y_c=\dfrac{C_1}x+\dfrac{C_2}{x^4}$

As a guess for the particular solution, let's back up a bit. The reason the choice of $y=x^r$ works for the characteristic solution is that, in the background, we're employing the substitution $t=\ln x$ , so that $y(x)$ is getting replaced with a new function $z(t)$ . Differentiating yields

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac1x\dfrac{\mathrm dz}{\mathrm dt}$
$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac1{x^2}\left(\dfrac{\mathrm d^2z}{\mathrm dt^2}-\dfrac{\mathrm dz}{\mathrm dt}\right)$

Now the ODE in terms of $t$ is linear with constant coefficients, since the coefficients $x^2$ and $x$ will cancel, resulting in the ODE

$\dfrac{\mathrm d^2z}{\mathrm dt^2}+5\dfrac{\mathrm dz}{\mathrm dt}+4z=e^{2t}\sin e^t$

Of coursesin, the characteristic equation will be $r^2+6r+4=0$ , which leads to solutions $C_1e^{-t}+C_2e^{-4t}=C_1x^{-1}+C_2x^{-4}$ , as before.

Now that we have two linearly independent solutions, we can easily find more via variation of parameters. If $z_1,z_2$ are the solutions to the characteristic equation of the ODE in terms of $z$ , then we can find another of the form $z_p=u_1z_1+u_2z_2$ where

$u_1=-\displaystyle\int\frac{z_2e^{2t}\sin e^t}{W(z_1,z_2)}\,\mathrm dt$
$u_2=\displaystyle\int\frac{z_1e^{2t}\sin e^t}{W(z_1,z_2)}\,\mathrm dt$

where $W(z_1,z_2)$ is the Wronskian of the two characteristic solutions. We have

$u_1=-\displaystyle\int\frac{e^{-2t}\sin e^t}{-3e^{-5t}}\,\mathrm dt$
$u_1=\dfrac23(1-2e^{2t})\cos e^t+\dfrac23e^t\sin e^t$

$u_2=\displaystyle\int\frac{e^t\sin e^t}{-3e^{-5t}}\,\mathrm dt$
$u_2=\dfrac13(120-20e^{2t}+e^{4t})e^t\cos e^t-\dfrac13(120-60e^{2t}+5e^{4t})\sin e^t$

$\implies z_p=u_1z_1+u_2z_2$
$\implies z_p=(40e^{-4t}-6)e^{-t}\cos e^t-(1-20e^{-2t}+40e^{-4t})\sin e^t$

and recalling that $t=\ln x\iff e^t=x$ , we have

$\implies y_p=\left(\dfrac{40}{x^3}-\dfrac6x\right)\cos x-\left(1-\dfrac{20}{x^2}+\dfrac{40}{x^4}\right)\sin x$

4 0

2 years ago

Hello please can some one help me I don’t know how to do these math

erik [133]

1) Put all the numbers in numerical order :
15, 23, 24, 25, 25, 25, 27
The median is the middle of the numbers : 25
Mode is the value that occurs more often : 25

2) Put all the numbers in numerical order :
2, 3, 3, 3, 3, 4, 4, 5
The middle of the numbers is 3 and 3
so, 3 + 3 = 6
6 : 2 = 3

Median = 3
Mode = 3

3) Put all the numbers in numerical order :
5, 7, 8, 9, 9, 10, 10, 10, 12
Median = 9
Mode = 10

4) Put all the numbers in numerical order :
0, 1, 1, 2, 2, 3, 3, 3, 4, 4

Median
2 + 3 = 5 : 2 = 2,5
Mode = 3

5) Put all the numbers in numerical order :
12, 13, 15, 18, 25
Median = 15
Mode = 0 (None)

6) Put all the numbers in numerical order :
1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5
Median = 3
Mode = 3 and 4

7) Put all the numbers in numerical order :
6, 8, 9, 10, 10, 12

Median
9 + 10 = 19 : 2 = 8
Mode = 10

8) Put all the numbers in numerical order :
28, 30, 30, 30, 30, 31, 31, 31, 31, 31, 31, 31

Median
31 + 31 = 62 : 2 = 31
Mode = 31

5 0

3 years ago