All categories

3 years ago

Write the linear function for the graph shown in slope-intercept form.

Mathematics

1 answer:

Dovator [93]3 years ago

4 0

Answer:

upper left graph: y = 3/4x-3

lower right graph: x = 3

Step-by-step explanation:

You might be interested in

Find a power series solution of the differential equation y" + 4xy = 0 about the ordinary point x = 0.

Studentka2010 [4]

Answer:

$y(x)\ =\ \sum_{m=0}^{\infty}\dfrac{-(-1)^m.{(4x)}^{m+1}}{2m!}\ +\ \sum_{m=0}^{\infty}\dfrac{-(-1)^m.(4x){m+1}}{(2m+1)!}.$

Step-by-step explanation:

Given differential equation is

y'' + 4y = 0 <u> </u> (1)

We have to find the power series solution of given differential equation about the ordinary point x = 0.

Power series solution of any given differential equation can be given by

$y(x)\ =\ C_0+C_1.x+C_2.\dfrac{x^2}{2!}+C_3.\dfrac{x^3}{3!}+....$

$=\ \sum_{n=0}^{\infty}C_n.\dfrac{x^n}{n!}$

$=>y'(x)\ =\ \sum_{n=1}^{\infty}\dfrac{n.C_n.x^{n-1}}{n!}$

$=>y''(x)\ =\ \sum_{n=2}^{\infty}\dfracf{n.(n-1)C_n.x^{n-2}}{n!}$

Now, by putting these values in equation (1), we have

$\sum_{n=2}^{\infty}\dfracf{n.(n-1)C_n.x^{n-2}}{n!}\ +\ 4x\sum_{n=0}^{\infty}C_n.\dfrac{x^n}{n!}\ =\ 0$

$=>\ \sum_{n=0}^{\infty}\dfracf{(n+1).(n+1)C_{n+2}.x^{n}}{n!}\ +\ 4x\sum_{n=0}^{\infty}C_n.\dfrac{x^n}{n!}\ =\ 0$

$=>\ \sum_{n=0}^{\infty}[(n+1).(n+2)C_{n+2}+4xC_n]x^n\ =\ 0$

$=>\ (n+1).(n+2).C_{n+2}+4x.C_n\ =\ 0$

$=>\ C_{n+2}\ =\ \dfrac{-4x}{(n+1)(n+2)}.C_n$

for n = 0

$C_2\ =\ \dfrac{-4x}{2}.C_0$

for n = 1

$C_3\ =\ \dfrac{-4x}{6}.C_1$

for n = 2

$C_4\ =\ \dfrac{-4x}{12}.C_2$

$=\ \dfrac{16x^2}{24}.C_0$

for n = 3

$C_5\ =\ \dfrac{-4x}{20}.C_3$

$=\ \dfrac{16x^2}{120}$

for n=4

$C_6\ =\ \dfrac{-4x}{30}C_4$

$=\ \dfrac{-64.x^3}{720}.C_0$

As we can see for

for even value of n i.e n = 2m where m is any integer.

$C_2m\ =\ \sum_{m=0}^{\infty}\dfrac{-(-1)^m.{(4x)}^{m+1}}{2m!}$

for odd value of n i.e n =2m+1 , where m is any integer.

$C_{2m+1}\ =\ \sum_{m=0}^{\infty}\dfrac{-(-1)^m.(4x)^{m+1}}{(2m+1)!}$

So, the power series solution about the ordinary point x=0, can be given by

$y(x)\ =\ \sum_{n=0}^{\infty}\dfrac{C_n.x^n}{n!}$

$=\ \sum_{m=0}^{\infty}\dfrac{-(-1)^m.{(4x)}^{m+1}}{2m!}\ +\ \sum_{m=0}^{\infty}\dfrac{-(-1)^m.(4x)^{m+1}}{(2m+1)!}.$

4 0

3 years ago

Solve this equation x/4-20=-12

Naddika [18.5K]

Answer:

X=32

Step-by-step explanation:

First Find common denominator

Combine fractions with common denominator

Multiply the numbers

Multiply all terms by the same value to eliminate

And I think you got it from there :))))))))))))))

6 0

3 years ago

Read 2 more answers

A number plus itself, plus twice itslef, plus 4 times itself, is equal to -104. what is the number?

Nutka1998 [239]

Let's represent this unknown number with the variable 'n'
n + n + 2n + 4n = -104

Explanations:
'n+n' - a number plus itself
'+2n' - plus twice itself
'+4n' - plus 4 times itself

Anyway:
n + n + 2n + 4n = -104
Simplify:
8n = -104
Divide both sides by 8:
n = -13

The number is -13
Good luck! If you need me to explain something in more depth, just ask :))
-T.B.

8 0

3 years ago

A data set has a mean of 112 and a standard deviation of 2.5.

Ahat [919]

Answer with explanation:

Mean of the data set $\mu$ = 112

Standard Deviation of the data set $\sigma$ =2.5

Since , 50% of data lies on both side of the mean.

Z at 50% = 0.1915

Margin of error for this data set

$=Z_{50 \text{percent}}\times\frac{\sigma}{\sqrt{\mu}}\\\\=0.1915 \times \frac{2.5}{\sqrt{112}}\\\\=0.1915 \times \frac{2.5}{10.58}\\\\=0.1915 \times 0.2362\\\\=0.0452$

Margin of error=0.045(approx)

4 0

4 years ago

Read 2 more answers

Put the following numbers in order from least to greatest 0.0579. 5. 0.5. 0.59. 0.0599. 0.05

Leno4ka [110]

I'm guessing the numbers are 0.0579, 5, 0.5, 0.59, 0.0599, & 0.05 (use commas not dots in future questions)
least to greatest.
0.05, 0.0579, 0.0599, 0.5, 0.59, 5

hope this helps

3 0

3 years ago

Read 2 more answers