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3 years ago

Please help and explain if so thank you

Mathematics

1 answer:

AVprozaik [17]3 years ago

7 0

How many days are in a year? 365. it started out as 88 inches subtracted that by 115 then add the 3.

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Eddie has a globe that he is going to unfold and lay flat to hang on the wall as a map. If the radius of the globe is 22.5 cm, w

nirvana33 [79]

Answer:

B. 6358.5 square centimeters. This is right.

5 0

3 years ago

can someone show me how to find the general solution of the differential equations? really need to know how to do it for the upc

mariarad [96]

The first equation is linear:

$x\dfrac{\mathrm dy}{\mathrm dx}-y=x^2\sin x$

Divide through by $x^2$ to get

$\dfrac1x\dfrac{\mathrm dy}{\mathrm dx}-\dfrac1{x^2}y=\sin x$

and notice that the left hand side can be consolidated as a derivative of a product. After doing so, you can integrate both sides and solve for $y$ .

$\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1xy\right]=\sin x$
$\implies\dfrac1xy=\displaystyle\int\sin x\,\mathrm dx=-\cos x+C$
$\implies y=-x\cos x+Cx$

- - -

The second equation is also linear:

$x^2y'+x(x+2)y=e^x$

Multiply both sides by $e^x$ to get

$x^2e^xy'+x(x+2)e^xy=e^{2x}$

and recall that $(x^2e^x)'=2xe^x+x^2e^x=x(x+2)e^x$ , so we can write

$(x^2e^xy)'=e^{2x}$
$\implies x^2e^xy=\displaystyle\int e^{2x}\,\mathrm dx=\frac12e^{2x}+C$
$\implies y=\dfrac{e^x}{2x^2}+\dfrac C{x^2e^x}$

- - -

Yet another linear ODE:

$\cos x\dfrac{\mathrm dy}{\mathrm dx}+\sin x\,y=1$

Divide through by $\cos^2x$ , giving

$\dfrac1{\cos x}\dfrac{\mathrm dy}{\mathrm dx}+\dfrac{\sin x}{\cos^2x}y=\dfrac1{\cos^2x}$
$\sec x\dfrac{\mathrm dy}{\mathrm dx}+\sec x\tan x\,y=\sec^2x$
$\dfrac{\mathrm d}{\mathrm dx}[\sec x\,y]=\sec^2x$
$\implies\sec x\,y=\displaystyle\int\sec^2x\,\mathrm dx=\tan x+C$
$\implies y=\cos x\tan x+C\cos x$
$y=\sin x+C\cos x$

- - -

In case the steps where we multiply or divide through by a certain factor weren't clear enough, those steps follow from the procedure for finding an integrating factor. We start with the linear equation

$a(x)y'(x)+b(x)y(x)=c(x)$

then rewrite it as

$y'(x)=\dfrac{b(x)}{a(x)}y(x)=\dfrac{c(x)}{a(x)}\iff y'(x)+P(x)y(x)=Q(x)$

The integrating factor is a function $\mu(x)$ such that

$\mu(x)y'(x)+\mu(x)P(x)y(x)=(\mu(x)y(x))'$

which requires that

$\mu(x)P(x)=\mu'(x)$

This is a separable ODE, so solving for $\mu$ we have

$\mu(x)P(x)=\dfrac{\mathrm d\mu(x)}{\mathrm dx}\iff\dfrac{\mathrm d\mu(x)}{\mu(x)}=P(x)\,\mathrm dx$
$\implies\ln|\mu(x)|=\displaystyle\int P(x)\,\mathrm dx$
$\implies\mu(x)=\exp\left(\displaystyle\int P(x)\,\mathrm dx\right)$

and so on.

6 0

3 years ago

What is the LCD for the given equation?

velikii [3]

Answer:

(x-3)^2

Step-by-step explanation:

The LCD is (x-3)^2 This is becuse x-3 is on both equations.

5 0

3 years ago

Shannon uses 30 inches of ribbon to make one bow how many feet of ribbon are needed to make 10 bows

coldgirl [10]

First, we need to calculate the amount of ribbon in inches, and then convert it into feet.

Since 30 inches of ribbon is used in one bow, to make 10 bows, we need multiply:

30 x 10 = 300

Now, we need to convert the inches to feet.

300 in = 25 ft

Our answer is 25 ft of ribbon.

Hope this helped!

6 0

3 years ago

Read 2 more answers

You have a playlist with 19 pop songs and 29 R&B songs. You randomize and hit play. How many songs do you have to listen to

ivann1987 [24]

Answer:

The answer is 20 songs.

Step-by-step explanation:

i) there are 19 pop songs

ii) there are 29 R&B songs

iii) the number of songs that have to be listened to in order to guarantee you hear one pop song and one R&B song

= 19 + 1 = 20 songs.

3 0

3 years ago