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3 years ago

Compute the total pay:

Mathematics

1 answer:

stiv31 [10]3 years ago

3 0

Answer:

$112.65

Step-by-step explanation:

7.25 x 8 = 58

58 + 54.65 = 112.65

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What is the total cost of a sweatshirt if the regular price is $42 and the sales tax is 5.5?

elixir [45]

42*5.5%+42=44.31
So the total cost is $44.31

3 0

3 years ago

(x^2y+e^x)dx-x^2dy=0

klio [65]

It looks like the differential equation is

$\left(x^2y + e^x\right) \,\mathrm dx - x^2\,\mathrm dy = 0$

Check for exactness:

$\dfrac{\partial\left(x^2y+e^x\right)}{\partial y} = x^2 \\\\ \dfrac{\partial\left(-x^2\right)}{\partial x} = -2x$

As is, the DE is not exact, so let's try to find an integrating factor µ(x, y) such that

$\mu\left(x^2y + e^x\right) \,\mathrm dx - \mu x^2\,\mathrm dy = 0$

*is* exact. If this modified DE is exact, then

$\dfrac{\partial\left(\mu\left(x^2y+e^x\right)\right)}{\partial y} = \dfrac{\partial\left(-\mu x^2\right)}{\partial x}$

We have

$\dfrac{\partial\left(\mu\left(x^2y+e^x\right)\right)}{\partial y} = \left(x^2y+e^x\right)\dfrac{\partial\mu}{\partial y} + x^2\mu \\\\ \dfrac{\partial\left(-\mu x^2\right)}{\partial x} = -x^2\dfrac{\partial\mu}{\partial x} - 2x\mu \\\\ \implies \left(x^2y+e^x\right)\dfrac{\partial\mu}{\partial y} + x^2\mu = -x^2\dfrac{\partial\mu}{\partial x} - 2x\mu$

Notice that if we let µ(x, y) = µ(x) be independent of y, then ∂µ/∂y = 0 and we can solve for µ :

$x^2\mu = -x^2\dfrac{\mathrm d\mu}{\mathrm dx} - 2x\mu \\\\ (x^2+2x)\mu = -x^2\dfrac{\mathrm d\mu}{\mathrm dx} \\\\ \dfrac{\mathrm d\mu}{\mu} = -\dfrac{x^2+2x}{x^2}\,\mathrm dx \\\\ \dfrac{\mathrm d\mu}{\mu} = \left(-1-\dfrac2x\right)\,\mathrm dx \\\\ \implies \ln|\mu| = -x - 2\ln|x| \\\\ \implies \mu = e^{-x-2\ln|x|} = \dfrac{e^{-x}}{x^2}$

The modified DE,

$\left(e^{-x}y + \dfrac1{x^2}\right) \,\mathrm dx - e^{-x}\,\mathrm dy = 0$

is now exact:

$\dfrac{\partial\left(e^{-x}y+\frac1{x^2}\right)}{\partial y} = e^{-x} \\\\ \dfrac{\partial\left(-e^{-x}\right)}{\partial x} = e^{-x}$

So we look for a solution of the form F(x, y) = C. This solution is such that

$\dfrac{\partial F}{\partial x} = e^{-x}y + \dfrac1{x^2} \\\\ \dfrac{\partial F}{\partial y} = e^{-x}$

Integrate both sides of the first condition with respect to x :

$F(x,y) = -e^{-x}y - \dfrac1x + g(y)$

Differentiate both sides of this with respect to y :

$\dfrac{\partial F}{\partial y} = -e^{-x}+\dfrac{\mathrm dg}{\mathrm dy} = e^{-x} \\\\ \implies \dfrac{\mathrm dg}{\mathrm dy} = 0 \implies g(y) = C$

Then the general solution to the DE is

$F(x,y) = \boxed{-e^{-x}y-\dfrac1x = C}$

5 0

3 years ago

What is the solution set of the compound inequality x+1<-2x+11<3x+5

VikaD [51]

Answer:

6/5 < x < 10/3 is the desired solution.

Step-by-step explanation:

Here, the given compound inequality is :

x + 1 < -2 x + 11 < 3 x + 5

Now, consider the first two term of the inequality, we get:

x + 1 < -2 x + 11

Subtracting 1 from both sides, we get:

x + 1 - 1 < -2 x + 11 - 1

or, x < -2x + 10

or, x + 2x < 10

or, 3 x < 10

or, x < 10/3

Similarly, considering the last two terms of the given inequality, we get:

-2 x + 11 < 3 x + 5

Subtracting 11 from both sides, we get:

-2 x + 11 - 11 < 3 x + 5 - 11

or, - 2 x < 3 x-6

or, 6 < 5 x

or, x > 6/5

Hence, combining two solutions, we get: 6/5 < x < 10/3

So, the desired value of x should be more than (6/5) but less than (10/3)

6 0

3 years ago

9-r=r, for r Wth even is math

mote1985 [20]

Answer:

9/2

Step-by-step explanation:

Move the variables to one side.

So:

9 - r = r

+r = +r

9 = 2r

Now divide both sides by 2

9/2 or 4.5

4 0

3 years ago

Which of the following can be prepositions? a. past c. under b. except d. all of the above Please select the best answer from th

spayn [35]

Answer:

Step-by-step explanation:

Hello!

Prepositions are words that describe a noun's directional location, time, place, et cetera.

For example, the sentence:

Angela misplaced her toy under the bed: under is the preposition since it describes where the toy is at. All of these answer choices are prepositions

7 0

3 years ago