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3 years ago

15

Jackie bought 2/ packages of papers for $5.80 each and 4 notebooks for d dollars each she spent $32 for the packages of paper an

d the notebooks Write
and equation using D that represents the situation above

1 answer:

Xelga [282]3 years ago

6 0

Answer:

2(5.80)+4d=32

Step-by-step explanation:

11.6+4d=32

32-11.6=20.4

4d=20.4

d=5.1

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2 years ago

Consider the differential equation: xy′(x2+7)y=cos(x)+e3xy. Put the differential equation into the form: y′+p(x)y=g(x), determin

icang [17]

Answer:

Linear and non-homogeneous.

Step-by-step explanation:

We are given that

$\frac{xy'}{(x^2+7)y}=cosx+\frac{e^{3x}}{y}$

We have to convert into y'+P(x)y=g(x) and determine P(x) and g(x).

We have also find type of differential equation.

$y'=\frac{(x^2+7)y}{x}(cosx+\frac{e^{3x}}{y}}$

$y'=\frac{(x^2+7)cosx}{x}y+\frac{(x^2+7)e^{3x}}{x}$

$y'-\frac{cosx(x^2+7)}{x}y=\frac{e^{3x}(x^2+7)}{x}$

It is linear differential equation because this equation is of the form

y'+P(x)y=g(x)

Compare it with first order first degree linear differential equation

$y'+P(x)y=g(x)$

$P(x)=-\frac{cosx (x^2+7)}{x},g(x)=\frac{e^{3x}(x^2+7)}{x}$

$\frac{dy}{dx}=\frac{(x^2+7)(ycosx+e^{3x})}{x}$

Homogeneous equation

$\frac{dy}{dx}=\frac{f(x,y)}{g(x,y)}$

Degree of f and g are same.

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Degree of f and g are not same .

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3 0

3 years ago

Two airplanes are flying in the air at the same height: airplane A is flying east at 250 mi/h and airplane B is flying north at

just olya [345]

Answer:

decreasing at 390 miles per hour

Step-by-step explanation:

Airplane A's distance in miles to the airport can be written as ...

a = 30 -250t . . . . . where t is in hours

Likewise, airplane B's distance to the airport can be written as ...

b = 40 -300t

The distance (d) between the airplanes can be found using the Pythagorean theorem:

d^2 = a^2 + b^2

Differentiating with respect to time, we have ...

2d·d' = 2a·a' +2b·b'

d' = (a·a' +b·b')/d

__

To find a numerical value of this, we need to find the values of its variables at t=0.

a = 30 -250·0 = 30

a' = -250

b = 40 -300·0 = 40

b' = -300

d = √(a²+b²) = √(900+1600) = 50

Then ...

d' = (30(-250) +40(-300))/50 = -19500/50 = -390

The distance between the airplanes is decreasing at 390 miles per hour.

3 0

4 years ago