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3 years ago

A grocery store sells a bag of 4 oranges for $3.80. How much does one orange cost?

Mathematics

1 answer:

grin007 [14]3 years ago

7 0

Answer:

95 cents

Step-by-step explanation:

3.80/4 = 0.95

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Which equation could have been used to create this table?

Lyrx [107]

Answer:

y = 3x

Step-by-step explanation:

(1,3) (2,6)

The first step is to find the rate of change ( or slope)

m = (y2-y1)/(x2-x1)

m = (6-3)/(2-1)

m = 3/1

m = 3

Then we need to use the point slope form of the equation of a line

y-y1 = m(x-x1)

y-3 = 3(x-1)

Distribute the 3

y-3 = 3x-3

Add 3 to each side

y-3+3 = 3x-3+3

y = 3x

8 0

3 years ago

Read 2 more answers

(X^2+y^2+x)dx+xydy=0 Solve for general solution

aksik [14]

Check if the equation is exact, which happens for ODEs of the form

$M(x,y)\,\mathrm dx+N(x,y)\,\mathrm dy=0$

if $\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}$ .

We have

$M(x,y)=x^2+y^2+x\implies\dfrac{\partial M}{\partial y}=2y$

$N(x,y)=xy\implies\dfrac{\partial N}{\partial x}=y$

so the ODE is not quite exact, but we can find an integrating factor $\mu(x,y)$ so that

$\mu(x,y)M(x,y)\,\mathrm dx+\mu(x,y)N(x,y)\,\mathrm dy=0$

is exact, which would require

$\dfrac{\partial(\mu M)}{\partial y}=\dfrac{\partial(\mu N)}{\partial x}\implies \dfrac{\partial\mu}{\partial y}M+\mu\dfrac{\partial M}{\partial y}=\dfrac{\partial\mu}{\partial x}N+\mu\dfrac{\partial N}{\partial x}$

$\implies\mu\left(\dfrac{\partial N}{\partial x}-\dfrac{\partial M}{\partial y}\right)=M\dfrac{\partial\mu}{\partial y}-N\dfrac{\partial\mu}{\partial x}$

Notice that

$\dfrac{\partial N}{\partial x}-\dfrac{\partial M}{\partial y}=y-2y=-y$

is independent of x, and dividing this by $N(x,y)=xy$ gives an expression independent of y. If we assume $\mu=\mu(x)$ is a function of x alone, then $\frac{\partial\mu}{\partial y}=0$ , and the partial differential equation above gives

$-\mu y=-xy\dfrac{\mathrm d\mu}{\mathrm dx}$

which is separable and we can solve for $\mu$ easily.

$-\mu=-x\dfrac{\mathrm d\mu}{\mathrm dx}$

$\dfrac{\mathrm d\mu}\mu=\dfrac{\mathrm dx}x$

$\ln|\mu|=\ln|x|$

$\implies \mu=x$

So, multiply the original ODE by x on both sides:

$(x^3+xy^2+x^2)\,\mathrm dx+x^2y\,\mathrm dy=0$

Now

$\dfrac{\partial(x^3+xy^2+x^2)}{\partial y}=2xy$

$\dfrac{\partial(x^2y)}{\partial x}=2xy$

so the modified ODE is exact.

Now we look for a solution of the form $F(x,y)=C$ , with differential

$\mathrm dF=\dfrac{\partial F}{\partial x}\,\mathrm dx+\dfrac{\partial F}{\partial y}\,\mathrm dy=0$

The solution F satisfies

$\dfrac{\partial F}{\partial x}=x^3+xy^2+x^2$

$\dfrac{\partial F}{\partial y}=x^2y$

Integrating both sides of the first equation with respect to x gives

$F(x,y)=\dfrac{x^4}4+\dfrac{x^2y^2}2+\dfrac{x^3}3+f(y)$

Differentiating both sides with respect to y gives

$\dfrac{\partial F}{\partial y}=x^2y+\dfrac{\mathrm df}{\mathrm dy}=x^2y$

$\implies\dfrac{\mathrm df}{\mathrm dy}=0\implies f(y)=C$

So the solution to the ODE is

$F(x,y)=C\iff \dfrac{x^4}4+\dfrac{x^2y^2}2+\dfrac{x^3}3+C=C$

$\implies\boxed{\dfrac{x^4}4+\dfrac{x^2y^2}2+\dfrac{x^3}3=C}$

5 0

3 years ago

Sam, John, Matt, and Bob are going to drive to Florida. It is a 8 1/4 hour drive. Sam drove 1 1/3 hours. John drove 1 5/6 hours.

vovangra [49]

Answer:

Step-by-step explanation:?

7 0

3 years ago

Read 2 more answers

How do I solve all this

Cerrena [4.2K]

Number five is .45 repeating

3 0

2 years ago

why mathematics is the very important in a small business? is mathematics is helpful to you? explain

kodGreya [7K]

Mathematics is very important in a small business is because when you make money transactions with other people you need to know how to count money correctly and your calculations can’t be wrong. Mathematics is definitely helpful to me because Artificial Intelligence is taking on jobs, so we have to step up our game.

7 0

3 years ago