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3 years ago

If an object on earth weighs 42 lbs, what is its weight on the moon?

Mathematics

1 answer:

Bogdan [553]3 years ago

5 0

Answer:

6.93 lbs.

Step-by-step explanation:

The weight on the moon is approximately 16.5% of what you would weigh on Earth. Using this information, we can say that 16.5% of 42 lbs would equal how much the object would weigh on the moon.

I prefer to convert percentages the decimal way, so let's do it that way. 16.5% is 0.165 as a decimal, so now all we have to do is multiply 0.165 by 42 (since we are saying 16.5% of 42 lbs), and we get 6.93 lbs.

Hope this helps! :)

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14) Find the slope of the line containing the points (5, 3) and (-7, 2).

Zina [86]

Answer:

1/12

Step-by-step explanation:

Step one:

given data

the line containing the points (5, 3) and (-7, 2).

x1= 5

y1= 3

x2= -7

y2=2

Step two:

The slope is given as

Slope= y2-y1/x2-x1

substitute

Slope= 2-3/-7-5

Slope= -1/-12

Slope = 1/12

7 0

2 years ago

(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

The coordinate plane shows the floor plan for a swimming pool. What is the area of the pool’s border?"

emmasim [6.3K]

A = Area
L= Length = 15
W + widith = 10
A = 150
The pool area is L = 10
w= 5
A= 50
So the area of the perimeter = 100 square meters

5 0

3 years ago

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7xy + 8z - 2z + 12xy + 10z

cestrela7 [59]

Answer:

19xy + 16z

Step-by-step explanation:

combine like terms

7xy +1 2xy= 19xy

8z - 2z + 10z = 16z

7 0

3 years ago

Ashley has a box of donuts to distribute among her colleagues. There are eight chocolate donuts, twelve glazed donuts, ten jelly

Serjik [45]

According to one source, the answer is "C. Randomly select and replace a donut 72 times. Then, observe how close to 18 times a glazed donut is drawn. "

Thank you for your question. Please don't hesitate to ask in Brainly your queries.

8 0

3 years ago

Read 2 more answers