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3 years ago

How much matter in the universe is comprised of atoms

Mathematics

1 answer:

alexandr1967 [171]3 years ago

8 0

Answer:

4.6 percent

Step-by-step explanation:

4.6 percent of the energy in the universe is made of atoms, the rest is all dark energy/matter.

Note: This does not belong in mathematics.

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Use lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f(x,y = xyz; x^

Snezhnost [94]

I'm assuming the constraint involves some plus signs that aren't appearing for some reason, so that you're finding the extrema subject to $x^2+2y^2+3z^2=96$ .

Set $f(x,y,z)=xyz$ and $g(x,y,z)=x^2+2y^2+3z^2-96$ , so that the Lagrangian is

$L(x,y,z,\lambda)=xyz+\lambda(x^2+2y^2+3z^2-96)$

Take the partial derivatives and set them equal to zero.

$\begin{cases}L_x=yz+2\lambda x=0\\L_y=xz+4\lambda y=0\\L_z=xy+6\lambda z=0\\L_\lambda=x^2+2y^2+3z^2-96=0\end{cases}$

One way to find the possible critical points is to multiply the first three equations by the variable that is missing in the first term and dividing by 2. This gives

$\begin{cases}\dfrac{xyz}2+\lambda x^2=0\\\\\dfrac{xyz}2+2\lambda y^2=0\\\\\dfrac{xyz}2+3\lambda z^2=0\\\\x^2+2y^2+3y^2=96\end{cases}$

So by adding the first three equations together, you end up with

$\dfrac32xyz+\lambda(x^2+2y^2+3z^2)=0$

and the fourth equation allows you to write

$\dfrac32xyz+96\lambda=0\implies \dfrac{xyz}2=-32\lambda$

Now, substituting this into the first three equations in the most recent system yields

$\begin{cases}-32\lambda+\lambda x^2=0\\-32\lambda+2\lambda y^2=0\\-32\lambda+3\lambda z^2=0\end{cases}\implies\begin{cases}x=\pm4\sqrt2\\y=\pm4\\z=\pm4\sqrt{\dfrac23}\end{cases}$

So we found a grand total of 8 possible critical points. Evaluating $f(x,y,z)=xyz$ at each of these points, you find that $f(x,y,z)$ attains a maximum value of $\dfrac{128}{\sqrt3}$ whenever exactly none or two of the critical points' coordinates are negative (four cases of this), and a minimum value of $-\dfrac{128}{\sqrt3}$ whenever exactly one or all of the critical points' coordinates are negative.

6 0

3 years ago

It took Azul 1.75 hours to bike The Blue Mountain Trail. Azul averaged 12.5 miles per hour. What is the best estimate for the le

Kryger [21]

The answer is 26 because if you round 12.5 it would be 13 and of you would round 1.75 it would be 2. After you do this you would multiply the 2 numbers and get 26 which is your answer.

5 0

3 years ago

Read 2 more answers

Which expression has the same value as -18 divided by -9?

jenyasd209 [6]

Answer:

<h3>-8 divided by (-4)</h3>

Step-by-step explanation:

-18 divided by -9 is <u>+2</u> and that is what you want.

-18 divided by 2 is -9, not correct.

-12 divided by (-3) is +4, not correct.

-10 divided by 5 is -2, not correct.

Leaving the <em>correct</em> answer: -8 divided by (-4) is <u>+2</u>.

Remember: a negative times a negative equals a positive.

8 0

3 years ago

An aerial photograph from a U-2 spy plane is taken of a building suspected of housing nuclear warheads. When the photograph is t

NISA [10]

Answer:

Building is 56.58 feet long.

Step-by-step explanation:

Consider the provided information.

An aerial photograph from a U-2 spy plane is taken of a building suspected of housing nuclear warheads.

When the photograph is taken, the angle of elevation of the sun is 30°.

By comparing the shadow cast by the building in question to the shadows of other objects of known size in the photograph, scientists determine that the shadow of the building in question is 98 feet long.

As we know: $\tan\theta=\frac{opp}{adj}$

The value of tan 30 degrees is $\frac{1}{\sqrt{3} }$

$\tan30=\frac{h}{98}$

$\frac{1}{\sqrt{3}}=\frac{h}{98}$

$h=\frac{98}{\sqrt{3}}$

$h=56.58$

Hence, Building is 56.58 feet long.

8 0

4 years ago

Which ordered pair can be included in the table of values shown below for the equation p=25x-2?

pishuonlain [190]

Answer:

(0,-2)

Step-by-step explanation:

So since you are given the equation, p=25x-2, all you really need to do is plug in the ordered pairs and see which satisfies the equation.

This means makes both side have the same number value.

Let's try (x,p)=(-2,-2):

p=25x-2 with (x,p)=(-2,-2)

-2=25(-2)-2

-2=-50-2

-2=-52

-2 and -52 do not represent the same number so (-2,-2) is not a point on the given line.

Let's try (x,p)=(-2,0):

p=25 x -2 with (x,p)=(-2,0)

0=25(-2)-2

0=-50-2

0=-52

0 and -52 do not represent the same number so (-2,0) is not a point on the given line.

Let's try (x,p)=(0,-2):

p=25 x -2 with (x,p)=(0,-2)

-2=25(0)-2

-2=0 -2

-2=-2

-2 and -2 are the same number and so (0,-2) is a point on the line.

Let's try (x,p)=(0,0)

p=25 x -2 with (x,p)=(0,0)

0 =25(0)-2

0 = 0 -2

0 = -2

0 and -2 are not the same number so (0,0) is not a point on this line.

6 0

4 years ago

Read 2 more answers