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Ilia_Sergeevich [38]
2 years ago
10

Astronomers have found water on mars.

Physics
1 answer:
vodomira [7]2 years ago
4 0

The thin atmosphere of Mars is thought to be due to the planet's lack of a magnetic field, which has allowed the Solar wind to blow away much of the gas the planet once had. Venus, despite still having a thick atmosphere of CO2, surprisingly has a similar problem

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Find the area of the part of the plane 5x 3y z = 15 that lies in the first octant.
Lunna [17]

This part of the plane lies above a triangle with boundaries x=0 and y=0 along the coordinate axes, as well as the line

z=0 \implies 5x + 3y = 15 \implies y = \dfrac{15 - 5x}3

When y=0, we have 15-5x=0\implies x=3. So this triangle is the set

T = \left\{(x,y)\in\Bbb R^2 ~:~ 0\le x\le3 \text{ and } 0\le y\le\dfrac{15-5x}3\right\}

Also, when x=0, we have y=\frac{15}3=5. So the triangle has length 3 and width 5, hence area 1/2•3•5 = 15/2.

Let z=f(x,y) = 15 - 5x - 3y. Then the area of the plane over T is

\displaystyle \iint_T dA = \iint_T \sqrt{1 + \left(\frac{\partial f}{\partial x}\right)^2 + \left(\frac{\partial f}{\partial y}\right)^2} \, dx \, dy

We have

\dfrac{\partial f}{\partial x} = -5 \implies \left(\dfrac{\partial f}{\partial x}\right)^2 = 25

\dfrac{\partial f}{\partial y} = -3 \implies \left(\dfrac{\partial f}{\partial y}\right)^2 = 9

\implies\displaystyle \iint_T dA = \sqrt{35} \iint_T dx\,dy = \boxed{\frac{15\sqrt{35}}2}

since the integral

\displaystyle \iint_TdA

is exactly the area of T, 15/2.

8 0
2 years ago
A boy throws a baseball onto a roof and it rolls back down and off the roof with a speed of 3.05 m/s. If the roof is pitched at
vekshin1

1) Time in the air: 0.78 s

The motion of the ball is a projectile motion, which consists of two independent motions:

- A horizontal motion with constant horizontal velocity

- A vertical motion with constant downward acceleration of

g=-9.8 m/s^2 (acceleration of gravity)

The initial vertical velocity is

u_y = u sin \theta = (3.05)(sin(-40^{\circ}))=-1.96 m/s

where the negative sign means the direction is downward.

The vertical position of the ball is given by

y(t) = h + u_y t + \frac{1}{2}gt^2

where

h = 4.50 m is the initial heigth of the ball when it starts falling down

The ball reaches the ground when y = 0, so we have:

0 = 4.50 -1.96t-4.9t^2

This is a second-order equation; solving for t, we get

t = -1.18 s

t = 0.78 s

We discard the negative solution since it has no physical meaning, so we can say that the ball spent 0.78 s in the air.

2) Horizontal distance: 1.83 m

For this second part of the problem, we just have to consider the horizontal motion of the ball.

As we said previously, the motion of the ball along the horizontal direction is a uniform motion with constant velocity, which is given by

v_x = u cos \theta = (3.05)(cos (-40.0^{\circ}))=2.34 m/s

where u = 3.05 m/s is the initial speed and \theta the angle of projection.

For a uniform motion, we can use the following relationship between distance covered and velocity:

d=v_x t

and substituting t = 0.78 s, we find the total distance travelled along the horizontal direction by the ball before reaching the ground:

d=(2.34)(0.78)=1.83 m

7 0
3 years ago
Which word means "to get away from something"? <br> a become b dream c escape d practice
klemol [59]

The correct answer is - c. escape.

The word ''escape'' means to get away from something. This word can be used for multiple different situations, and it can refer to both physical and psychological matters.

In a physical sense it can be used to escape from certain unpleasant, or dangerous situation. Example: I have to escape from this prison.

In a psychological sense it can be used to escape, move away, from a certain state of mind. Example: I have to find an escape from my depressive thoughts.

5 0
3 years ago
Which of these is an example of a chemical reaction that occurs at a very slow rate?
spin [16.1K]

Answer:

acid rain

Explanation:

cause it desolved in slow ways

8 0
3 years ago
Read 2 more answers
What is 3.75 x 10^-7?
pogonyaev

Answer:

Explanation:

3.75 * 10^-7

=3.75 * 1/10^7

=3.75/10000000

=3/800000000

any base which has it's power negative do it's reciprocal then the power will be positive.

8 0
3 years ago
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