I need help with this, I can't figure it out.
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Distribute the product:

a×b = (8i + j - 2k) × (5i - 3j + k)

a×b = 8i × (5i - 3j + k) + j × (5i - 3j + k) - 2k × (5i - 3j + k)

a×b = (40 (i×i) - 24 (i×j) + 8 (i×k))

… … … + (5 (j×i) - 3 (j×j) + k×j)

… … … + (-10 (k×i) + 6 (k×j) - 2 (k×k))

Recall the definition of the cross product:

i×i = j×j = k×k = 0 (the zero vector)

i×j = k

j×k = i

k×i = j

and for any two vectors x and y, we have x×y = -(y×x).

So we have some cancellation and rewriting:

a×b = (40 (i×i) - 24 (i×j) + 8 (i×k))

… … … + (5 (j×i) - 3 (j×j) + j×k)

… … … + (-10 (k×i) + 6 (k×j) - 2 (k×k))

a×b = (-24k - 8j) + (-5k + i) + (-10j - 6i)

a×b = -5i - 18j - 29k

Then

b×a = -(a×b) = 5i + 18j + 29k

Answer:

change is imperceptible

          w_f = 7.272  10⁻⁵ rad / s

Explanation:

For this exercise we can use the conservation of angular momentum.

Initial. Before the crash

        L₀ = I w₀

final. After the crash

         L_f = I w_f + p r

where the moment is

        p = mv

As the system is formed by the two bodies, the forces during the impact are internal, therefore the angular momentum is conserved

        L₀ = L_f

        I w₀ = I w_f + m v r

        w_f = w₀ - [tex]m \frac{ v \ r }{I}[/tex]

We can approximate the Earth to a sphere, so its angular momentum is

       I = 2/5 M r²

we substitute

         w_f = w₀ - [tex]\frac{5 \ m \ v}{2 \ M \ r}[/tex]

We can find the angular velocity of the Earth with the duration of a spin which is the period of one day

        w₀ = 2π / T

        T = 24 h (3600 s / 1h) = 86 400 s

         w₀ = 2π / 86400

         w₀ = 7.272 10⁻⁵ rad / s

let's calculate

         w_f = 7.27 10⁻⁵ - [tex]\frac{5 \ 250 \ 10^{13} \ 33.0 \ 10^{3} }{ 2 \ 5.98 \ 10^{24} \ 6.37 10^{6} }[/tex]

         w_f = 7.272 10⁻⁵ - 1.0829 10⁻¹³

         w_f = 7.27199999 10⁻⁵

this change is imperceptible

          w_f = 7.272  10⁻⁵ rad / s

Answer: The path will be a parabola.

Explanation: The path is a parabola because the motion described is a projectile motion, in which an object thrown or projected is subjected only to the acceleration.

In this motion, velocity must be constant and horizontal and acceleration is perpendicular compared to the direction of the velocity. In these conditions, the path is a parabola and the motion is a projectile.

Answer:

Ti and O

Explanation:

It is what it is.

Answer:

B. Ti and O

Explanation:

A.P.E.X

Answer:

B) The molecule is small enough so that quantum effects are important.

Explanation:

The molecules of water behave like wave and their motion cannot be accurately predicted by classical physics laws but can be properly predicted by quantum theory.

Classical physics describes matter that behave like solid particles while quantum effect describes matter that behaves like waves.

Therefore, the correct option is B.

Answer: 4R

Explanation:R=pL/A

R second wire=p2L/1/2A

=4R

Answer:

its the top 3 can confirm on plato

Explanation:

Answer:

plato

Explanation:

Answer:

7976 Pascals significant figure= 7.9*10^3

Explanation:

formula of hpg = height*density*gravitational energy

.80*10*997=7976 pascals

Answer:

1.092 cycles

Explanation:

We need to convert the arc length of 6.86 radians into cycles.

We know that,

1 radian = 0.1592 cycles

To convert 6.86 radians to cycles, we use unitary method.

6.86 radian = (0.1592 × 6.86) cycles

= 1.092 cycles

Hence, there are 1.092 cycles in 6.86 radians. Hence, this is the required solution.

25.10 or 24.6m/s both answers are correct

Explanation:

firstly , divide the multiply with 2 and divide the result by acceleration due to gravity which is 9.8m/s or 10m/s

123*2=246

246/9.8 or 10

= 25.10 or 24.6m/s

Answer:

Explanation:

Let us calculate the average velocity .

Average velocity = total distance / total time

Time taken to drive first 15 mi

= 15 / 60 = .25 h

Time taken to drive next 15 mi

= 15 / 30 = .5 h

Total time = .25 + .5 = .75 h

Total distance = 30 mi

average speed = 30 / .75

= 40 mi / h

So average speed is 40 mph which is less than given velocity of 45 mph .

Hence if she travels at 45 mph , she will take less time .

Answer:

Fn=m(a + g) :

Explanation:

nf=a(m +g)

an=f(g+m)

Answer:

100

w=f*s

20*5=100....

100 Joules of work is done on the cart.

Work done by a force is defined as the product of the displacement and the component of the applied force on the object in the direction of displacement. When we push a block with some force, the body moves with some acceleration, so it is called work done.

Work done is expressed as W=Fd and its unit is joules which can be defined as the amount of work done by a force in Newton is applied to an object, as a result of which it is displaced in meter.

For above given information,

Force= 20 N

Distance= 5 m

So, work done= 20*5= 100 Joules

Thus, 100 Joules of work is done on the cart.

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That depends on the circle's radius, which you neglected to mention.

If the radius is 1 meter, then an arc of 3.05 degrees is 5.32 centimeters long.

If the radius is 1 kilometer, then an arc of 3.05 degrees is 53.2 meters long.

Answer:

there are 2188 people at the game

Explanation:

Given the data in the question;

we know that decibel is defined as; dB = 10log(l/l₀)

so if one produces an intensity l₁, it results in 69.6 dB

69.6 = 10log(l₁/l₀) ---- equ1

also. if x number of people produces this intensity, it result to 103 dB

103 = 10log(xl₁/l₀)

103 = 10( log(l₁/l₀) + log(x) )

103 = 10log(l₁/l₀) + 10log(x) ----- equ2

input equation 1 into to equation 2

103 = 69.6 + 10log(x)

10log(x) = 103 - 69.6

10log(x) = 33.4

divide both side by 10

log(x) = 3.34

x = [tex]10^{3.34}[/tex]

x = 2187.76 ≈ 2188

Therefore, there are 2188 people at the game

Answer:

Volume of cube is equal to two times the weight of replaced water [tex]1000[/tex] Kg

Explanation:

Length of one side of cube is [tex]1[/tex] meter

Volume of cube [tex]= 1* 1* 1 = 1[/tex] cubic meter

Half of the wood sank

Hence, the volume of water replaced will be equal to half the volume of cube

Volume of water replaced [tex]= \frac{1}{2} = 0.5[/tex] cubic meter

Density of water [tex]1 * 10^3[/tex] kg/m3

Weight of water replaced

[tex]= 1 * 10^3 * 0.5\\= 500[/tex]Kg

Volume of cube is equal to two times the weight of replaced water

[tex]= 2* 500 = 1000[/tex] Kg

Answer:

A negative slope results when an individual is moving away

Explanation:

Answer:

i dont know!

Explanation:

Answer:

1. ELE to KE = Electrical energy conversion to kinetic energy.

2. KE to ELE = kinetic energy conversion to electrical energy.

3. CE to ELE = chemical energy conversion to electrical energy.

Explanation:

The Law of Conservation of Energy states that energy cannot be destroyed but can only be transformed or converted from one form to another.

Some examples of energy are chemical energy, electrical energy, kinetic energy, sound energy, potential energy, light energy, etc.

The transformation of energy from one form to another are described below;

1. A hair dryer plugged into the wall: it involves the conversion of electrical energy to kinetic energy. The energy type present in the wall socket is electrical energy which powers the hair dryer to have kinetic energy i.e the energy possessed due to motion of hair dryer.

2. A hand crank generator emergency radio: it illustrates the conversion of kinetic energy to electrical energy. The hand crank generator possess kinetic energy as it is being wounded before it is then converted into electrical energy which powers the radio.

3. A battery operated fan: it illustrates the conversion of chemical energy to electrical energy. The cells present in battery possess chemical energy that is being converted into electrical energy to power the fan.

Answer:

It will no light because the electric source is the only thing required to power the bulb.

Explanation:

Answer:

mass and distance

Explanation:

mass, and distance. The force of gravity depends directly upon the masses of the two objects, and inversely on the square of the distance between them.

Answer:

Potential difference [tex]V=1.6\times 10^{-10}\ V[/tex]

Explanation:

Capacitance of capacitor, C = 0.9 MF

Charge, [tex]Q=1.4\times 10^{-4}\ C[/tex]

We need to find the amount of potential difference. We know that,

[tex]Q=CV[/tex]

V is potential difference

So,

[tex]V=\dfrac{Q}{C}\\\\V=\dfrac{1.4\times 10^{-4}}{0.9\times 10^6}\\\\V=1.6\times 10^{-10}\ V[/tex]

So, the required potential difference is [tex]1.6\times 10^{-10}\ V[/tex].

Answer:

4

Explanation:

The momentum of the object is 100 kgm/s, therefore the magnitude of the velocity of the object is 4 meters per second.

Momentum of an object is the product of its mass and velocity. Momentum is the quantity of motion which is made up of the amount of matter which is being moved and the velocity at which the object moves. When we walk, run, etc., then we have momentum.

p = m × v

where, p is the momentum of the object,

m is the mass of the object,

v is the velocity of the object

p = 100 kgm/s

m = 25 kg

p = m × v

v = p/m

v = 100/ 25

v = 4 m/s

Therefore, the magnitude of velocity of the object is 4 meters per second.

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Answer:

The number of O₂ molecules that are left in the cylinder is 1.70x10²⁴.

Explanation:

The number of oxygen molecules can be found using the Ideal Gas law:

[tex] PV = nRT [/tex]        

Where:

P: is the pressure = 100 psi

V: is the volume = 10 L

n: is the number of moles =?

T: is the temperature = 20 °C = 293 K

R: is the gas constant = 0.082 L*atm/(K*mol)

Hence, the number of moles is:

[tex]n = \frac{PV}{RT} = \frac{100 psi*\frac{1 atm}{14.7 psi}*10 L}{0.082 L*atm/(K*mol)*293 K} = 2.83 moles[/tex]

Now, the number of molecules can be found with Avogadro's number:

[tex]n_{m} = \frac{6.022 \cdot 10^{23}\: molecules}{1\: mol}*2.83 moles = 1.70 \cdot 10^{24} \: molecules[/tex]

Therefore, the number of O₂ molecules that are left in the cylinder is 1.70x10²⁴.

I hope it helps you!              

Answer:

Its radius is thought to be around 1400 times than of our sun, and its luminosity 270,000 greater than our sun. Also, if a star has the same radius as the sun but a higher surface temperature, the hotter star exceeds the sun in luminosity

Explanation:

As the solar radius of the star increases, the brightness of the star also increases.

Luminosity is defined as the measure of brightness of a celestial object or the relative quantity of light.

Here,

Solar radius is a unit of distance, which is used to determine the size of the stars relative to the sun.

The size of the star and the luminous intensity are directly proportional. As the size of the star increases, the luminosity of the star also increases. Therefore, larger stars shine more brighter than the smaller ones.

The brightness of a star is directly proportional to the square of its solar radius. Therefore, the luminosity increases with increase in solar radius.

Hence,

As the solar radius of the star increases, the brightness of the star also increases.

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Answer:

True

Explanation:

Friction occurs because no surface is perfectly smooth. Even surfaces that look smooth to the unaided eye make look rough or bumpy when viewed under a microscope. You know that friction produces heat. That’s why rubbing your hands together makes them warmer. But do you know why? Friction causes the molecules on rubbing surfaces to move faster, so they have more energy. This gives them a higher temperature, and they feel warmer. Heat from friction can be useful. It not only warms your hands.