problem 6: Consider two vectors A and B, expressed in unit vector notations as A = a1i + a2j and b = b1i + b2j.

Answers

Answer 1

The scalar product of two vectors A and B can be expressed as A · B = a1b1 + a2b2.

For the given vectors A = a1i + a2j and B = b1i + b2j, the scalar product is A · B = a1b1 + a2b2.

The scalar product of two vectors is a number that can be calculated by multiplying each of the vectors’ components together and then adding them together.

In the given vectors, A and B, the scalar product is calculated by taking the product of the components of each vector and then adding them together.

The components of vector A are a1i and a2j, and the components of vector B are b1i and b2j. When these components are multiplied together and added, we get A · B = a1b1 + a2b2, which is the scalar product of the two vectors.

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Related Questions

Sloan is running with a momentum of 1850 kg m/s and has a mass of 58 kg. What is her velocity?

Answers

Answer:

v = 31.89 m/s

Explanation:

p = m × v

1,850 = 58 × v

58v = 1,850

v = 1,850/58

v = 31.89 m/s

You drive a bumper car into another bumper car whose driver has a much larger body mass than you do. Who experiences more of a jolt, you or the other driver?

Answers

Answer:

both drivers experience the same force. just with different "results"

Explanation:

Answer:

You do

Explanation:

Momentum is mass*velocity. So Newton's 3rd law equal and opposite reaction. Because you weigh less you will have more force act on you than the driver who weighs more.

HELP pleaseee which nucleus completes the following equation?

HELP pleaseee which nucleus completes the following equation?

Answers

Answer:

its D

Explanation:

i just got it correct on a. p. e. x. :)

According to the law of conservation of energy, which changes would

increase the total energy of a system?

A. An addition of 400 J of GPE and a loss of 250 J of thermal energy

B. An addition of 100 J of thermal energy and a loss of 450 J of

kinetic energy

C. An addition of 200 J of kinetic energy and a loss of 250 J of

thermal energy

D. An addition of 300 J of thermal energy and a loss of 450 J of

kinetic energy

Answers

Answer:

Correct option is (a)

Explanation:

According to conservation of energy: Total energy of system remains conserved or we can say total energy = constant

(a) 400J of GPE is added and 250J of thermal energy is lost

⇒ Total energy = 400-250 J  = 150 J

hence, 150J energy is increased

(b) 100J of thermal energy is added and 450J of kinetic energy is lost

⇒ Total energy = 100-450 J  = -350 J

hence, 350J energy is decreased or lost by system

(c)200J of kinetic energy is added and 250J of thermal energy is lost

⇒ Total energy = 200-250 J  = -50 J

hence, 50J energy is decreased or lost by system

(d)300J of thermal energy is added and 450J of kinetic energy is lost

⇒ Total energy = 300-450 J  = -150 J

hence, 150J energy is decreased or lost by system

Therefore, correct option is (a)

Answer: Correct option is (A)

Explanation:

According to conservation of energy: Total energy of system remains conserved or we can say total energy = constant

(a) 400J of GPE is added and 250J of thermal energy is lost

⇒ Total energy = 400-250 J  = 150 J

hence, 150J energy is increased

(b) 100J of thermal energy is added and 450J of kinetic energy is lost

⇒ Total energy = 100-450 J  = -350 J

hence, 350J energy is decreased or lost by system

(c)200J of kinetic energy is added and 250J of thermal energy is lost

⇒ Total energy = 200-250 J  = -50 J

hence, 50J energy is decreased or lost by system

(d)300J of thermal energy is added and 450J of kinetic energy is lost

⇒ Total energy = 300-450 J  = -150 J

hence, 150J energy is decreased or lost by system

Therefore, correct option is (a)

scientific thinking usually starts with what?

Answers

Answer:

Ask a question.

Explanation:

Your question is the basis of any theory.

Pictures A and B show the result when cars model convergent movement. What happens when two cars converge?

Answers

Answer:

bad

Explanation:

Ft-Fg= ma solve for Ft?

Answers

Post a picture please

how could you test the idea that solar enefgy is required for the hydrolisis of water during phtotosyntheiss

Answers

One way to test this hypothesis would be to conduct an experiment in which water is subjected to light sources of varying intensity.

What is phtotosyntheiss?

Photosynthesis is a process used by plants and some other organisms to convert light energy, typically from the sun, into chemical energy that can be used to fuel biological processes. During photosynthesis, light energy is absorbed by chlorophyll molecules in the plant's leaves and is then used to convert carbon dioxide and water into sugars and oxygen. This process provides the oxygen we breathe and the food we eat, making it one of the most important processes on Earth.

During the experiment, the rate of hydrolisis can be measured, and this data can then be compared to determine if the energy from the solar source is required for hydrolisis. Additionally, a control experiment can be conducted using light sources that do not contain solar energy, such as a light bulb, to compare to the solar energy experiment. This will allow scientists to determine the effect of the solar energy on the rate of hydrolisis, and confirm or refute the hypothesis.

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The wetter the surface, the friction

Answers

Answer: Water can either increase or decrease the friction between surfaces.

Suppose a(t) = 2 measured in seconds. Vt + 4e -5, V(0) = - 4, and S(0) = 5, where act), v(t) and s(t) represent the acceleration, velocity and distance from the starting point of an object. Distance is measured in meters and time is a. Find v(t). b. Find s(t). c. Find the velocity when t = 9. a. v(t) = b. s(t) = C. The velocity is m/sec. (Type an integer or decimal rounded to two decimal places as needed.)

Answers

a) The value of the required velocity is v(t) = t²/2 - 4t + 4e⁻⁵

b) The value of the required distance is S(t) = t³/6 - 2t² + 4e⁻⁵t + 5

c) The value of the velocity when t = 9 is approximately -28.2 m/sec

(a)To find v(t), we need to integrate a(t) first

a(t) = 2∫

a(t) dt = ∫ 2

dt = 2t + C1

Here, C1 is the constant of integration

Next, we need to integrate v(t) by substituting the value of a(t) into it

v(t) = ∫ (2t + C1)

dt= t² + C1t + C2

Here, C2 is another constant of integration

v(0) = - 4⇒ C2 = - 4

Also, given: v(t) = Vt + 4e⁻⁵

Comparing the above two equations:

v(t) = Vt + 4e⁻⁵ = t² + C1t - 4

On differentiating with respect to t, we geta(t) = 2

Therefore, we get the differential equation as:

Vt + 4e⁻⁵ = t² + C1t - 4 - - - - - - (1)

To find v(t), we need to solve this differential equation

Substituting t = 0, in (1), we get

-4 + 4 = 0 + C1(0)⇒ C1 = 0

Therefore, the differential equation becomes:

Vt + 4e⁻⁵ = t² - 4

On differentiating the above equation w.r.t t, we get:

a(t) = 2

Therefore, we get

v(t) = t²/2 - 4t + 4e⁻⁵ - - - - - - (2)

Thus, the required velocity is given by:

v(t) = t²/2 - 4t + 4e⁻⁵

Part (b) To find s(t), we need to integrate v(t) first

v(t) = t²/2 - 4t + 4e⁻⁵∫ v(t)

dt = ∫ (t²/2 - 4t + 4e⁻⁵)

dt= t²/6 - 2t² + 4e⁻⁵t + C3

Here, C3 is the constant of integration

Also, given that S(0) = 5⇒ C3 = 5

Therefore, we get

S(t) = t³/6 - 2t² + 4e⁻⁵t + 5 - - - - - - (3)

Thus, the required distance is given by:

S(t) = t³/6 - 2t² + 4e⁻⁵t + 5

Part (c) To find the velocity when t = 9We can use the value of v(t) obtained in part (a)⇒ v(9) = (9)²/2 - 4(9) + 4e⁻⁵⇒ v(9) = - 28.2 (approx)

Thus, the velocity when t = 9 is -28.2 (approx)m/sec.

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1. An airplane flies with a constant speed of 720 km/h. How long will it take to travel a distance of 1500
kilometers?

Answers

Answer:

\(125\:\mathrm{minutes\: or\: }2.08\bar{3}\: \mathrm{hours}\)

Explanation:

Speed is given by \(s=\frac{d}{t}\), where \(d\) is distance travelled and \(t\) is time. Rearranging this equation, we have \(t=\frac{d}{s}\).

Plugging in our given information:

\(t=\frac{d}{s}=\frac{1500\:\mathrm{km}}{720\:\mathrm{km/h}}=2.08\bar{3}\: \mathrm{hours}\)

Thus, our answer is:

\(2.08\bar{3}\: \mathrm{hours}\cdot \frac{60\:\mathrm{minutes}}{1\:\mathrm{hour}}=\fbox{$125\:\mathrm{minutes}$}\)

a skier starts at rest at the top of a hill with 350 J of gravitational potential energy. Assuming energy is conserved, what is her final kinetic energy at the lowest point

Answers

Answer:

350Joules

Explanation:

According to law of Conservation of energy, the amount of energy at the used up at the start is equal to that at the end.

The initial energy used up is gravitational potential energy

Final energy at the lowest point is kinetic energy.

If the energy is conserved then it means energy is not used up during the process hence;

Initial Potential energy = Final kinetic energy

If the gravitational potential energy is 350Joules then her final kinetic energy at the lowest point will also be 350Joules

A circuit has a current of 3. 6 A and a resistance of 5. 0 Ω. What is the voltage applied to the circuit? 0. 72 V 1. 4 V 8. 6 V 18 V.

Answers

Answer:

18 V

Explanation:

According to Ohm's Law, current equals voltage divided by resistance. (I=V/R)

Using this, we can rearrange the equation to have it solved for voltage.

V=IR

Then, you plug in the values for the current and the resistance.

V=(3.6)x(5.0)

V=18

Find the distance traveled in 27 seconds by an object traveling at a constant velocity of 15 feet per second.

Answers

The distance d travelled by in object is 68.58 m

What is velocity ?

velocity is defined as rate of change of displacement d of the object with respect to rate of change in time t. In mathematics It is written as :

v = d/t

it should be noted that, velocity is nothing but speed in particular direction. That is velocity is vector quality having both magnitude and direction where as speed is just the magnitude of velocity.

1 feet = 0.3048 m

15 feet = 4.572 m

Now, calculating the distance d travelled by in object :

d = vt

d = 4.572 x 27

d = 68.58 m

Therefore, the distance d travelled by in object is 68.58 m

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Energy is not
1. a scalar.
2.operationally defined.
3.measured in joules.
4.created or destroyed.

Answers

Explanation:

think4

pleas! mark me s brainliest please please

I think 4 is correct

the total energy of a system is 300j. if the potential energy is 40j what is the kinetic energy if the object started 300m above the ground?

Answers

Answer:

43.3 m/s.

Explanation:

Assuming the potential energy is due to the gravitational potential energy, we can use the conservation of energy to find the kinetic energy:

Total energy = Potential energy + Kinetic energy

Kinetic energy = Total energy - Potential energy

Kinetic energy = 300 J - 40 J = 260 J

However, we need to know the mass of the object to convert the kinetic energy to velocity. We can use the potential energy to find the mass:

Potential energy = mgh

40 J = m(9.81 m/s^2)(300 m)

m = 0.137 kg

Now we can use the kinetic energy to find the velocity:

Kinetic energy = (1/2)mv^2

260 J = (1/2)(0.137 kg)v^2

v^2 = (2*260 J) / 0.137 kg

v = 43.3 m/s (rounded to one decimal place)

Therefore, the kinetic energy is 260 J and the velocity of the object when it reaches the ground is 43.3 m/s.

A man can use a snowblower to move snow in 5 minutes. If he moves it with a shovel, will take 20 minutes. He will use more power with which process?

Answers

Answer:

the second process of using the the shovel to move the snow as it takes a longer time meaning more power is expended

Why do planets like Jupiter and Saturn have large gas atmospheres while Mercury and Mars do not?
options:

Because Jupiter and Saturn have more mass


Because of each planets distance from the Sun


Because of their different orbits around the Sun


Because they were formed at different times

Answers

The solar system shows the planets in their orbits around the sun in this order: Mercury, Venus, Earth with Moon, Mars, Jupiter, Saturn. Fixed stars are around the outside of the orbit of Saturn.

Explanation:

Aristarchus of Samos was an ancient Greek astronomer and mathematician who presented the first known heliocentric model that placed the Sun at the center. So I had to choose the choice that was most similar to that.

A force of 6.0 N gives a 2.0 kg block an acceleration of 3.0
m/s² to the right.
The force of friction acting on the block is
N.

Answers

Answer: I think it’s 0N

Heat is the measurement of energy from all the particles that are in a substance.
Please select the best answer from the choices provided : T/F

Answers

Explanation:

the correct answer is (true) if am not mistaking incase am wrong sorry

Sally and Misha pushed a cart toward the right with a force of 24 N each. If Jeff pushed on the cart in the opposite direction, how much force would he need to use to cause the cart to experience balanced forces? (Answer with a number)​

Answers

Answer:

F = 48 [N]

Explanation:

To solve this problem we must use Newton's third law, which tells us that the sum of forces on a body must be equal to zero, that is, the body is in static equilibrium or in equilibrium.

ΣF = 0

24 + 24 - F = 0

F = 24 + 24

F = 48 [N]

Note: Jeff's force should be equal to the sum of Sally and Misha's forces, but in the opposite direction.

10. Makiko pulls her sister Keko of mass 18 kg along a horizontal sidewalk at a constant speed of 1.2 m/s by applying a force of 0.91 x 102 N [27° above the horizontal]. What is the coefficient of ki

Answers

The coefficient of kinetic friction between Makiko and her sister is approximately 0.226.

μ = (F_friction) / (F_normal)

where:

μ is the coefficient of kinetic friction,

F_friction is the force of friction,

F_normal is the normal force.

First, we need to find the normal force acting on Keko. Since they are on a horizontal surface and moving at a constant speed, the normal force is equal in magnitude and opposite in direction to the gravitational force:

F_normal = m * g

where:

m is the mass of Keko, and

g is the acceleration due to gravity (approximately 9.8 m/s^2).

Given:

mass of Keko (m) = 18 kg

F_normal = 18 kg * 9.8 m/s^2

F_normal = 176.4 N

Next, we can calculate the force of friction (F_friction) using the force applied by Makiko. The force of friction can be determined by resolving the applied force into horizontal and vertical components.

F_friction = F_applied * sin(θ)

where:

F_applied is the applied force, and

θ is the angle above the horizontal (27°).

Given:

applied force (F_applied) = 0.91 x 10^2 N

angle above the horizontal (θ) = 27°

F_friction = (0.91 x 10^2 N) * sin(27°)

F_friction ≈ 39.97 N

Now we can calculate the coefficient of kinetic friction (μ):

μ = F_friction / F_normal

μ = 39.97 N / 176.4 N

μ ≈ 0.226

Therefore, the coefficient of kinetic friction between Makiko and her sister is approximately 0.226.

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Can someone please explain these or help answer them? ​

Can someone please explain these or help answer them?

Answers

Answer:

41.57.

Explanation:

Sometimes if you type in google "area of a regular hexagon, it will give you a calculator you can use to solve your math questions.

Answer:41.57

Hope this help

how to calculate load​

Answers

Add together the wattage capacity of all general lighting branch circuits.
Add in the wattage rating of all plug-in outlet circuits.
Add in the wattage rating of all permanent appliances (ranges, dryers, water heaters, etc.)
Subtract 10,000.
Multiply this number by .40
Add 10,000.
Look for the full wattage rating of permanent air conditioners, and the wattage rating heating appliances (furnace plus space heaters), then add in whichever is the larger of these two numbers. (You don't heat and cool at the same time, so don't need to add both numbers.)
Divide the total by 240.

the answer should give you the suggested amperage needed to power a home adequately.

Activity of integration Most of the people in a certain village called Bileafe where much tobacco is grown bought vehicles after tobacco sales. However, no sooner than later many of the vehicles either broke down or they were parked at home since fuel became expensive to afford. As a student of chemistry, develop a message for the owners of the cars in this village explaining why the vehicles should be kept well even if they are spoilt, where they should be kept, and what kind of change they will undergo if not properly kept. You can use the resources to help you develop the message.​

Answers

They will be instructed to park their cars in a cool dry environment in order to prevent rusting of the vehicle parts.

What is Rusting?

This is defined as a chemical change in which Iron reacts with Oxygen to form a new substance called Iron oxide.

Iron oxide is usually brownish in color and further corrodes the metal parts. It is also referred to as a Chemical change in chemistry due to new substance being formed.

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PLZZ ANSWER THE QUESTION ​

PLZZ ANSWER THE QUESTION

Answers

The answer is negative and strong because the line is going downwards and the dots are tight

The image shows positivle and negative charged particles bouncing around. Which state of matter is most likely represented in the image?​

The image shows positivle and negative charged particles bouncing around. Which state of matter is most

Answers

Answer:

Gas Solid Liquid Plasma

Explanation:

Answer:

plasma

Explanation:

plasma has charged particles and ions and electrons floating around

The density of an object can be found using
(A) Pascal's Law
(B)Hooke's Law
(C)Archimedes' Principle
(D)Principle of floatation

Answers

Principle of floatation.

a boulder and a pebble are sitting on a cliff which has greater grvitational potential energy and why? a cheetah and a person are racing both has the same mass whifh has greater kinetic energy and why.​

Answers

since both boulder and pebble are at the same height from ground, the one with the greater mass would have more GPE. Cheetah has greater KE. as KE = 0.5mv^2 so since both person and cheetah have the same mass, cheetah would obviously have greater speed, v thus greater KE

An infinite line of charge with charge density λ1 = 1.8 μC/cm is aligned with the y-axis as shown.
1)What is Ex(P), the value of the x-component of the electric field produced by by the line of charge at point P which is located at (x,y) = (a,0), where a = 8.6 cm?
2) What is Ey(P), the value of the y-component of the electric field produced by by the line of charge at point P which is located at (x,y) = (a,0), where a = 8.6 cm?
3) A cylinder of radius a = 8.6 cm and height h = 8.5 cm is aligned with its axis along the y-axis as shown. What is the total flux Φ that passes through the cylindrical surface? Enter a positive number if the net flux leaves the cylinder and a negative number if the net flux enters the cylnder.
4) Another infinite line of charge with charge density λ2 = -5.4 μC/cm parallel to the y-axis is now added at x = 4.3 cm as shown.
5) What is the total flux Φ that now passes through the cylindrical surface? Enter a positive number if the net flux leaves the cylinder and a negative number if the net flux enters the cylnder.
6) The initial infinite line of charge is now moved so that it is parallel to the y-axis at x = -4.3cm. What is the new value for Ex(P), the x-component of the electric field at point P?
7) What is the total flux Φ that now passes through the cylindrical surface? Enter a positive number if the net flux leaves the cylinder and a negative number if the net flux enters the cylnder. N-m2/C

Answers

To solve the given problems, I will assume you are referring to a Cartesian coordinate system, where the x-axis is horizontal and the y-axis is vertical. To find the x-component of the electric field (Ex) at point P, we can use the formula:

Ex(P) = (k * λ1 * a) / (2πε₀ * (a² + y²)^(3/2))

Where:

k is the Coulomb's constant (approximately 8.99 × 10^9 N m²/C²)

λ1 is the charge density of the line of charge

a is the x-coordinate of point P

ε₀ is the permittivity of free space (approximately 8.85 × 10^12 C²/N m²)

y is the y-coordinate of point P, which is 0 in this case

Plugging in the given values, we get: Ex(P) = (8.99 × 10^9 N m²/C² * 1.8 × 10^(-6) C/cm * 8.6 cm) / (2π * 8.85 × 10^(-12) C²/N m² * (8.6 cm)²). Calculate the expression to find the value of Ex(P). Since the line of charge is aligned with the y-axis and point P is located on the x-axis (y = 0), the y-component of the electric field (Ey) at point P is zero.

Ey(P) = 0. To calculate the total flux (Φ) passing through the cylindrical surface, we can use Gauss's Law. Since the cylinder is symmetric, the electric field is constant and perpendicular to the surface at all points. The flux passing through the surface is given by:

Φ = E * A

Where:

E is the magnitude of the electric field

A is the area of the cylindrical surface

Calculate the expression to find the value of Φ. When the second line of charge with charge density λ2 is added, the electric field at point P will change. To find the new values of Ex(P) and Ey(P), we need to calculate the electric field contribution from both line charges and add them together. Follow the same approach as in problem 3 to calculate the new total flux Φ passing through the cylindrical surface. When the initial line of charge is moved parallel to the y-axis at x = -4.3 cm, the x-component of the electric field at point P (Ex(P)) will change. Use the same formula as in problem 1 with the new position of the line of charge to calculate the new value of Ex(P).

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Random variable X and Y have the following joint probability distribution. (a) Find P(X + Y which of the following sets of policies appears to be most influenced by a liberal ideology? choose 1 answer: choose 1 answer: (choice a) establish a universal healthcare program to insure all americans a establish a universal healthcare program to insure all americans (choice b) create strict identification requirements for voting b create strict identification requirements for voting (choice c) ban transgender individuals from serving in the military c ban transgender individuals from serving in the military (choice d) expand production of oil, coal, and natural gas industries d expand production of oil, coal, and natural gas industries In this chapter, we have looked at rectangular prisms and their surface area and volume. We developed formulas for both measurements.We used the net of a rectangular prism to see all of the faces and calculate the surface area. 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Write the equation of the line that passes through the point (-4,-9) and has a slope of 1/2. which of the following would be correct, given the following information? estimated manufacturing overhead $374,400 estimated direct labor hours 20,800 actual manufacturing overhead $402,000 actual direct labor hours 23,000 multiple choice overhead is overapplied by $12,000. overhead is underapplied by $12,000. overhead is underapplied by $27,600. overhead is overapplied by $27,600. A group of customers at a fast food restaurant bought 8 hamburgers, 6 large orders of fries, and 6 large sodas for $26.10. A second group ordered 10 hamburgers, 6 orders of large fries, and 8 large sodas and paid $31.60. A third group bought 3 hamburgers, 2 large fries, and 4 large sodas for $10.95. Determine the price of each food item (hamburger, large fries, and large soda). Sketch the region enclosed by the given curves. x = 8y^2, x = 5 + 3y^2. What is its area? 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Normally when scientists and philosophers says that some behavior is human nature they mean that --Hint see Kupperman, Theories of Human Nature. - everybody should act like that. - everyone always acts that way. - almost anybody would act that way in the same situation - nobody really acts like that Describe three ways in which a formal group may exercise control over it's members. you know roughly the decrease in vo2max that occurs on the summit of mount everest vs. that at sea level. you have a client that weighs 198 lb and has a vo2 max of 4.8 l/min. provide the following information 1) what is this persons relative vo2 max at sea level (in ml/min/kg), 2) roughly, what would their vo2 max be at the top of everest after acclimation? 5. What are the spans of the following pressure gages: The gage measures pressure from 70 cm Hg vacuum to 200 kPa. 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