If a · b = 20, a = 4, and the angle between the vectors a and b is 30°, what is the magnitude of vector b? Incorrect: Your answer is incorrect.
Answer:
The magnitude of [tex]\vec b[/tex] is approximately 5.774.
Explanation:
According to the definition of dot product:
[tex]\vec a\bullet \vec b = \|\vec a \|\cdot \|\vec b\|\cdot \cos \theta[/tex]
Where:
[tex]\|\vec a\|[/tex], [tex]\|\vec b\|[/tex] - Norms (or magnitudes) of [tex]\vec a[/tex] and [tex]\vec b[/tex], dimensionless.
[tex]\theta[/tex] - Internal angle between [tex]\vec a[/tex] and [tex]\vec b[/tex], measured in sexagesimal degrees.
The magnitude of [tex]\vec b[/tex] is therefore cleared:
[tex]\|\vec b\| = \frac{\vec a \bullet \vec b}{\|\vec a\|\cdot \cos \theta}[/tex]
Given that [tex]\vec a \bullet \vec b = 20[/tex], [tex]\|\vec a\| = 4[/tex] and [tex]\theta = 30^{\circ}[/tex], the magnitude of [tex]\vec b[/tex] is:
[tex]\|\vec b\| = \frac{20}{4\cdot \cos 30^{\circ}}[/tex]
[tex]\|\vec b\| \approx 5.774[/tex]
The magnitude of [tex]\vec b[/tex] is approximately 5.774.
charlie drove his car around the block at a constant velocity, true or false, why or why not
Answer:
The given statement is false.
Explanation:
When you change position or direction as well as move rapidly, the velocity changes. So, if you're traveling or moving around over a block, you're shifting a lot of speed but instead, you likely won't it will be at a continuous rate or pace.Along with its quickest-changing direction, it might travel at reasonable acceleration but never of constant velocity.
1. Which statement about friction is true?(1 point) A. Static friction and kinetic friction in a system always act in the same direction as each other and in the opposite direction of the applied force. B. Static friction and kinetic friction in a system always act in the same direction as each other and in the same direction as the applied force. C. Static friction and kinetic friction in a system always act in opposite directions of each other and in the same direction as the applied force. D. Static friction and kinetic friction in a system always act in opposite directions of each other and in the opposite direction of the applied force. 2. A brick is resting on a smooth wooden board that is at a 30° angle. What is one way to overcome the static friction that is holding the brick in place?(1 point) A. roughen up the texture of the wooden board B. press down on the brick in a direction that is perpendicular to the board C. lower the board so it's level with the ground D. raise the board to a higher angle
Answer:
true 1Ay 2D
Explanation:
1) In this exercise you are asked to investigate which statements are true
A) True. The friction force opposes the movement caused by the external force,
B) False. Mantuano in the opposite direction force
C) False. The static and scientific friction force act in the same direction, since the second appears when the movement does not start and the static friction decreases.
D) Fale the static and kinetic friction forces act in the same direction
2) How to overcome friction on a ramp
A) False. If the texture of the surface becomes rough, the friction force increases
B) False. Pressing the brick against the surface increases the normal and as the friction is proportional to the normal, it also increases
C) False. By lowering the table the weight component in the friction direction decreases
D) True. When lifting the board, the weight component increases and therefore can become greater than the friction
Wx-fr = ma
W sin tea - my mg cos tea = m a
As it increases, the sine increases and the cosine decreases.
What is the slope of the line passing through the points (7,4) and (2, 10)?
Answer:
the equation of a straight line is y = m x + b where m is the slope and
b is the y intercept at x = 0
so y1 = x1 + b and y2 = m x2 + b where (x1, y1) and (x2, 2 are points on the line.
y2 - y1 = m (x2 - x1) or m = (y2 - y1) / (x2 - x1)
For the given points
m = ( 10 - 4) / (2 - 7) = - 6 / 5 for the slope
The Carson family's pancake recipe uses 2 teaspoons of baking powder for every 1/3 of a teaspoon of salt. How much baking powder would they need if they used 1 teaspoon of salt?
Answer:
6 teaspoons of baking powder required.
Explanation:
Given that
According to the recipe of pancake,
For every [tex]\frac{1}{3}[/tex] teaspoon of salt, 2 teaspoons of baking baking powder is required.
To find:
How much baking powder will be needed, if 1 teaspoon of salt was used ?
Solution:
This problem can be solved using ratio.
[tex]\frac{1}3[/tex] teaspoon of salt : 2 teaspoons of baking powder
Let us multiply the above ratio with 3.
[tex]\frac{1}{3}\times 3[/tex] teaspoon of salt : 2 [tex]\times[/tex] 3 teaspoons of baking powder
OR
1 teaspoon of salt : 6 teaspoons of baking powder
So, answer is 6 teaspoons of baking powder required.
Also, we can use the unitary method:
[tex]\frac{1}3[/tex] teaspoon of salt needs = 2 teaspoons of baking powder
1 teaspoon of salt needs = [tex]\frac{2}{\frac{1}3}[/tex] teaspoons of baking powder
1 teaspoon of salt needs = 2 [tex]\times[/tex] 3 = 6 teaspoons of baking powder needed
So, the answer is:
6 teaspoons of baking powder required.
Answer:
6 teaspoons of baking powder
Explanation:
This is a simple ratio question.
Every 1/3 of a teaspoon of salt requires 2 teaspoons of baking powder.
Therefore, 1 teaspoon of salt will require:
= 1 x 2/1/3
= 2 x 3 = 6 teaspoons of baking powder
Hence, 6 teaspoons of baking powder would be needed if they had used 1 teaspoon of salt.
How would you convert steps and jumps to meters?
Explanation:
by inches to centimeter u can convert to meters
17. A force of 150N is applied at an angle of 60°
to the horizontal to pull a box through a
distance of 50m. Caleulate the work done.
B. 3750J C.6495J
E. 8660J
A. 1500J
R 7500J
Answer:7,500J
Explanation:
Work done=force× distance
a basketball has a positive or negative a acceleration when thrown
Answer:
A negative acceleration
Explanation:
When thrown, the basketball leaves the hands of the thrower with an initial velocity. This initial velocity is then gradually decelerated (negative acceleration) by drag forces, and its gravitational attraction to the earth, until the ball comes to rest. The acceleration on a thrown basketball is therefore negative.
please help ASAP thanks
Answer:
Precipitation
Explanation:
Ocean water may evaporate and precipitate into the river.
help me whenever possible.
Answer:
7. Option D. 8.4×10¯⁴ m/s North.
8. Option B. 2 m/s
Explanation:
7. Determination of the speed of the snail.
The following data were obtained from the question:
Distance travalled (d) = 15 m
Time (t) = 300 mins
Speed (S) =?
Next, we shall convert 300 mins to secs. This can be obtained as follow:
1 min = 60 secs
Therefore,
300 mins = 300 × 60 = 18000 secs
Finally, we shall determine the speed of the snail as follow:
Distance travalled (d) = 15 m
Time (t) = 18000 secs
Speed (S) =?
Speed = Distance travelled /time
Speed = 15 / 18000
Speed = 8.3×10¯⁴ m/s
Since the snail travelled due north, the speed is therefore 8.3×10¯⁴ m/s North.
8. Determination of speed of the runner.
The following data were obtained from the question:
Distance travalled = 8 m
Time = 4 secs
Speed =?
Speed = Distance travalled / time
Speed = 8/4
Speed = 2 m/s
Therefore, the speed of the runner is 2 m/s.
What is the purpose of a kink in a thermometer?
Answer:
A 'kink' in the glass tube which breaks the mercury as it contracts, storing the highest temperature reading. The glass tube is shaped like a lens to magnify the thin mercury thread. Shaking the thermometer resets the mercury back into the bulb.
Kink in the Mercury thermometer helps to prevents the falling of mercury present in capillary tube into bulb. It ensures that the user takes the correct reading of temperature. That's the reason a person before taking a new reading must give a sudden shake to the clinical thermometer so that the mercury level comes to normal .
b
Alpha Centauri has an apparent magnitude of -0.27, whereas the apparent
magnitude of Alpha Crucis is 0.77. Identify which star appears brighter when observed from
Earth. Explain your answer.
Answer:
Alpha centauri will be brighter than Alpha Crucis .
Explanation:
Apparent magnitude of a star measures how bright a star is .
This scale is reverse logarithmic ie , the brighter the star , the lower is its magnitude . A magnitude equal to 5 scale higher represents less magnitude by a factor of 1/ 100 . In this way a difference of 1 magnitude represents a brightness ratio of 2.512 . Hence a star of brightness magnitude of 7 is less bright by a factor 2.512 than that of a star magnitude of 6 .
we do not get hurt while jumping of aeroplane with a parachute,Why?
Answer:
this is because of air resistance
Explanation:
air resistance is a type of friction in air. It acts on the parachute as an upward force and slows the person speed while falling.
name the three scale of temperature
Answer:
Three scales of temperature are
Celcius scale
Fahrenheit scale
Kelvin scale
Explanation:
Hope it will help :)
Answer:
Celsius (is the most used)FahrenheitKelvinA marble with a density of 2 g/cm3 is dropped into a beaker containing 50 ml of water and the the water level rises to 55ml. what is the mass of the marble
Answer:
10g
Explanation:
"the toy car is about 3 inches long"is an example of a ________ observation
It's a quantitative observation because it includes numerical data.
You find a micrometer (a tool used to
measure objects to the nearest 0.001 mm) that has
been badly bent. How would it compare to a new,
high-quality meterstick in terms of its precision? Its
accuracy?
Explanation:
If the micrometer is still in the working condition, it will be hard for the observer to find its accuracy or precision, which could be matched with the meter stick. Its accuracy can be compromised in comparison with the undamaged micrometer, but it would be more chances of highly precise.
The error which is find in the damaged micrometer would be less than as compared to the width of the hash marks on the stick.
Answer:
The bent micrometer will be more precise but less accurate than the meterstick
Explanation:
Does adding fertilizer affect the growth of a plant
Answer:
yes it does affect the growth of plants
A 0.40 kg mass hangs on a spring with a spring constant of 12 N/m. The system oscillated with a constant amplitude of 12 cm. What is the maximum acceleration of the system
Answer:
The maximum acceleration of the system is 359.970 centimeters per square second.
Explanation:
The motion of the mass-spring system is represented by the following formula:
[tex]x(t) = A\cdot \cos (\omega \cdot t + \phi)[/tex]
Where:
[tex]x(t)[/tex] - Position of the mass with respect to the equilibrium position, measured in centimeters.
[tex]A[/tex] - Amplitude of the mass-spring system, measured in centimeters.
[tex]\omega[/tex] - Angular frequency, measured in radians per second.
[tex]t[/tex] - Time, measured in seconds.
[tex]\phi[/tex] - Phase, measured in radians.
The acceleration experimented by the mass is obtained by deriving the position equation twice:
[tex]a (t) = -\omega^{2}\cdot A \cdot \cos (\omega\cdot t + \phi)[/tex]
Where the maximum acceleration of the system is represented by [tex]\omega^{2}\cdot A[/tex].
The natural frequency of the mass-spring system is:
[tex]\omega = \sqrt{\frac{k}{m} }[/tex]
Where:
[tex]k[/tex] - Spring constant, measured in newtons per meter.
[tex]m[/tex] - Mass, measured in kilograms.
If [tex]k = 12\,\frac{N}{m}[/tex] and [tex]m = 0.40\,kg[/tex], the natural frequency is:
[tex]\omega = \sqrt{\frac{12\,\frac{N}{m} }{0.40\,kg} }[/tex]
[tex]\omega \approx 5.477\,\frac{rad}{s}[/tex]
Lastly, the maximum acceleration of the system is:
[tex]a_{max} = \left(5.477\,\frac{rad}{s})^{2}\cdot (12\,cm)[/tex]
[tex]a_{max} = 359.970\,\frac{cm}{s^{2}}[/tex]
The maximum acceleration of the system is 359.970 centimeters per square second.
A man performed 500 J of work moving a couch in his living room. It took him 10 seconds to move the couch. What was his power?  A. 50 W  B. 490 W  C. 5000 W  D. 100 W
Answer:
A. 50 W
Explanation:
Power = work / time
P = 500 J / 10 s
P = 50 W
You are riding your bike and steadily pulling your little brother
Plus
in his red wagon while someone standing still watches you and
your little brother go by. He has a ball, and he throws the ball forward at a
velocity of 2.5 m/s relative to his body while you are pulling the wagon at a
velocity of 4.5 m/s. At what speed does the person who is standing nearby see
the ball go by?
the velocity at which the boy see the ball go by is 7ms-1
Please Answer ASAP :)
The weight of a body of certain mass becomes zero in space. Why? Write with reason
Because theres no gravity, so it means that gravity = 0.
using the weight formula
weight = mass × gravity
= mass × 0
= 0N
two students are watching a person riding a skate board up and down a ramp. each student shares what they think about the energy of the skate boarder as they ride up and down the ramp.
Elisa: i think the skateboarder has the more total energy at the top bottom of the ramp then the bottom of the ramp
raymond: i think the skateboarder has the same total energy at all points of the ramp
which student do you agree with? why/
Answer:
I agree with Raymond because total energy is conserved
Explanation:
The law of conservation of energy states that energy is neither created nor destroyed, but is transformed from one form to another. As the skateboarder goes up and down the ramp, there is the interconversion of energy between kinetic and potential energy, assuming energy is not lost to heat or other forms of energy.
Kinetic energy is energy in motion, and potential energy is energy at rest. As the skateboarder descends the ramp, the motion increases and the potential energy is converted to kinetic energy, and maximum kinetic energy is attained at the lowest point on the ramp because that is where speed is greatest. However, as the skateboarder ascends the ramp, the kinetic energy decreases progressively and is being converted to potential energy, which is greatest at the top of the ramp, where the skateboarder is momentarily at rest, and speed is zero. Hence at each point on the ramp, total energy is the same.
Skater A skates toward Skater B and gently pushes Skater B away. If the skaters are in a closed system, which statement is correct about the total momentum of the system?(1 point)
A) Total momentum decreases.
B) Total momentum remains the same.
C) Total momentum increases.
D) Total momentum may increase or decrease depending on the duration of the collision.
Answer:
1. Total momentum remains the same.
2.The brain moves inside the skull with a force equal and opposite to that of the impact.
3. Nina experiences a force equal to f.
4. The impulse of the collision in system A is twice the impulse of the collision in system B.
5. the greater the mass of the person, the greater the force of the punch
Explanation: Just took it! 100% :)
If the skaters are in a closed system the total momentum remains the same.
In a closed system the total momentum is always conserved.
By applying the principle of conservation of linear momentum, the total momentum before the push of skater A, will be equal to the total momentum after the push.
The equation is given as;
Initial momentum = final momentum
[tex]m_au_a + m_bu_b = m_av_a + m_bv_b[/tex]
where;
u and v represents the initial and final velocity of both skaters.
Thus, we can conclude that if the skaters are in a closed system the total momentum remains the same.
Learn more here: https://brainly.com/question/7538238
Two resistors connected in series (R1, R2) are connected to two resistors that are connected in parallel (R3,R4). The series-parallel combination is connected to a battery. Each resistor has a resistance of 10.00 Ohms. The wires connecting the resistors and battery have negligible resistance. A current of 2.00 A runs through resistor R1. What is the voltage supplied by the voltage source?
Answer:
50volts
Explanation:
Each of the resistance is 10ohms. 2 in series and 2 in parallel. it means the 2 parallel can combines with total of 10×10÷(10+10)= 5ohms and combine in series with 10ohms which is 10+10+5= 25ohms. in series connection, we have same current flowing. therefore the voltage source will be 25ohms × 2amps = 50volts
Please help An object is observed to move under the following equation of motion ... x(t) = A√t ... take A =√2. Determine the equations for the velocity and acceleration as a function of time. Write each equation in differential equation format, including second-order, if necessary.
Explanation:
Function of distance w.r.t time :
[tex]x(t) = \: y = \sqrt{2t} [/tex]
Differentiate w.r.t time to get velocity :
[tex] \frac{dy}{dt} = v = \frac{1}{ \sqrt{2t} } [/tex]
Differentiate w.r.t time to get Acceleration :
[tex] \frac{d^2y}{dx^2} = a \: = - \frac{1}{2t \sqrt{2t} } [/tex]
Maggie completed a 10000-m race at an average speed of 160
m/min. If Tom took 12.5 fewer minutes to complete the race,
what was Tom's average speed?
Answer:
200m/minExplanation:
The formula for calculating distance covered = Speed * time
If Maggie completed a 10000-m race at an average speed of 160
m/min, the the time taken by Maggie to complete the race will be expressed as;
Time = Distance/Speed
Time = 10000/160
Time = 62.5 minutes
If it took Tom 12.5 fewer minutes to complete the race, then the time taken by tom to finish the same race will be 62.5 - 12.5 = 50minutes.
To get Tom's average speed, we will use the same formula as above;
From Distance = Speed * Time
Speed = Distance/Time
Since both of them completed the same distance, distance covered by Tom is also 10000m
Tom's speed = 10000/50
Tom's speed = 200m/min
Hence Tom's average speed is 200m/min
Which of the following scenarios represents the best use of a scientific model?
a predicting weather patterns
b. studying the result of mixing two chemicals
c. studying the effect of oil spills on plant growth
d.studying the speed of a ball down an inclined plane
Answer:
Predicting weather patterns is the answer :-)
Explanation:
what is the most used muscle on humans ?
Answer:
the heart
Explanation:
Daily the heart pumps at least 2,500 gallons (9,450 liters) of blood. The heart has the ability to beat over 3 billion times in a person's life.
A car is traveling at 50 m/s and slows down to 10 m/s in 5 seconds. What is
the car's acceleration? (Remember what is needed when an object slows
down) *
Answer:
-8m/s2
Explanation:
it decelerate. initial velocity u=50m/s and final velocity v= 10m/s and the time t= 5s
using this equation v= u+at
a= v-u/t= 10-50/5=-40/5= -8m/s2
Answer:
[tex] \boxed{\sf Acceleration \ (a) = -8 \ m/s^2} [/tex]
Given:
Initial velocity (u) = 50 m/s
Final velocity (v) = 10 m/s
Time taken (t) = 5 seconds
To Find:
Acceleration (a) of the car
Explanation:
From equation of motion we have:
[tex] \boxed{ \bold{v = u + at}}[/tex]
By substituting value of v, u & t in the equation we get:
[tex] \sf \implies 10 = 50 + 5a \\ \\ \sf \implies 5a + 50 = 10 \\ \\ \sf \implies 5a = 10 - 50 \\ \\ \sf \implies 5a = - 40 \\ \\ \sf \implies a = - \frac{40}{5} \\ \\ \sf \implies a = - 8 \: m {s}^{ - 2} [/tex]
[tex] \therefore[/tex]
Acceleration (a) of the car = -8 m/s²