When an item procedures the rate of light. it's miles described as theory of relativity
In the theory of relativity, it implies that as a moving object approaches the speed of light, which is about 186,000 miles per second, the length of the object appears to shrink to zero, relative to the position of the observer.
Why is the Lorentz force independent of the frame of reference?Lorentz pressure is understood to be independent of body due to the fact because of the combine impact of electric and magnetic fields which is understood to be now no longer body structured as visible in Lorentz Transformation. This is the reason why we do not define electromagnetic fields, electric and magnetic fields together.
Note that Lorentz pressure is stated to be body impartial because dome of its components are acknowledged to return back up as a end result of shifting of body of reference, and this makes them to cancel every other out and therefore they make the resultant lorentz pressure same.
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A calorimeter for which mc = 25 J K−1 contains
140 g of a liquid. An immersion heater is used to
provide energy at a rate of 40 W for a total time of
4.0 min. The temperature of the liquid increases by
15.8 °C. Calculate the specific heat capacity of the
liquid. State an assumption made in reaching this
result.
The liquid's specific heat capacity is 4.2 kJ kg⁻¹ K⁻¹.
In a calorimeter, mc = 25 J K⁻¹.
The calorimeter contains m(l) = 140 g = 140 × 10⁻³ kg of liquid.
The energy is provided at a rate of Q = 40 W for a time of 4 minutes.
The liquid's temperature increases by ΔT = 15.8° C = 15.8° K.
Q = mcΔT
The equation tells you how much heat is given (Q or E), how much of that heat changes the material's temperature T, and how much of that heat is applied to a mass-m material with a specific heat capacity (c).
Now, the heat supplied will be:
Q = mcΔT + m(liquid) c(liquid)ΔT
Q = mcΔT + m(l) c(l)ΔT
c(l) = ( Q - mcΔT ) / m(l)ΔT
Now, the heat supplied is Q = 40 W = 40 J/s = 40 × 4 × 60s = 9600 J
c(l) = { ( 9600 - 25 × 15.8 ) / [ (140 × 10⁻³) × 15.8 ] }
c(l) = ( 9600 - 395 ) / [ 2212 × 10⁻³ ]
c(l) = 9205 / 2212 × 10⁻³
c(l) = 4.1614 × 10³ = 4.2 kJ kg⁻¹ K⁻¹
The specific heat capacity of the liquid is 4.2 kJ kg⁻¹ K⁻¹.
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how many millicoulombs (mc) of charge is stored in a 152 µf capacitor when 150 v is applied to it? 1μf
The charge stored in capacitor is 22.8 mC.
We need to know about capacitors to solve this problem. Capacitor is a device that stores electric charge. The charge stored in capacitor can be determined as
Q = C . V
where Q is charge, C is capacitance and V is voltage.
From the question above, we know that
C = 152 µF = 152 x 10¯⁶ F
V = 150 V
By substituting the following parameters, we can calculate the charge
Q = C . V
Q = 152 x 10¯⁶ . 150
Q = 0.0228 C
Convert to millicoulombs
Q = 0.0228 C
Q = 0.0228 x 10³ mC
Q = 22.8 mC
Hence, the charge stored in capacitor is 22.8 mC.
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As officer konstantin explains, when driving at 60 mph, in four seconds, you've traveled?
when driving at 60 mph, in four seconds, you've travelled 107.29 m
What is speed?Speed is the distance travelled per unit. Mathematically, it can be expressed as:
Speed = distance / time
How to convert 60 mph to m/sWe'll begin by converting 60 mph to m/s. This can be o btained as follow:
1 mph = 0.44704 m/s
Therefore,
60 mph = (60 mph × 0.44704 m/s) / 1 mph
60 mph = 26.8224 m/s
How to determine the distanceThe distance travelled can be obtained as follow:
Time = 4 sSpeed = 26.8224 m/sDistance =?Speed = distance / time
Cross multiply
Distance = speed × time
Distance = 26.8224 × 4
Distance = 107.29 m
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Which key difference between carbon and silicon makes carbon better suited to forming molecules for living things?
Carbon has the right number of outer electrons to form a wide range of molecules.
Oxidized carbon is a gas at room temperature, rather than a solid.
Carbon has a greater atomic mass, allowing for stronger molecules.
Carbon is a naturally occurring element, so it is readily available.
Oxidized carbon is a gas at room temperature, rather than a solid is the difference between carbon and silicon which makes carbon better suited to forming molecules for living things and is denoted as option B.
What is Carbon?This is referred to an element with as symbol of C and an atomic number of 6. It has four valence electrons and is able to form different types of substances by sharing the electrons with other elements which resulting in the formation of a new product.
It also has the ability to form multiple bonds which makes it unique and is present in nature in the form of gas, solids etc and is used by plants to manufacture food during photosynthesis.
Plants are a major source of food for animals and the oxidized carbon which is carbon dioxide which is a gas at room temperature is the reason why they are better suited to form molecules for living things.
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Answer:
B
Explanation:
Perform the following multiplication and write the product in trigonometric form. write the magnitude in exact form. write the argument in radians and round it to two decimal places if necessary.
The magnitude of →PQ is represented symbolically as | →PQ |. The Distance Formula can be used to determine a vector's magnitude if its start and end points' coordinates are known.
What is magnitude ?The magnitude or size of a mathematical item defines whether it is larger or smaller than other objects of the same kind in mathematics. Formally speaking, the size of an object is the outcome of the class of objects it belongs to being ordered (or ranked) and shown.
Magnitude in physics can be interpreted as either a quantity or a distance.
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a river flows toward the east. because of your knowledge of physics, you head your boat 53 degrees west of north
Velocity of the current is 2.7 m/s and the velocity of the boat relative to the water is 4.8 m/s.
Define the velocity?The pace at which a moving object's location changes as seen from a specific frame of reference and as measured by a specific time standard is known as its velocity. In kinematics, the area of classical mechanics that studies how bodies move, velocity is a fundamental idea.
Given:
[tex]West\;of\;north\;angle,\;\alpha=56\;^{\circ}[/tex]
[tex]Velocity\;of\;boat\;relative\;to\;shore,\;V_{b} = 4 m/s[/tex]
From the right angle triangle ABC, (see the attached figure)
[tex]sin\;\alpha=\frac{V_{b} }{V_{b,c} }[/tex]
[tex]V_{b,c}=\frac{V_{b} }{sin\;\alpha}[/tex]
Substitute the known values in the above equation,
[tex]V_{b,c}=\frac{4}{sin\;56^{\circ}}[/tex]
By solving the above equation, We get
[tex]Velocity\;of\;boat\;relative\;to\;water,V_{b,c}=4.8\;m/s[/tex]
[tex]cos\;\alpha=\frac{V_{c} }{V_{b,c} }[/tex]
[tex]V_{c}={V_{b,c}}\times{cos\;\alpha}[/tex]
Substitute the known values in the above equation,
[tex]V_{c}={4.8}\times{cos\;56^{\circ}}[/tex]
By solving the above equation, We get
[tex]Velocity\;of\;current,\;V_{c}=2.7\;m/s[/tex]
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if the water in a lake is everywhere at rest, what is the pressure as a function of the distance from the surface?
The pressure as a function of the distance from the surface is 101325 + 10055.25h
One must go h = 10.1 m down before the pressure is 1 atm greater than the pressure at the surface.
What are the pressure and absolute pressure?In order to determine absolute pressure, a complete vacuum is used. In contrast, gauge pressure is the amount of pressure that is measured in relation to atmospheric pressure, also referred to as barometric pressure. The average barometric pressure at sea level is 14.7 PSIA, while the absolute pressure of a complete vacuum is 0 PSIA.
The pressure at sea level = 1 atm = 101325 Pa
Density of sea water = 1025 kg/ m^(3)
Pressure due to fluid height = pgh
Absolute pressure = 101325 + 1025(9.81) h
= 101325 + 10055.25h
where h= 0 at sea level at increases downward
101325 = 1025(9.81)h
h = 10.1 m
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The complete question is:
"If the water in a lake is everywhere at rest, what is the pressure as a function of distance from the surface? The air above the surface of the water is at standard sea-level atmospheric conditions. How far down must one go before the pressure is 1 atm greater than the pressure at the surface?"
I already did the first slide but its there to just give you an idea
Answer:ok
Explanation:ok
A moving average can be used to smooth:__________
1) cyclical variation
2) seasonal variation
3) irregular variation
4) all responses are correct
A moving average can be used to smooth:3) irregular variation
What is irregular variation ?
Irregular with the aid of its call says “wrong”. these are those variations which aren't predictable. They do now not observe some pattern which may be expected. It totally follows in opposition to the rules. It includes the pandemic, endemic, other sicknesses spread, environmental disasters, and irregular variation. greater particularly, floods, earthquakes, draughts, and many others comes under the umbrella of irregular variations.
In time series, we do no longer make any estimation of parameters or speculation checking out. The simplest purpose is to find the versions/trends in facts. this alteration may be everyday or irregular. ordinary variations includes linear, seasonal, and cyclic variations. whereas, abnormal variations are all rest of the variations that aren't blanketed with the aid of the everyday versions. those irregular variations are never predictable. We don't have any facts about the length of this alteration, whether it's miles short time period or long time variation. moreover, irregular variations are stationary variations.
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What is the instantaneous velocity of the sloth at time t = 8s?
The calculated value is AO=3.2sec.
The limit of average velocity as elapsed time approaches zero, or the derivative of x with respect to t: v (t) = d d t x (t), is the instantaneous velocity of an object. v (t) equals d d t x (t). Instantaneous velocity is a vector having a dimension of length per time, similar to average velocity.
In contrast to instantaneous velocity, which is determined by the slope of the tangent line, average velocity is defined as the change in position (or displacement) during the course of transit.
So, we obtain
cosθ= 5/4
= 4AO
So, we obtain AO=3.2sec.
The complete question is- Position-time graph is shown, which is a semicircle from t=2 to t=8 sec. Find time t at which the instantaneous velocity, is equal to average velocity over first t seconds.
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How does the atmosphere affect life on earth? Include both positive and negative effects.
The Earth's atmosphere blocks the sun's rays as they travel toward us. The atmosphere's layers act as a filter, allowing just the radiation needed to support life to pass through while blocking the dangerous radiation from reaching the Earth's surface. Our globe is warmed by the sun's energy as it travels through the atmosphere, supplying light energy for photosynthesis and powering the biogeochemical cycles in the Earth's systems. The object that cannot pass through, on the other hand, is reflected back into space.
The global temperature does, however, increase as more heat is trapped by the atmosphere. Global warming is the name of this occurrence.
Global warming is the phenomenon that results in a change in our climate. Natural calamities like wildfires, flooding, and severe storms occur more frequently when this happens.
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occam's razor states that choose one: a. if two hypotheses fit the facts equally well, choose the one with fewer assumptions. b. the laws of nature are the same everywhere in the universe. c. the universe is expanding in all directions. d. patterns in nature are really manifestations of random occurrences.
Option a: if two hypotheses fit the facts equally well, choose the one with fewer assumptions.
Occam's razor states that principle of problem solving is that entities should not multiply more than necessary
Occam's Razor is the process of gathering information to make the search for the truth easier. In science, it gets rid of all assumptions that have no bearing on the predictions of the hypothesis. If you have several hypotheses that could explain an observation, it is usually best to start with the simplest one.
Occam's Razor is often at the root of a paradigm shift, where an established theory is replaced by a simpler alternative that also fits the data. For example, Ptolemy's epicycles were replaced by a simpler theory that explained the data without multiplying the elements.
Therefore Option (a) is correct.
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At highway speeds, anautomobileis capable of an acceleration of about 1.6m/s2. at this rate, how long does it take to accelerate from 80km/hto 110km/h?
At highway speeds, an automobile is capable of an acceleration of about 1.6m/s2. at this rate, it take to accelerate from 80km/h to 110km/h is 5.2084s.
What is velocity?Velocity is the directional speed of a object in motion as an indication of its rate of change in the position as observed from a particular frame of reference and as measured by a particular standard of the time (e.g. 60 km/h northbound). Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of the bodies.
Velocity is a physical vector quantity; both the magnitude and direction are needed to define it. The scalar absolute value (magnitude) of velocity is called the speed, being a coherent derived unit whose quantity is measured in the SI (metric system) as meters per second (m/s or m⋅s−1). If there is a change in the speed, direction or both, then the object is said to be undergoing an acceleration
Therefore,
v = v0 + at, where v is the final velocity, v0 is initial velocity, a is acceleration and t is time, solve for t:
t = (v - v0) / a,
note that all the variables must be in the same units, we want m/s which is a:
110 km / hour = (110 * 1000) / (60 * 60) = 30.5556 m/s:
80 km / hour = (80 * 1000) / (60 * 60) = 22.2222 m/s:
t = (30.5556 - 22.2222) / 1.6 = 5.2084 s
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Point a is located 0.197 m away from a charge of - 3.52 x 10-9 c. point b is located 0.506 m away from the charge. what is the electric potential difference vb - va between these two points?
The correct answer is -98.2V.
The gravitational potential energy and the electrostatic potential energy are practically identical. In relation to the gravitational potential energy notion, we explore the electric potential energy formula. An electric charge will store the external work done on it in the form of electric potential energy or electrostatic potential energy when it is exposed to an external electric field. As a result, the external work performed by an agent in getting a charge or system of charges from infinity to the desired location without accelerating the charge is defined as the electric potential energy.
The electric potential at A due to the charge
V_A= 1/4πε_0 Q/r_A = - 9×10^9× - 3.52 x 10-9 /0.197=-160.8V
Electric potential at B due to the charge
V_B=1/4πε_0 Q/r_B= - 9×10^9× - 3.52 x 10-9 /0.506=-62.6V
V_B-V_A=-160.8-(-62.6)
=-98.2V
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if the man is moving from a position of 0 m to 6 m in 3 seconds he will move than he would have if he moved from a position of – 4 m to 0 m in 3 seconds.
His relative speed in the first case will be faster than the second one.
Think about two bodies going in the same direction but at different speeds.
Let x km/hr be the first body's speed.
And the second body moves at a speed of y km/hr.
They are moving at a relative speed of (x - y) km/hr, where x>y.
After then, the time when the two bodies collide equals the distance travelled divided by the relative speed, or dkm/(x - y) km/hr.
We now understand that an object's relative speed is its speed in relation to another object.
Therefore, if the time after which both bodies move is provided, let's assume that time = t hours.
Distance travelled in t hours is then calculated as follows: (x - y) km/hr * t hrs.
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a vector has an x component of -22.5 units and a y component of 37.4 units. find the magnitude and direction of this vector.
The magnitude of the vector is 43.81 units and the direction of the vector is 120.89 degrees with a +x-axis counterclockwise.
What is the magnitude and direction of a vector?The length for a certain vector (let's say v) can be calculated by using the symbol |v|, which stands for the magnitude of a vector formula. In essence, this measurement represents the separation between the vector's starting and ending points. We apply the distance formula to get the vector's magnitude.
Its direction indicates where it points. Although vector direction can be expressed in a number of ways, degrees are the most frequent notation.
The magnitude of the given vector will be
[tex]\vec{r} &=x i+y j \\\vec{r}=-22.5 \hat{i}+37.6 \hat{j} \\{[\vec{r}] } &=\sqrt{(22.5)^2+(37.6)^2} \\&=43.81 units[/tex]
The direction of the vector will be
tanα=[tex]\frac{y}{x}\\[/tex]
[tex]=tan^{-1}(\frac{y}{x})\\=tan^{-1}(\frac{37.6}{22.5}\\=59.103 degree[/tex]
Therefore, the direction of the vector is 120.89 degrees with the +x-axis counterclockwise.
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a medicine ball has 10 J of energy and is thrown upward with a velocity of 2 m/s. what is its mass
The bending of light as it moves from one medium to another with differing indices of refraction is due to a change in what property of the light? group of answer choices
Refraction is the result of a wave's direction changing as it travels from one medium to another due to a change in speed. When light travels through a fast medium and into a slow medium, the light beam is refracted, which causes it to bend in the direction of the boundary between the two media.
What is Refraction ?When light travels through a fast medium and into a slow medium, the light beam is refracted, which causes it to bend in the direction of the boundary between the two media.
The term "refraction" refers to the way light bends as it travels through transparent materials (it also occurs with sound, water, and other waves). Because of this bending brought on by refraction, we are able to make lenses, magnifying glasses, prisms, and rainbows.
Refraction occurs when light enters a medium from another and experiences a change in speed. Light bends toward the normal when it transitions from air to water due to the decrease in speed.
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There are 9 different positions on a baseball team. if a team has 13 players how many different line-ups can the team make? the team can make different line-ups.
The team can make different line-ups in 13!(13−9)!=13!4! ways.
For the first spot in the lineup, there are 13 possibilities, for the second spot there are 12 possibilities, continuing in this fashion there are 5 possibilities for the ninth spot in the lineup. So there are
13 × 12 × • • • × 5 = 259459200
possibilities.
To write it succinctly
13!(13−9)!=13!4!
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A girl rides her bike up a steep hill 2.4 kilometers in 8 minutes. What is her speed?
Answer:
0.3km/min
Explanation:
2.4/8=24/80=3/10=0.3
Carbon atoms have an atomic radius of 70 picometers, or 7.0 x 10 meters (1 m = 10 pm). if exactly 1 mole of carbon atoms were lined up in a row, about how long would the line of atoms be?
By Avogadro's number, the carbon atoms length is 8.428 x 10¹³ m.
We need to know about Avogadro's number to solve this problem. Avogadro's number is the number that explains how many carbon atoms are in one mol. The Avogadro's number is
Na = 6,02 × 10²³ atoms / mol
From the question above, we know that
n = 1 mol
r = 70 pm = 70 x 10¯¹² m
By using Avogadro's number, we can calculate how many carbon atoms
N = Na . n
N = 6,02 × 10²³ x 1
N = 6,02 × 10²³ atoms
As we know one atom's length is equal to its diameter, Hence
atom length = d
atom length = 2 x r
atom length = 2 x 70 x 10¯¹²
atom length = 140 x 10¯¹² m
Calculate the length of 1 mol Carbon atoms length
length = N x atom length
length = 6,02 × 10²³ x 140 x 10¯¹²
length = 8.428 x 10¹³ m
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If a car accelerates from a stand still to 60 km/s in 10 seconds what is its acceleration
Answer:
I think it's 6 km/s^2
Explanation:
We know that velocity is 60 km/s and time is 10 seconds.
We need to find acceleration, so we need to use a=v/t.
Add in your numbers into the equation giving you a=60 km/s divided by 10s.
Your units for acceleration are km/s^2
Your answer should end up being 6 km/s^2
Hope I'm right and if I'm wrong I hope my physics teacher doesn't see this...
The passage of a current of 0.750 a for 25.0 min deposited 0.369 g of copper from a 4 solution. from this information, calculate the molar mass of copper.
The passage of a current of 0.750A for 25.0 min deposited 0.369 g of copper from a solution. From this information, the molar mass of copper is 63.3u.
How to calculate the molar mass of copper?
First we will convert the time from mins to sec,
Hence,
Time = 25min = 25*60 sec
Current = 0.75A
Electricity passed is given by:
[tex]Q=I\times T \\Q=0.75 \times25\times60\\Q=1125C[/tex]
The reaction that will take place is:
[tex]Cu^{2+}+2e^_- } \rightarrow Cu[/tex]
Hence, there are 2 atoms of copper.
We know, Faraday's number is 96500, and as there are 2 atoms of copper, therefore, the value of Z = 96500*2.
We are given that the deposited mass is 0.369g
Hence, the molar mass of copper will be:
[tex]M=\frac{2\times 96500 \times 0.369}{1125}=63.3u[/tex]
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how does it take bee to travel 90 miles of she travels a constant speed of 60 mph in her car?
a, 2 hours and 15 minutes
b, 1 hour and 30 minute
c, 1/2 an hour
d, 30 minutes
e, 45 minutes
help pls
Answer:
b
Explanation:
90 miles
60 mph (miles per hour)
1 hour = 60 minutes = 60 miles
90 miles - 60 miles = 30 miles
30 miles = 30 minutes
1 hour and 30 minutes
A rocket is accelerating upward from the surface of earth with an acceleration of 4. 4 m/s2. On board the rocket is a 0. 060 kg chicken egg. What is the apparent weight of the egg?.
The apparent weight of the egg is 0.264N
Here the rocket is accelerating upward from the surface of the earth. The egg is on the rocket.
The acceleration due to gravity is 4.4m/[tex]s^{2}[/tex].
The mass of a chicken egg is 0.060 kg.
Form Newton's second law, the net force acting on a body is equal to the product of mass and acceleration due to gravity.
So form Newton's second law we know the formula i.e.,
F = mass × acceleration
= 0.06 × 4.4
= 0.264N
Therefore the apparent weight of the egg is 0.264N.
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what is the distance fallen for a ball in free fall 1 s after being dropped from a rest position? what is the distance for a 5- s drop?
The distance fallen for a ball in free fall 1s from a rest positon. Hence it falls 5m in 1s and 125m in 5s.
Initial velocity (u) = 0
Gravitational acceleration (g) (g) = 10 m/s2
Using equation of motion,
S=ut+1/2 at2
for t=1s, a=g , u=0
s=0×t + 1/2g ×1
s= 1/2 × 10
s= 5 m
t=5s,
s=0×t + 1/2g ×5×5
s= 1/2 × 10 × 25
s= 5 × 25
s= 125 m
What is a simple definition of distance?The distance between two points, objects, lines, etc. Remoteness is the quality of being physically separated from another thing or person.
a line is drawn in the universe.
To walk seven miles in one hour would be too time-consuming.
a big area:
A wide body of water encircled the ship.
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part b run the video frame-by-frame again. now describe the car’s velocity (speed and direction) over time.
Velocity is the direction in which an object is moving and serves as a measure of the pace at which its position is changing as seen from a particular point of view.
What do you mean by motion?Motion in physics is the phenomenon in which an object shifts in relation to time. Motion is quantitatively characterized in terms of the body's change in position with respect to the observer's frame of reference as well as the velocity, acceleration, and speed of the body. Kinematics is the area of physics that studies forces and how they affect motion, while dynamics is the area that studies motion in relation to its causes.
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What make race condition bad? name and briefly desribe two distince factors needed for a race
when two computer program processes, or threads, attempt to access the same resource at the same time and cause problems in the system and it makes race condition bad.
Which of the following conditions can result in a race condition?When race conditions develop. When two threads access a shared variable at the same time, a race condition occurs. The first thread reads the variable, and the second thread reads the variable's value. A race condition is an undesirable situation that occurs when a device or system attempts to perform two or more operations at the same time, but the operations must be performed in the correct sequence due to the nature of the device or system.A race condition is a program condition in which the behavior is dependent on the relative timing or interleaving of multiple threads or processes. One or more of the possible outcomes may be harmful, resulting in a bug. This is referred to as nondeterministic behavior.
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a student is provided with a battery-powered toy car that the manufacturer claims will always operate at a constant speed. the student must design an experiment in order to test the validity of the claim. which of the following measuring tools can the student use to test the validity of the claim? select two answers.
Correct question is -
A student is provided with a battery-powered toy car that the manufacturer claims will always operate at a constant speed. The student must design an experiment in order to test the validity of the claim. Which of the following measuring tools can the student use to test the validity of the claim?
a. Photogates placed at the beginning, end, and at various locations along the track that the car travels on.
b. A meterstick to measure the distance of the track that the car travels on.
c. A motion detector that is oriented perpendicular to the direction that the car travels.
d. A mass balance to determine the mass of the car
a. Photogates positioned at the beginning, give up, and at numerous locations along the music that the car travels on.
b. A meterstick to degree the distance of the track that the automobile travels on.
Physics may be described as the field or branch of technology that normally offers with nature and residences of count, motion and electricity with admire to space, pressure and time.on this scenario, a student is provided with a battery-powered toy vehicle that the manufacturer claims will continually function at a consistent speed. The student have to layout an test so as to check the validity of the declare.
consequently, to check the validity of the declare, the student must use the following measuring tools;
a. Photogates placed at the beginning, cease, and at diverse places alongside the song that the automobile travels on. This tool is normally used to degree time with admire to the price of change of the interruption or block of an infra-pink beam.b. A meterstick to measure the space of the track that the car travels onsubsequently, with those two gadgets the student can successfully measure or determine the validity of the declare.
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Consider two vectors A⃗ and B⃗ and their re- sultant A⃗ + B⃗ . The magnitudes of the vectors A⃗ and B⃗ are, respectively, 13.9 and 5.9 and they act at 53◦ to each other.
B⃗
A⃗ + B⃗
A⃗
Find the magnitude of the resultant vector A⃗ + B⃗ .
Use the dot product identity,
[tex]\vec x \cdot \vec y = \|\vec x\| \|\vec y\| \cos(\theta)[/tex]
where [tex]\theta[/tex] is the measure of the angle between the two vectors [tex]\vec x,\vec y[/tex]. Note that
[tex]\vec x \cdot \vec x = \|\vec\| \|\vec x\| \cos(0) = \|\vec x\|^2[/tex]
Applying the identity to [tex]\vec x = \vec y = \vec A + \vec B[/tex] and using the distributive and commutative properties of the dot product, we get
[tex](\vec A + \vec B) \cdot (\vec A + \vec B) = (\vec A \cdot \vec A) + 2 (\vec A \cdot \vec B) + (\vec B \cdot \vec B)[/tex]
which is equivalent to
[tex]\|\vec A + \vec B\|^2 = \|\vec A\|^2 + 2\|\vec A\|\|\vec B\| \cos(\theta) + \|\vec B\|^2[/tex]
Now, we're given [tex]\|\vec A\| = 13.9[/tex], [tex]\|\vec B\| = 5.9[/tex], and [tex]\theta=53^\circ[/tex], so that
[tex]\|\vec A + \vec B\| = \sqrt{13.9^2 + 2\cdot13.9\cdot5.9\cos(53^\circ) + 5.9^2} \approx \boxed{18.1}[/tex]