Answers
The following equation represents the value (y) of a car based on its age (x).
[tex]y=-800x+12000[/tex]We are told that the value of a car of the given model, based on its age, is less than $6000.
So, we can write
[tex]6000<-800x+12000[/tex]Let us solve the above inequality for x.
[tex]\begin{gathered} 6000<-800x+12000 \\ 6000-12000<-800x \\ -6000<-800x \\ \frac{-6000}{-800}<\frac{-800x}{-800} \\ 7.5>x \\ x<7.5 \end{gathered}[/tex]This means that the age of the car is less than 7.5 years.
Therefore, the possible range of values that could represent the age of the car is 0 to 7.5 years.
[tex]0Related Questions
Find the y-component of thisvector:12.0 m73.3°Remember, angles are measured fromthe +X axis.y-component (m)
Answers
Given data:
The magnitude of the given vector is,
[tex]A=12.0\text{ m}[/tex]An angle between the given vector and +x axis is,
[tex]\theta=73.3^o[/tex]The formula of y-component is as follows:
[tex]A_y=A\sin \theta[/tex]Here,
[tex]A\text{ is the magnitude of the given vector-A}[/tex]Now, substitute known values in above equation;
[tex]\begin{gathered} A_y=12\text{ m}\times\sin 73.3^o \\ A_y=11.49\text{ m} \end{gathered}[/tex]Therefore, the y-component of the given vector is 11.49 m
in a particle accelerator a proton moves at constant speed 0.750c in a circle of radius 663 m. what is the net force on the proton?
Answers
In a particle accelerator a proton moves at constant speed 0.750c in a circle of radius 663 m. The net force on the proton will be .0127 * [tex]10^{-11}[/tex] N
Any object moving in a circle (or along a circular path) experiences a centripetal force. That is, there is some physical force pushing or pulling the object towards the center of the circle.
Force = m ( [tex]v^{2} / R[/tex])
m= mass
v = speed
R = radius
force = 1.67 * [tex]10^{-27}[/tex] * [tex](0.75 * 3 * 10^{8}) ^{2}[/tex] / 663 = 0.0127 * [tex]10^{-11}[/tex] N
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What is the maximum speed at which a cyclist can move on a bend and at an angle from the vertical, he should deviate to the side of the bend, so as not to fall, if the coefficient of friction of the wheel from the road is 0.4 and the radius of curvature of the road is 100m
Answers
Given,
The coefficient of friction between the wheel and the road, μ=0.4
The radius of curvature of the road, r=100 m
The centripetal force for the cyclist to move in the curved path is provided by the friction between the road and the wheel.
Thus,
[tex]\begin{gathered} \frac{mv^2}{r}=\mu mg \\ \Rightarrow v^2=r\mu g \\ v=\sqrt[]{r\mu g} \end{gathered}[/tex]Where m is the mass of the cyclist and the cycle and g is the acceleration due to gravity.
in four hours, a hiker in a canyon goes from 892ft to 256 ft above the canyon floor. Find the hikers vertical speed.
Answers
From the given question, we can deduce the following information:
• Time, t = 4 hours
,• The hiker goes from 892 ft to 256 ft above the canyon floor.
Let's find the vertical speed of the hiker.
To find the speed, apply the formula:
[tex]speed=\frac{dis\tan ce}{time}[/tex]To find the distance, we have:
Distance covered = 256 ft - 892 ft = -636 ft.
Hence, to find the vertical speed, we have:
[tex]\begin{gathered} speed=\frac{dis\tan ce}{time} \\ \\ \text{speed}=\frac{-636}{4}=-159\text{ ft/h} \\ \end{gathered}[/tex]Therefore, the vertical speed of the hiker is -159 feet per hour.
ANSWER:
A 0.24 kg blob of clay strikes a wall with an Initial velocity of 25 m/s the clay come to a stop against the wall in 91 ms what is the average impact force on the clay
Answers
ANSWER
65.9N
EXPLANATION
The impact force of an object is
[tex]F=\frac{\Delta p}{\Delta t}[/tex]And the change in momentum is
[tex]\Delta p=m(v_f-v_i)[/tex]We know that the mass of the blob of clay is 0.24kg, its initial velocity is 25m/s and its final velocity is 0m/s. Also, the time of the collision is 91 ms.
The force is:
[tex]F=\frac{m(v_f-v_i)}{\Delta t}[/tex]To be consistent with the units, we have to write the time in seconds, not milliseconds:
[tex]F=\frac{0.24\operatorname{kg}(0-25)m/s}{0.091s}[/tex][tex]F\approx-65.9N[/tex]This result is negative because this is the force the clay exerts on the wall. By Newton's third law, the impact force on the clay is the force with the same magnitude and opposite direction. Therefore, the average impact force on the clay is 65.9N
How much does James have to pay for a vaccum cleaner that he uses for 4 hours a week. In James's neighborhood, the cost of electricity is 27 cents per kwhr.The power is P = 800 W
Answers
Given:
The power of the vacuum cleaner is P = 800 W = 0.8 kW
The time consumption is t = 4 hours a week.
The cost of electricity is 27 cents per kWh
To find the cost of the electricity for using the vacuum cleaner for a week.
Explanation:
First, we need to find the energy.
The energy can be calculated as
[tex]\begin{gathered} E=P\times t \\ =0.8\times4 \\ =3.2\text{ kWh} \end{gathered}[/tex]The cost of electricity per week due to vacuum cleaner will be
[tex]27\times3.2=86.4\text{ cents}[/tex]Final Answer: The cost of electricity James has to pay for a vacuum cleaner for using it 4 hours a week is 86.4 cents.
which choice are equivalent to the expression below? check all that apply. 4 square root 5answer choices: square root of 16*6, square root of 32*3, square root of 96, square of 24, 96, square root of 4*36
Answers
Given
4 square root 6
[tex]4\sqrt[]{6}[/tex]Wich choices are equivalent to the expression below
[tex]\begin{gathered} \sqrt[]{16}\sqrt[]{6} \\ \sqrt[]{32}\sqrt[]{3} \\ \sqrt[]{96} \end{gathered}[/tex]The first three options are the correct answers.
You're standing on a ramp that is inclined at a 25 degree angle. The weight (Fg) experienced is 50N. What is the parallel force (Fx) and the perpendicular force (Fy)?I need to do the following: 1. Draw a free body diagram2.Identify Givens and Unknowns3.Identify the Equations4.Set up the equation using the givens and unknowns5.Solve
Answers
Answer:
Fx = 21.13 N
Fy = 45.32 N
Explanation:
In this case, the free body diagram is:
We can see that there is a right triangle formed by the weight (Fg) and the ramp. So, we can calculate the value of angle θ.
25 + 90 + θ = 180
115 + θ = 180
θ = 180 - 115
θ = 65
Because the sum of the interior angles of a triangle is always 180 degrees.
Now, we can calculate the parallel force and the perpendicular force using the trigonometric functions sine and cosine, so
Fx = Fg cos θ
Fy = Fg sin θ
So, replacing Fg = 50 N and θ = 65, we get:
Fx = 50 cos(65) = 21.13 N
Fy = 50 sin(65) = 45.32 N
Therefore, the answers are:
Fx = 21.13 N
Fy = 45.32 N
What is the equation for finding the gravitational force of an object? (1 point)
Answers
The equation for finding the gravitational force of an object is F = mg.
option D is the correct answer.
What is gravitational force of an object?Gravitational force is an attractive force that exists between all objects with mass due to the influence of the Earth's gravitational pull.
An object with mass attracts another object with mass.
The magnitude of the force is directly proportional to the masses of the two objects and inversely proportional to the square of the distance between the two objects according to Newton's law of universal gravitation.
Mathematically, the formula for gravitational force is given as;
F = mg
where;
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What is the area under the curve on the velocity time graph in physics represent
Answers
When given a graph of velocity vs time as the following:
The area under the curve represents the distance that the object has moved in the given time interval.
A bicycle wheel, of radius 0.300 m and mass 2.07 kg (concentrated on the rim), is rotating at 4.00 rev/s. After 59.0 s the wheel comes to a stop because of friction. What is the magnitude of the average torque due to frictional forces?
Answers
ANSWER:
0.079 J
STEP-BY-STEP EXPLANATION:
The average torque exerted due to friction force is:
[tex]\tau=I\alpha[/tex]Here, I is the moment of inertia and α is the angular acceleration.
The mass of wheel is concentrated at the rim. Therefore, the moment of inertia of wheel is,
[tex]I=m\cdot r^2[/tex]Here, m is the mass of wheel and r is the radius of wheel.
replacing:
[tex]\begin{gathered} I=2.07\cdot0.3^2 \\ I=0.1863\text{ kg}\cdot s^2 \end{gathered}[/tex]The angular speed is decreased from 4 rev/s to 0 rev/s in 59 sec. Therefore, the angular acceleration is calculated as:
[tex]\begin{gathered} \alpha=\frac{0-4}{59} \\ \alpha=0.068\cdot\frac{rev}{\sec}\cdot\frac{2\pi\text{ rad/rev}}{1rev/sec^2} \\ \alpha=-0.426rad/sec^2 \end{gathered}[/tex]The negative sign represents that the wheel is de-accelerating.
Replacing:
[tex]\begin{gathered} \tau=I\alpha \\ \tau=0.1863\cdot-0.426 \\ \tau=-0.079\text{J} \end{gathered}[/tex]The negative sign represents the direction of torque i.e. clockwise direction. Thus, the magnitude of average torque is 0.079 J.
A proton is accelerated through a potential difference of 100 V and then enters a region where it is moving perpendicular to a magnetic field B = 0.20 T. Calculate the radius of the circular path in which it will travel.
Answers
The radius of the circular path in which it will travel inside the magnetic field will be 7mm.
Magnetic field is the area around a magnet or an electric charge in which the effect of magnetism is felt.
Magnetic field of the proton = B = 0.20 T
Electric potential difference of the proton = E = 100 V
Kinetic energy of proton = 100p = [tex]\frac{1}{2}m v^{2}[/tex]
[tex]v = \sqrt{\frac{2*100e}{m} }[/tex]
The centripetal acceleration is provided by the magnetic field.
therefore,
[tex]\frac{mv^{2} }{r} = evB[/tex]
mv = eBr
[tex]r = \frac{mv}{eB}[/tex]
m = 1.67 × [tex]10^{-27}[/tex] kg
e = 1.60 × [tex]10^{-19}[/tex] C
B = 0.20 T
v = [tex]\sqrt{\frac{2*100e}{m} }[/tex] = 13.8 × [tex]10^{4}[/tex] m/s
on putting the values of all the quantities in the equation of r, we get
r = 0.07 m
r = 7 mm
The radius of the circular path is 7 mm.
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Pascal's principle states that:all liquids exert pressure downward.pressure will move toward areas where pressure is lowest.applied pressure will be transmitted throughout a fluid.None of the choices are correct.
Answers
According to Pascal's principle states that applied pressure will be transmitted throughout a fluid.
Thus, third one is the correct option.
Victor is driving south. He is traveling at 12 m/s, when he enters an area with a new speed limit. Aver a period of 6 seconds, his speed increases from 12 m/s to 29 m/s. What is Victor’s acceleration during this period?
Answers
Answer:
1.1417 m/s²
Explanation:
Acceleration = final velocity - initial velocity/ time
a= [tex]\frac{v-u}{t}[/tex]
a= [tex]\frac{29-12}{12}[/tex]
a= [tex]\frac{17}{12}[/tex]
a= 1.417 m/s² or [tex]\frac{17}{12}[/tex] m/s² in fraction form
The mass of a satellite orbiting Earth is 15000 kg.
Answers
Newton's universal law of gravity
[tex]F=G\frac{m1\cdot m2}{r^2^{}}[/tex]Where:
F= force between objects
m1= mass 1 = 15,000 kg
m2= mass 2 = 6x10^24
r = distance = 34,000,000 m
G= universal contant of gravitation = 6.67 x10^-11
Replacing:
[tex]F=6.67\cdot10^{-11}\cdot\frac{15,000\cdot6x10^{24}}{(34,000,000)^2}[/tex]F= 5,193 N
Write a rule for the sequence. 3, -3, -9, -15. A. Start with 3 and add -6 repeatedly B. Start with -6 and add 3 repeatedly C. Start with 3 and 6 repeatedly D. Start with 3 and subtract -6 repeatedly
Answers
Substract two consecutive terms of the sequence to see if there is a common difference:
[tex]\begin{gathered} (-3)-(3)=-3-3=-6 \\ (-9)-(-3)=-9+3=-6 \\ (-15)-(-9)=-15+9=-6 \end{gathered}[/tex]As we can see, there is a common difference of -6.
Then, if a number of the sequence is given, the next one can be found by adding -6 (which is the same as subtracting 6).
Notice that the first term of the sequence is 3.
Then, the rule for the sequence is to start with 3 and add -6 repeatedly.
Therefore, the correct choice is option A) Start with 3 and add -6 repeatedly.
Circuit breakers are connected in series so that the circuit will open in case of dangerously high current.TrueFalse
Answers
Circuit breakers are connected in series so that the circuit will open in case of dangerously high current.
that is True
Light of wavelength 589 nm in vacuum passes through a piece of fused quartz of index of refraction n = 1.458. (a) Find the speed of light in fused quartz. (b) What is the wavelength of this light in fused quartz? (c) What is the frequency of the light in fused quartz?
Answers
The speed of light in fused quartz 2.058 * [tex]10^{8}[/tex] m/s
The wavelength of the light in fused quartz 404.322 * [tex]10^{-9}[/tex] m
The frequency of the light in fused quartz 0.00509 * [tex]10^{17}[/tex] hz
refractive index of a material = speed of light in vacuum / speed of light in that medium
1.458 = 3 * [tex]10^{8}[/tex] / speed of light in that medium
speed of light in fused quartz = 3 * [tex]10^{8}[/tex] / 1.458 = 2.058 * [tex]10^{8}[/tex] m/s
frequency = c / lambda = 3 * [tex]10^{8}[/tex] / 589 * [tex]10^{-9}[/tex] = 0.00509 * [tex]10^{17}[/tex] hz
wavelength of light in fused quartz = speed of light in fused quartz / frequency
= 2.058 * [tex]10^{8}[/tex] / 0.00509 * [tex]10^{17}[/tex] = 404.322 * [tex]10^{-9}[/tex] m = 404.322 nm
wavelength = wave velocity in fused quartz / frequency
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you have entered a 134-mile biathlon that consists of a run and a bicycle race. During your run, your average velocity is 6 miles per hour, and during your bicycle ace, your average velocity is 29 miles per hour. You finish the race in 7 hours. What is the distance of the run? What is the distance of the bicycle race?upposeWhat is the distance of the run?miles
Answers
ANSWER:
Distance of the run: 18 miles
Distance of the bicycle race: 116 miles
STEP-BY-STEP EXPLANATION:
Given:
Total distance = 134 miles
Total time = 7 hours
Average velocity during running = 6 mph
Average velocity during bicycle = 29 mph
Let x be the running distance and y be the bicycle distance.
We know that velocity equals distance in a given time, like this:
[tex]\begin{gathered} v=\frac{d}{t} \\ \\ \text{ Therefore:} \\ \\ t=\frac{d}{v} \end{gathered}[/tex]Knowing the above, we can establish the following system of equations:
[tex]\begin{gathered} t_1+t_2=7\rightarrow\frac{d_1}{v_1}+\frac{d_2}{v_2}=7\rightarrow\frac{x}{6}+\frac{y}{29}=7\text{ \lparen1\rparen} \\ \\ x+y=134\rightarrow x=134-y\text{ \lparen2\rparen} \end{gathered}[/tex]We substitute the second equation in the first and obtain the following:
[tex]\begin{gathered} \frac{134-y}{6}+\frac{y}{29}=7 \\ \\ \frac{(134-y)(29)+6y}{6\cdot29}=7 \\ \\ \frac{3886-29y+6y}{174}=7 \\ \\ 3886-23y=7\cdot174 \\ \\ y=\frac{1218-3886}{-23}=\frac{-2668}{-23} \\ \\ y=116\rightarrow\text{ bicycle distance} \\ \\ \text{ now, for x:} \\ \\ x=134-116 \\ \\ x=18\rightarrow\text{ running distance} \end{gathered}[/tex]Therefore:
The distance of running is 18 miles and the distance by bicycle is 116 miles.
Viewers of Star Trek hear of an antimatter drive on the Starship Enterprise. One possibility for such a futuristic energy source is to store antimatter charged particles in a vacuum chamber, circulating in a magnetic field, and then extract them as needed. Antimatter annihilates with normal matter, producing pure energy. What strength (in T) magnetic field is needed to hold antiprotons, moving at 6.10 ✕ 107 m/s in a circular path 1.70 m in radius? Antiprotons have the same mass as protons but the opposite (negative) charge. (Enter the magnitude.)
Answers
Data:
B=?, v=6.10*10^7 m/s, R=1.70m, m=1.67*10^(-27)kg, q=-1.6*10^(-19)C
Answer:
Firstly, we need to remember the formula for the Magnetic force, which is:
[tex]F_m=|q|vB[/tex]However, in this scenario the magnetic force will act as a centripetal force, thus:
[tex]F_m=\frac{mv^2}{R}[/tex]If we equal both of them:
[tex]|q|vB=\frac{mv^2}{R}\Rightarrow B=\frac{mv}{|q|R}[/tex]Replacing our values:
[tex]B=\frac{1.67*10^{-27}*6.1*10^7}{1.6*10^{-19}*1.7}=0.3745T[/tex]Then, our magnetic field will be B=0.3745T
The wire feed controls the amperage during the welding process. A control knob labeled in metric units shows a maximum wire-feed speed of 160 mm/sec. What is this maximum speed in inches per minute?The maximum speed is ___ inches per minute.
Answers
Answer: 378 inches per minute
Explanation:
We want to convert 160 mm/sec to inches per minute.
Recall,
1 mm = 0.03937 inches
1 second = 0.01667 minutes
Thus,
160 mm/sec = 160 x 0.03937 inches/0.01667 minutes
= 378 inches per minute
The fundamental frequency of a pipe is the lowest resonant frequency. Is this true or false?
Answers
By definition, the fundamental frequency of an object is the lowest frequency such that the object resonates.
Then, the answer is:
[tex]\text{True}[/tex]Answer:
By definition, the fundamental frequency of an object is the lowest frequency such that the object resonates.
Then, the answer is: true
Explanation:
the position of an object is given by: x(t)=2t^3-35t^2+10 what is the acceleration of the object at t=250 seconds?
Answers
We are given that a particle's position is determined by the function:
[tex]x\left(t\right)=2t^3-35t^2+10[/tex]We are asked to determine the acceleration of the object. To do that we will first determine the first derivative of the position with respect to time, i. e. the velocity of the particle:
[tex]\frac{dx}{dt}=\frac{d}{dt}(2t^3-35t^2+10)[/tex]Now, we distribute the derivative operator:
[tex]\frac{dx}{dt}=\frac{d}{dt}(2t^3)-\frac{d}{dt}(35t^2)+\frac{d}{dt}(10)[/tex]Now, we use the following rule to determine each derivative:
[tex][/tex]Could really some help answering this question I don’t really understand! :)
Answers
Given:
Object A is at a higher temperature than object B.
Here, there is a difference in temperature.
Temperature flow is similar to water flow.
The water stops flowing if the water level becomes the same in botht containers.
Similarly, thermal energy transfers between the objects until the objects have changed the temperature by the same amount.
Thus, option B is correct.
2. A Carnot engine operates between a 1500 C reservoir and a -20 C reservoir. What is the efficiency of the engine?1. 83%2. 86 %3. 99 %4. 1.3 %
Answers
The efficiency of a Carnot engine is given by
[tex]\eta=1-\frac{T_C}{T_H}[/tex]Where TC is the temperature of the cold source in kelvin and TH is the temperature of the hot source in kelvin.
Let us first convert the given temperatures from celsius to kelvin.
[tex]\begin{gathered} T_C=-20+273=253K \\ T_H=1500+273=1773K \end{gathered}[/tex]So, the efficiency is
[tex]\begin{gathered} \eta=1-\frac{253}{1773} \\ \eta=0.857 \\ \eta=85.7\% \end{gathered}[/tex]Rounding off to a whole number
[tex]\eta=86\%[/tex]Therefore, the efficiency of the engine is 86%
How far will a bike travel if you pedal at 13 m/s for 7 seconds?
Answers
Given
[tex]\begin{gathered} v=13\text{ m/s} \\ t=7\text{ s} \end{gathered}[/tex]The distance covered is given as,
[tex]s=vt[/tex]Here, s is the distance travelled, v is the speed and t is the time .
Substituting all known values,
[tex]\begin{gathered} s=(13\text{ m/s)}\times(7\text{ s)} \\ =91\text{ m} \end{gathered}[/tex]Therefore, the bike will travel 91 m is 7 second.
of the following and draw a neat, properly labelled free body diagram. Indicate the size of forces with the lengths of the arrows. i.e., if two forces are the same size draw them the same length and if one is much bigger draw it much longer. a) The Space Shuttle accelerating vertically just after leaving the launch pad.
Answers
We will have that the diagram will be the following:
Here "F" is the force the shuttle is using to take off, friction is the friction with the air and "W" is the weight of the shuttle.
Classify the types of forces below into four groups in the table provided. Write only the letters to represent the forces. Give a heading for each group in the table.
A The force which prevents a glass bottle from slipping out of your hand
B The force which makes it difficult to climb a steep mountain
C The force which gives you weight
D The force which makes it difficult for you to push down a float in water
E The force which causes a parachutist to fall when he jumps out of a helicopter
F The force which slows down an airplane moving in air
G The force which makes a compass turns
Answers
Gravity force, friction force and buoyant force are the types of forces given below.
A) The force which prevents a glass bottle from slipping out of your hand- friction force
B) The force which makes it difficult to climb a steep mountain- gravity
C) The force which gives you weight- gravity
D) The force which makes it difficult for you to push down a float in water- buoyant force
E) The force which causes a parachutist to fall when he jumps out of a helicopter- gravity
F) The force which slows down an airplane moving in air- friction force
G) The force which makes a compass turns- gravity
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A capacitor is constructed of two large, identical, parallel metal plates separated by a small distance d. A battery fully charges the capacitor and is then disconnected. If, instead of separating the plates, the empty space between the plates is filled with a slab of insulating material that has a dielectric constant κ= 2, which of the following correctly describes the change, if any, of the voltage across the capacitor, the electric field between the plates, and the energy stored in the capacitor? 1) Voltage halvesElectric field halves Energy halves 2. Voltage halves Electric field halves Energy does not change 3. Voltage does not change Electric field does not change Energy halves 4. Voltage does not changeElectric field halves Energy halves 5. Voltage does not change Electric field does not change Energy does not change
Answers
The capacitance of a capacitor of a parallel plate is given by:
[tex]C=\frac{kA\cdot\epsilon_o}{d}[/tex]Where:
[tex]\begin{gathered} \epsilon_o=_{\text{ }}Vacuum_{\text{ }}permittivity \\ k=_{\text{ }}Dielectric_{\text{ }}constant=2 \\ A=_{\text{ }}Area_{\text{ }}of_{\text{ }}the_{\text{ }}plates \\ d=_{\text{ }}distance_{\text{ }}betwen_{\text{ }}the_{\text{ }}plates \end{gathered}[/tex]We also know:
[tex]\begin{gathered} Q=\frac{q}{V} \\ so\colon \\ \frac{q}{V}=\frac{kA\cdot\epsilon_o}{d} \\ V=\frac{qd}{kA\cdot\epsilon_o} \\ if \\ k=2 \\ V=\frac{1}{2}(\frac{qd}{kA\cdot\epsilon_o}) \end{gathered}[/tex]As we can see the voltage halves
And since:
[tex]\begin{gathered} E=\frac{V}{d} \\ W=qV \end{gathered}[/tex]We can conclude that electric field and also the energy halve
An acorn is dropped and reaches the ground in 2.0s. What is the acorn’s velocity just as it hits the ground? How high above the ground was it released?
Answers
Take into account that the vertical distance traveled by the acorn can be calculated by using:
[tex]h=\frac{1}{2}gt^2[/tex]where,
g: gravitational acceleration constant = 9.8m/s^2
t: time acorn takes to hit the ground = 2.0s
h: height at which acorn is initially = ?
Replace the given values of the parameters into the previous formula and simplfiy:
[tex]h=\frac{1}{2}(9.8\frac{m}{s^2})(2.0s)^2=19.6m[/tex]Hence, the acorn was released from a high of 19.6m above the ground.
The velocity just after acorn hits the ground is given by:
[tex]\begin{gathered} v=gt \\ v=(9.8\frac{m}{s^2})(2.0s)=19.6\frac{m}{s} \end{gathered}[/tex]Hence, the speed is 19.6 m/s