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Physics 101 Mechanics Q&A Archive of May 28, 2023

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May 28 of 2023

39. A light beam in air is incident on the surface of a pond, making an angle of \( 20^{\circ} \) with respect to the surface. What are the angles of reflection and refraction?
27. What is the speed of light in air? In crown glass?
Please be specific.
33. How far does light travel underwater during a time interval of \( 1.50 \times 10^{-6} \mathrm{~s} \) ?
29. In what substance in Table 1.1 is the speed of light \( 2.290 \times 10^{8} \mathrm{~m} / \mathrm{s} ? \)
24: Thermodynamics is a branch of chemistry and physics that deals with energy. The basic function of the engine is to convert chemical energy (stored in the atomic bonds of the gasoline) to rotational kinetic energy (rotating shaft). There is at least one intermediate step and other form(s)ā€¦
Find the slope and y-intercept of this equation: x/3 + y/6 = 1 slope = 1 and y-intercept = -3 slope = -1 and y-intercept = 3 slope = -2 and y-intercept = 6 slope = 2 and y-intercept = -6
What is the force constant of the spring?
L OF ENGINEERING IINT OF CIVII \& INVIRONMINIAI I NGINI I IRING N 2 \( B C \) is supported by ball and socket supports at \( A \) and \( C \) and the ca )-lb suspended weight. What is the tension in cable \( \mathrm{BD} \) ? RSTION 3 coal wagon shown in the figure is used to haul coal from aā€¦
Air with a wet bulb temperature of 27 Ā°C and a relative humidity of 20% is fed into a dryer at a rate of 5,000 m3 /hr to dry slices of persimmons. The air leaving the dryer is saturated and cannot hold any more water vapor. The persimmons enter the dryer at a rate of 55 kg (wet weight)/hrā€¦
A voltage vs(t) = 10sin(5t) is applied to the RC circuit shown. The voltage vc(t) across the capacitor satisfies this differential equation: 0.2 dv(t)/dt + v(t) = 10sin(5t) What type of differential equation is this? second order non-homogenous differential equation second order homogenousā€¦
Question 33 (10 points) The derivative of f(x) = df(x)/dx = 2x - 2 What is f(x) with the initial condition f(1) = 2? f(x) = x^2 - 3x + 2 f(x) = x^2 - 2x + 3 f(x) = 3x^2 - 2x - 2 f(x) = x^2 + 3x - 2
The derivative of f(t) = df(t)/dt = -5 sin(5t). What is f(t)? f(t) = sin(5t) + C f(t) = cos(5t) + C f(t) = 3sin(t) + 4 f(t) = -cos(5t) + C
A particle is accelerated along a curved path L under the action of an applied force. f(x)= 5e^-x N. Determine the work done by this particle when it travelled from L= 0 to L= 3m. W=?(0 to L) f(x)dx Work done by the particle can be computed by the above formula. In this case, distance L inā€¦
Question 30 (10 points) Find the area, ( mathbf{A} ), covered by the curve ( f(x)=sin (x) ) between ( x=oldsymbol{pi} ) and ( mathbf{x}=mathbf{2 pi} ). [ A=int_{pi}^{2 pi} f(x) d x ] 2 ( -2 ) 1 ( -1 )
Differentiation lowers the power by 1 and Integration increases the power by 1 of the original function. TRUE OR FALSE
The slope of the graph of f(x) = xĀ² + 1 at (-1, 2) and (2, 5) are: -2 and -4 -2 and 4 2 and 4 2 and -4
Question 27 (10 points) The motion of a particle moving in a horizontal direction is described by its position ( mathrm{x}(mathrm{t}) ). ( x(t)=15+6 t+6 t^{2} ) Determine the velocity, ( v(t)=d x(t) / d t ) at ( t=2 s ), and acceleration, ( a=d v(t) / d t ) at ( t=2 s ). SI units of position isā€¦
Question 26 (10 points) The derivative of a constant is zero. True False
Question 25 (10 points) This curve has [ mathrm{y}(mathrm{x})=frac{1}{3} x^{3}-frac{7}{2} x^{2}+10 mathrm{x}+5 ] Two maxima Two minima One maximum and one minimum None of the above
In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. TRUE OR FALSE
Non-square matrices do not have determinants. TRUE OR FALSE
If A is a matrix with 1 row and 3 columns and B is a matrix with 3 rows and 1 column then we can say AxB = BxA TRUE OR FALSE
If a matrix A has 4 rows and 3 columns then one can determine the inverse matrix, A-1. TRUE OR FALSE
\( 1 \& \) MUSIC 10 - LAS 4.pdf Dexcases ow Acromers yeces wewer ment. Maerahase ? 4 Ars kime L. sase Basuany 3. Whais af the and is. Eares nam a. ane kalins c. - and thasmane (7) seare of hanab 8. chep blance Comany A. Buater itines 1. Pbilkewes Buhes Cantien Hesie Bantet A. Bowin sorith 8.ā€¦
A set of linear equations that describes a system can ONLY be solved by using matrix algebra. TRUE ORFALSE
Question 18 (10 points) The angle 4.621 radians is approximately equal to: 205.34 degrees 132.40 degrees 264.76 degrees 82.76 degrees
17
sin(x) and cos(x) are the only periodic functions that can be used for real world applications. True False
Simplify [(1 + j)/(1 - j)] - [(1 + j2)(2 + j2)] 2 + j5 2 - j5 - 2 + j6 None of the above
A complex number can be represented in both Polar and Cartesian coordinate systems. TRUE OR FALSE
Question 13 (6 points) Use the complex number: ( -2 / mathbf{j} ) Calculate ( r ) and ( heta ) ( r=2 ) and ( heta=90 ) degrees ( r=1 / 2 ) and ( heta=-90 ) degrees ( r=-2 ) and ( heta=-90 ) degrees ( r=1.414 ) and ( heta=0 ) degrees
The sum of the vectors A, B, C, and D is determined by drawing the vectors as a chain. Then the sum is a single vector joining the beginning of the first vector A to the end of the last vector D. TRUE OR FALSE
The length of a vector can be either positive or negative. TRUE OR FALSE
The Law of Sines and the Law of Cosines are applicable only to right-angle triangles. TRUE OR FALSE
A rock is thrown horizontally from the top of the cliff 88 m high, with a horizontal velocity of 25 m/s. Determine the time it takes for the rock when in motion before it reached the ground and the horizontal distance covered by the rock from the base of the cliff.
A triangle can have three sides as 30cm, 40cm, and 80cm. TRUE OR FALSE
Sandeep works at a lab with a huge circular particle accelerator. It has a diameter of 4 miles. What is the accelerator's circumference? Use 3.14 for ( pi ). If necessary, round your answer to the nearest hundredth. miles
A 50lb traffic light is hanging with two cables shown in the figure. Which cable has more tension? TAB is the tension in cable AB and TBC is the tension in cable BC. TAB is greater than TBC TBC is greater than TAB TAB = TBC None of the above.
Question 6 (7 points) A rocket is fired from the roof of a 50 ft. tall building as shown in the figure below. The height of the rocket from the ground is given by: y(t) = 150t - 16.1t^2 + 50 Find the approximate time required to reach the maximum height as well as the corresponding approximateā€¦
Consider the two-loop circuit shown in the figure below. The currents I1 and I2 (in amp) satisfy the following system of equations: 16I1 - 9I2 = 100 20I2 - 9I1 + 110 = 0 Calculate I1 and I2. The unit of current is Amp (A). I1 = - 2.25A and I2 = 1.60A I1 = 3.22A and I2 = -2.60A I1 = 4.22A and I2ā€¦
Question 2 (7 points) The intersection of these two linear equations: a) 3y + 7x ā€“ 1 = 0 b) x + y = 1 is x = -1 and y=3 x = 1/2 and y=-3/2 x = -1/2 and y=3/2 x = -2 and y=2 Question 3 (7 points) Find the slope and y-intercept of this equation: x/3 + y/6 = 1
5. Once in the night, a speeding taxi struck a man as he crossed the street. An eyewitness has testified that she thought the taxi (which did not stop) was blue. The man sued the Blue cab company for his medical expenses. The city where the accident occurred has only two taxi companies: Blueā€¦
This is an equation of a straight line: x + 1/x = 1 TRUE OR FALSE
a man pulls suitcase of mass 10.4 kh with force of 25 N inclined in horizontal at angle 30degree find magnitude of acceleration
A block of inertia m sits on a smooth surface. A light string is attached to it and placed over a solid pulley of inertia 3 m and radius R, and a ball of inertia m is attached to the free end of the string. If there is no slippage between string and pulley, determine the magnitude of theā€¦
A body of mass m is moving vertically downward from rest in a fluid that exerts a resistance force of magnitude kv on the body, where k is a positive constant and v is the speed of the body. The terminal speed of the body is:
A ball with mass is tied on a light string which passes through a tube in the smooth table. The ball has an initial speed vo and moving circularly with radius ro. Then pulling the string to make the radius to r1. The speed of the ball is:
The ā€¦ā€¦ā€¦lens focuses light beam in its focal point. A) longitudinal B) converging C) diverging D) plane
2- Typically a bullet leaves a stand and ?5 cquiber pistol (5.0-inbarrei) at a speed of \( 262 \mathrm{~m} / \mathrm{s} \). If it eakes \( 1 \mathrm{~ms} \) to traverse the barrel, determine the auerage acceleration experienced by the \( 16.2 \mathrm{~g} \) bulle.t withon the gun and thepā€¦
Question A solid at absolute temperature \( T \) is placed in an external magnetic field \( \mathrm{H}=30,000 \) gauss. The solid contains weakly interacting paramagnetic atoms of spin-1/2 so that the energy of each atom is \( \pm \mu \mathrm{H} \). If the magnetic moment \( \mu \) is equal toā€¦
What quantity of ice at 0 ā°C should be added to 55 kg of water at 90 ā°C in orfer to have only liquid at 37 ā°C? Consider the specific heat of water to be 4.186 kJ/(Kg K) and the latent heat of ice is 334 kJ/kg.
If you mix 1 kg of water at 95ā°C with 1 kg of ice at -5ā°C, what temperature will the mixture have? Is there enough heat to melt all the ice completely? Consider the specific heat of ice is 0.5 cal/(g ā°C), the fusion heat of ice is 90 cal/g and the specific heat of water is 1 cal/(g ā°C)
\( B_{i}=1.10 \mathrm{~T} \) (upward)
At 100 ā°C a glas jar is completely filled wuth 595 g of mercury. What mass of mercury is needed to fill the jar at -45 ā°C ? The coefficient of linear expansion of glass is 9x10^-6 ā°C^-1 and the coefficient of volumetric expansion of mercury is 1.8x10^-4 ā°C^-1.
A railway truck on a level,straight track is initially at rest.The truck is 2 marks given a quick, horizontal push by an engine so that it now rolls along the track. railway truck push from engi 4.3ms The engine is in contact with the truck for a time T= 0.54 s and the initial speed of theā€¦
An acrylic beaker (with a coefficient of linear expansion of 6.8x10^-5 ā°C^-1 ) is filled wuth mercury at 25ā°C, thus having a capacity of 500 mL. It is then cooled down to 15ā°C. Calculate the mass of mercury, measured at 15ā°C, that must be added to make the beaker completely full. Consider theā€¦
A circular tire of 1.2 m in diameter must be attached to a steel rim of the same diameter. In order to be able to adjust it, you want to heat up the tire until its radius is 5 mm greater than that of the rim. Knowing that the ambient temperature is 20ā°C and its coefficient of linear expansionā€¦
Consider a charge of q1 Ī¼C 7 fixed with a site near another charge of q2 Ī¼C 6. Evaluate the potential energy of q2, when the distance of q2 is 4 cm from charge q1?
Two children are sliding down a snowy hill which is inclined by 49.3 degrees with respect to horizontal. One has a rough sled which has a coefficient of kinetic friction between it and the snow of Ī¼k = 0.328; the other has a slippery sled which has a coefficient of kinetic friction between itā€¦
Find the reaction of the shaft at point shown. (b)
At a junction temperature of \( 25^{\circ} \mathrm{C} \), over what range of forward voltage drop \( v_{D} \) can \( (2.1) \) be approximated as \( i_{D} \approx I_{o} e^{v_{D} / V_{T}} \) with less than 1 percent error for a Ge diode?
The circuit of Fig. 2-32 adds a dc level (a bias voltage) to a signal whose average value is zero. If \( v_{S} \) is a \( 10-\mathrm{V} \) square wave of period \( T, R_{L}=R_{1}=10 \Omega \), and the diode is ideal, find the average value of \( v_{L} \). Fig. 2-32 \( 2 \mathrm{v} \) \( 6ā€¦
The dimession of the quantity \( E \times B \), where \( E \) represents the electric field and \( B \) the magnetic may be giver as a \( \left[M T^{-3}\right] \) (b) \( \left[M^{2} L T^{-5} A^{-2}\right] \) cc) \( \left[M^{2} L T^{3} A^{-1}\right] \) d \( \left[M L T^{-2} A^{-2}\right] \)
Write words or phrases as to your prior knowledge about the moon. Write your answers on the boxes provided in the sematic web.
lima \( F= \) dss \( \operatorname{sinathrxtratatignik} \) hner
A gold rod of uniform density and constant cross sectional area oscillates like a pendulum hung from one end. It has a period of 0.9 s at a certain temperature. If the coefficient of linear expansion of gold is 14.2x10^-6 determine the increase in tenperature that must be given to the rod soā€¦
\begin{tabular}{|c|c|c|c|c|c|c|} \hline & \( \begin{array}{c}\text { Voltmeter } \\ \text { reading } \\ V_{4}\end{array} \) & \( \begin{array}{c}\text { Voltmeter } \\ \text { reading } \\ V_{1}\end{array} \) & \( \begin{array}{c}\text { Voltmeter } \\ \text { reading } \\ V_{2}\end{array} \)ā€¦
A force P is used to hold a 200kg mass. If the h is 0.59m, calculate P. Take cross sectional area A1=0.05m and A2= 1m? Please give your answer in Si unit with 0 decimal. For example for pressure, 100000Pa not 100kPa. Please do not write unit in the answer box, for example 100000Pa = 100000
MEC105B - Assignment 02 \( f 6 \) \( -117 \) oaded truss. All triangles are isosceles. Force re positive if in tension, negative if in ompression. nswers: \[ B= \]
An clectric field is given by \( E_{x}=2 x^{3} \) i N/C. The potential of the point \( (1,-2) \), if potential of the point \( (2,4) \) is taken as zero, is (1) \( -7.5 \times 10^{3} \mathrm{~V} \) (2) \( 7,5 \times 10^{*} \mathrm{~V} \) (3) \( -15 \times 10^{3} \mathrm{~V} \) (4) \( 15 \timesā€¦
potential of the point (1, 2), if porchtinl of the point \( (2,4) \) is wkcn as rero is (1) \( -7.5: 10^{3} \mathrm{~V} \) \( (2) \cdot \pi \cdot \lim ^{2} \ln \) (3) \( -15 \times 10^{2} \mathrm{v} \) (4) \( 15+10,1 \)
3- A cars odometer reads \( 22687 \mathrm{~km} \) at the stan of a trip and \( 22791 \mathrm{~km} \) at the end. The trip Stook \&. 0 hours. What was the caris avengge speed in \( \mathrm{km} / \mathrm{h} \) and in \( \mathrm{m} / \mathrm{s} \) ?
3- A cais odomeeer reads \( 22687 \mathrm{~km} \) at the \( \mathrm{t} \)-9. of a trip and \( 22791 \mathrm{~km} \) at the end. The tip Stork 4.0 hours. What was the cari averge speed in \( \mathrm{km} / \mathrm{h} \) and in m\( / \mathrm{s} \) ?
The system of blocks on a frictionless surface in the diagram below is accelerating at \( 2 \mathrm{~m} / \mathrm{s}^{2} \). tension in the cord at \( \mathrm{X} \) ? \[ a-2.0 \mathrm{~m} / \mathrm{s}^{2} \longrightarrow \]
3- A cairs odometer reads \( 22687 \mathrm{~km} \) at the stint of \( a \) trip and \( 22791 \mathrm{~km} \) at the end. The trip Stook 4.0 hours. What was the cars avergge speed in \( \mathrm{km} / \mathrm{h} \) and in \( \mathrm{m} / \mathrm{s} \) ?
Two objects are connected as shown. The \( 12 \mathrm{~kg} \) cart is on a frictionless \( 42^{\circ} \) incline while the \( 15 \mathrm{~kg} \) block is on a horizontal surface having a coefficient of friction \( \mu=0.23 \). Determine the acceleration of the system of masses
2 According to Lt's computer, a robot that left it's cioset and traveled \( 1200 \mathrm{~m} \), hadan average speed of \( 20.0 \mathrm{~m} / \mathrm{s} \). Howlong didthe triptakes?
- Three kids in a parking lot caunch a rocket that rises into the air duing \( 9380 \mathrm{mlong} \) are in \( 40 \mathrm{~s} \). determine lts average speed.
2.18 rad/s^2 to rev/s^2
4.) Determine the ratio of \( F / L \) between two wires by setting up two long and straight parallel wires \( 0.09 \mathrm{~m} \) apart from each other. He also allows each wire to receive the same amount of current equal to \( 20 \mathrm{~A} \). What value of F/L will be obtained?
3) The magnetic force acting on a wire that is perpendicular to a \( 0.25 \mathrm{~T} \) uniform magnetic field is \( 3.4 \mathrm{~N} \). If the current in the wire is \( 2.75 \mathrm{~A} \), what is the length of the wire that is inside the magnetic field?
A littre turtle is placed at the origin of an each grid box is \( 1.0 \mathrm{~cm} \) by \( 1.0 \mathrm{~cm} \). the turtle wauks around for a while and finally ends up at point \( (24,10) \), that is, 24 boxes 9 wing the \( x \)-axas and 10 boxesalong the \( y \)-axis. determine theā€¦
the vertical. 2) A house has a floor of dimensions \( 22 \mathrm{~m} \) by \( 18 \mathrm{~m} \). The local magnetic field due to Earth has a horizontal component \( 2.6 \times 10-5 \mathrm{~T} \) and a downward vertical component \( 4.2 \times 10-5 \mathrm{~T} \). Calculate the magnetic flux.
A bug starts at point \( A \), crawls \( 8.0 \mathrm{~cm} \) east, then \( 5.0 \mathrm{~cm} \) south, \( 3.0 \mathrm{~cm} \) west and 4.0 Cm normh to point \( B \). (a) How far northand east is \( B \) from \( A \) ? (b) Find the displacement from \( A \) to \( B \) both graphically andā€¦
Determine the number of users that can transmit simultaneously on a TDD radio link with a forward link at of 50 MHz, radio channels of 200 kHz and each link support the speech channel of 8 speech channels supported, and no guard band is assumedā€‹
1. The average input to a manufacturing plant is \( 3,000 \mathrm{kVA} \) at a p.f. of 0.72 lagging a synchronous having an input of \( 1,300 \mathrm{kVA} \) is then installed and delivers a load of \( 600 \mathrm{Hp} \) at an efficiency of 8 Calculate the over-all KW input.
A 0.5 mole of gas at temperature 300 K expands isothermally from an initial volume of 2 L to 6 L. The value of gas constant, R = 8.31 J mol-1 K-1. Calculate(a) Work done by the gas (b) Heat added to the gas (c) Final pressure of the gas
Q. 3 show that the shape factor for minimum spherical aberration is given by \( \sigma=-\frac{2\left(n^{2}-1\right)}{n+2}\left(\frac{s^{\prime}-s}{s^{\prime}+s}\right) \), where \( \mathrm{n} \) is the refractive index of lens, \( s^{\prime} \) and \( s \) are the image and object distancesā€¦
Exercise No. 7 1. A \( 60 \mathrm{~kg} \) woman walking through an alley accidentally broke the heel of her left high-heeled shoes. Now the woman tries to balance on one heel of a pair of high-heeled shoes. If the heel is circular and has a radius of \( 0.500 \mathrm{~cm} \), what pressure doesā€¦
a mass oscillates on a spring with amplitude A and maximum velocity Vmax. The period of the oscillation is:
Q. 1 Show that for a spherical concave mirror, a calculation like that done for a refracting surface gives a third-order aberration of[a=frac{h^{4}}{4 R}left(frac{1}{s}-frac{1}{R}right)^{2}]where ( R ) is the magnitude of the radius of curvature.Q. 2 Using the result of problem Q. 1 determineā€¦
take theta2 to be -14 degrees. Theta 1 and theta 2 are measured from the x axis
please solve without integration
\( 11: 47 G \doteq \simeq \) a The horizontal velocity of the ball remains constant and \( v_{\mathrm{x}}=10 \mathrm{~m} \mathrm{~s}^{-1} \). b \( v^{2}=u^{2}+2 a x \) and \( v_{y}{ }^{2}=0^{2}+2\left(9.8 \mathrm{~m} \mathrm{~s}^{-2}\right)(1.0 \mathrm{~m}) \) and \( v_{y}=4.4 \mathrm{~m}ā€¦
The mass and volume of a body are found to be \( \pm 0.05 \mathrm{~kg} \) and \( 1.00 \pm 0.05 \mathrm{~m}^{3} \) respectively. Then maximum possible percentage error in its density a) \( 6 \% \) (b) \( 3 \% \) (c) \( 10 \% \) (d) \( 5 \% \) (e) \( 7 \% \) n an experiment, four quantities \( a,ā€¦
An 8 kg plunger is released from rest in the position shown in Fig. 15.15(a) and is stopped by two nested springs. The constant of the outer spring is k=3 kN/m and constant of the inner spring = 10 kN/m. Determine the maximum deflection of the outer spring.
why E?
INSTRUCTION: Answer the following questions as directed. Copy and write it in a 1 whole sheet of paper. Or you may choose to print this answer sheet. TABLE 1. Data on the Total Time and Time of the Ball in the Air \begin{tabular}{|c|c|c|} \hline Trial & Total Time (s) & Time, \(ā€¦
Objective: 1. The students will learn use of modern tools for design and simulation of Electrical Circuits and analyze them. The students will select an electrical circuits simulation plate-form and use it for detailed analysis of electrical circuits. Problem Statement 2. Select a suitableā€¦
20. The flow of river is \( 19 \mathrm{~m}^{3} / \mathrm{sec} \) produces a total brake power of \( 7000 \mathrm{~kW} \). It is proposed to install two turbines, one of which is twice the capacity of the other. The efficiency and specific speed of both units are assumed to be \( 80 \% \) and \(ā€¦
Activity 1 Energy in and out! \begin{tabular}{|l|l|l|} \hline & \multicolumn{1}{|c|}{ Energy in } & Energy out \\ \hline Candle & & \\ \hline Sand clock & & \\ \hline \( \begin{array}{l}\text { Arrow shoot from } \\ \text { cross bow }\end{array} \) & & \\ \hline \( \begin{array}{l}\text {ā€¦
A 45 N horizontal force pushes on a 3.7 kg mass resting on a horizontal surface. The surface exerts a friction force of 21 N against the motion. The acceleration of the 3.7 kg mass is ____ m/s^2.
2. For the cantilever beam with \( \mathrm{I}=20 \times 10_{6} \mathrm{~mm}_{4} \) shown below, Find the maximum tension and compression due to the applied concentrated load.
Find the slope and y-intercept of this equation: x/3 + y/6 = 1 slope = 1 and y-intercept = -3 slope = -1 and y-intercept = 3 slope = -2 and y-intercept = 6 slope = 2 and y-intercept = -6
A voltage vs(t) = 10sin(5t) is applied to the RC circuit shown. The voltage vc(t) across the capacitor satisfies this differential equation: 0.2 dv(t)/dt + v(t) = 10sin(5t) What type of differential equation is this? second order non-homogenous differential equation second order homogenousā€¦
Question 33 (10 points) The derivative of f(x) = df(x)/dx = 2x - 2 What is f(x) with the initial condition f(1) = 2? f(x) = x^2 - 3x + 2 f(x) = x^2 - 2x + 3 f(x) = 3x^2 - 2x - 2 f(x) = x^2 + 3x - 2
The derivative of f(t) = df(t)/dt = -5 sin(5t). What is f(t)? f(t) = sin(5t) + C f(t) = cos(5t) + C f(t) = 3sin(t) + 4 f(t) = -cos(5t) + C
A particle is accelerated along a curved path L under the action of an applied force. f(x)= 5e^-x N. Determine the work done by this particle when it travelled from L= 0 to L= 3m. W=?(0 to L) f(x)dx Work done by the particle can be computed by the above formula. In this case, distance L inā€¦
Question 30 (10 points) Find the area, ( mathbf{A} ), covered by the curve ( f(x)=sin (x) ) between ( x=oldsymbol{pi} ) and ( mathbf{x}=mathbf{2 pi} ). [ A=int_{pi}^{2 pi} f(x) d x ] 2 ( -2 ) 1 ( -1 )
Differentiation lowers the power by 1 and Integration increases the power by 1 of the original function. TRUE OR FALSE
The slope of the graph of f(x) = xĀ² + 1 at (-1, 2) and (2, 5) are: -2 and -4 -2 and 4 2 and 4 2 and -4
Question 27 (10 points) The motion of a particle moving in a horizontal direction is described by its position ( mathrm{x}(mathrm{t}) ). ( x(t)=15+6 t+6 t^{2} ) Determine the velocity, ( v(t)=d x(t) / d t ) at ( t=2 s ), and acceleration, ( a=d v(t) / d t ) at ( t=2 s ). SI units of position isā€¦
Question 26 (10 points) The derivative of a constant is zero. True False
Question 25 (10 points) This curve has [ mathrm{y}(mathrm{x})=frac{1}{3} x^{3}-frac{7}{2} x^{2}+10 mathrm{x}+5 ] Two maxima Two minima One maximum and one minimum None of the above
In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. TRUE OR FALSE
Non-square matrices do not have determinants. TRUE OR FALSE
If A is a matrix with 1 row and 3 columns and B is a matrix with 3 rows and 1 column then we can say AxB = BxA TRUE OR FALSE
If a matrix A has 4 rows and 3 columns then one can determine the inverse matrix, A-1. TRUE OR FALSE
A set of linear equations that describes a system can ONLY be solved by using matrix algebra. TRUE ORFALSE
Question 18 (10 points) The angle 4.621 radians is approximately equal to: 205.34 degrees 132.40 degrees 264.76 degrees 82.76 degrees
17
sin(x) and cos(x) are the only periodic functions that can be used for real world applications. True False
Simplify [(1 + j)/(1 - j)] - [(1 + j2)(2 + j2)] 2 + j5 2 - j5 - 2 + j6 None of the above
A complex number can be represented in both Polar and Cartesian coordinate systems. TRUE OR FALSE
Question 13 (6 points) Use the complex number: ( -2 / mathbf{j} ) Calculate ( r ) and ( heta ) ( r=2 ) and ( heta=90 ) degrees ( r=1 / 2 ) and ( heta=-90 ) degrees ( r=-2 ) and ( heta=-90 ) degrees ( r=1.414 ) and ( heta=0 ) degrees
The sum of the vectors A, B, C, and D is determined by drawing the vectors as a chain. Then the sum is a single vector joining the beginning of the first vector A to the end of the last vector D. TRUE OR FALSE
The length of a vector can be either positive or negative. TRUE OR FALSE
The Law of Sines and the Law of Cosines are applicable only to right-angle triangles. TRUE OR FALSE
A triangle can have three sides as 30cm, 40cm, and 80cm. TRUE OR FALSE
Sandeep works at a lab with a huge circular particle accelerator. It has a diameter of 4 miles. What is the accelerator's circumference? Use 3.14 for ( pi ). If necessary, round your answer to the nearest hundredth. miles
A 50lb traffic light is hanging with two cables shown in the figure. Which cable has more tension? TAB is the tension in cable AB and TBC is the tension in cable BC. TAB is greater than TBC TBC is greater than TAB TAB = TBC None of the above.
Question 6 (7 points) A rocket is fired from the roof of a 50 ft. tall building as shown in the figure below. The height of the rocket from the ground is given by: y(t) = 150t - 16.1t^2 + 50 Find the approximate time required to reach the maximum height as well as the corresponding approximateā€¦
Consider the two-loop circuit shown in the figure below. The currents I1 and I2 (in amp) satisfy the following system of equations: 16I1 - 9I2 = 100 20I2 - 9I1 + 110 = 0 Calculate I1 and I2. The unit of current is Amp (A). I1 = - 2.25A and I2 = 1.60A I1 = 3.22A and I2 = -2.60A I1 = 4.22A and I2ā€¦
Question 2 (7 points) The intersection of these two linear equations: a) 3y + 7x ā€“ 1 = 0 b) x + y = 1 is x = -1 and y=3 x = 1/2 and y=-3/2 x = -1/2 and y=3/2 x = -2 and y=2 Question 3 (7 points) Find the slope and y-intercept of this equation: x/3 + y/6 = 1
This is an equation of a straight line: x + 1/x = 1 TRUE OR FALSE
A block of inertia m sits on a smooth surface. A light string is attached to it and placed over a solid pulley of inertia 3 m and radius R, and a ball of inertia m is attached to the free end of the string. If there is no slippage between string and pulley, determine the magnitude of theā€¦
A body of mass m is moving vertically downward from rest in a fluid that exerts a resistance force of magnitude kv on the body, where k is a positive constant and v is the speed of the body. The terminal speed of the body is:
A ball with mass is tied on a light string which passes through a tube in the smooth table. The ball has an initial speed vo and moving circularly with radius ro. Then pulling the string to make the radius to r1. The speed of the ball is:
The ā€¦ā€¦ā€¦lens focuses light beam in its focal point. A) longitudinal B) converging C) diverging D) plane
A railway truck on a level,straight track is initially at rest.The truck is 2 marks given a quick, horizontal push by an engine so that it now rolls along the track. railway truck push from engi 4.3ms The engine is in contact with the truck for a time T= 0.54 s and the initial speed of theā€¦
Consider a charge of q1 Ī¼C 7 fixed with a site near another charge of q2 Ī¼C 6. Evaluate the potential energy of q2, when the distance of q2 is 4 cm from charge q1?
Two children are sliding down a snowy hill which is inclined by 49.3 degrees with respect to horizontal. One has a rough sled which has a coefficient of kinetic friction between it and the snow of Ī¼k = 0.328; the other has a slippery sled which has a coefficient of kinetic friction between itā€¦
a mass oscillates on a spring with amplitude A and maximum velocity Vmax. The period of the oscillation is:
why E?
A 45 N horizontal force pushes on a 3.7 kg mass resting on a horizontal surface. The surface exerts a friction force of 21 N against the motion. The acceleration of the 3.7 kg mass is ____ m/s^2.