Answers edited by ali ergin

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• A projectile is shot at a velocity of #3 m/s# and an angle of #pi/8 #. What is the projectile's peak height?
  
• What is the projection of #<3, -6, 2># onto #<0, 1, 3>#?
  
• What is the component form of a vector with an initial point of (-2, 3) and a terminal point of (-4, 7)?
  
• If a projectile is shot at a velocity of #52 m/s# and an angle of #pi/3#, how far will the projectile travel before landing?
  
• How can I calculate the focal point of concave mirror?
  
• The force applied against a moving object travelling on a linear path is given by #F(x)= 4x + 4#. How much work would it take to move the object over #x in [ 1, 5] #?
  
• How fast will an object with a mass of #16 kg# accelerate if a force of #64 N# is constantly applied to it?
  
• A charge of #-2 C# is at the origin. How much energy would be applied to or released from a # 4 C# charge if it is moved from # (7 ,5 ) # to #(9 ,-2 ) #?
  
• How much work would it take to push a # 8 kg # weight up a # 3 m # plane that is at an incline of # pi / 4 #?
  
• Two charges of # -4 C # and # -2 C# are positioned on a line at points # -1 # and # 4 #, respectively. What is the net force on a charge of # -4 C# at # 1 #?
  
• How do you integrate #int 1/sqrt(x^2-4x+13)dx# using trigonometric substitution?
  
• If a projectile is shot at an angle of #(7pi)/12# and at a velocity of #1 m/s#, when will it reach its maximum height?
  
• If a projectile is shot at an angle of #pi/6# and at a velocity of #18 m/s#, when will it reach its maximum height??
  
• How do you evaluate #log_4 27#?
  
• What is the average speed of an object that is not moving at #t=0# and accelerates at a rate of #a(t) =10-2t# on #t in [3, 5]#?
  
• What is the integral of #int sin^3 (x)cos^3 (x) dx#?
  
• A spring with a constant of #9 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #2 kg# and speed of #7 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?
  
• What is the distance between the following polar coordinates?: # (7,(5pi)/4), (2,(9pi)/8) #
  
• A block of silver has a length of 0.93 m, a width of 60 mm and a height of 12 cm. How do you find the total resistance of the block if it is placed in a circuit such that the current runs along its length? Along its height? Along its width?
  
• What is the slope of the line passing through the following points: # (2,6) ; (5,2)#?
  
• How do you evaluate the integral of #int (x-1)/(x^2+3x+2) dx# from 0 to 1?
  
• What is the cross product of #<3 ,1 ,-6 ># and #<-2 ,-4 , 8 >#?
  
• What is the cross product of #<-3, -1, 8 ># and #<-1, 4, -9 >#?
  
• Objects A and B are at the origin. If object A moves to #(-2 ,8 )# and object B moves to #(-5 ,-6 )# over #4 s#, what is the relative velocity of object B from the perspective of object A?
  
• How do you simplify #sqrt77*sqrt33#?
  
• Objects A and B are at the origin. If object A moves to #(-7 ,-9 )# and object B moves to #(1 ,-1 )# over #8 s#, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.
  
• Two charges of # -1 C # and # 5 C # are at points # (1,-5,3 ) # and # ( -3 , 9, 1 )#, respectively. Assuming that both coordinates are in meters, what is the force between the two points?
  
• Question #50cca
  
• How do you find the inverse of #y=3x^2-2# and is it a function?
  
• What is the angular momentum of a rod with a mass of #2 kg# and length of #6 m# that is spinning around its center at #3 Hz#?
  
• How much work would it take to push a # 9 kg # weight up a # 2 m # plane that is at an incline of # pi / 6 #?
  
• How do you find the definite integral of #int (1-2x-3x^2)dx# from #[0,2]#?
  
• A baseball is thrown straight up at 15 m/s. How high will it go?
  
• The velocity of an object with a mass of #3 kg# is given by #v(t)= sin 4 t + cos 3 t #. What is the impulse applied to the object at #t= pi /6 #?
  
• Two charges of # 9 C # and # 2 C# are positioned on a line at points # 6 # and # -4 #, respectively. What is the net force on a charge of # 3 C# at # 2 #?
  
• An object, previously at rest, slides #5 m# down a ramp, with an incline of #(3pi)/8 #, and then slides horizontally on the floor for another #12 m#. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?
  
• A spring with a constant of #6 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #1 kg# and speed of #4 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?
  
• What is the derivative of #x*x^(1/2)#?
  
• An object, previously at rest, slides #9 m# down a ramp, with an incline of #(pi)/6 #, and then slides horizontally on the floor for another #24 m#. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?
  
• A train traveled 325 miles in 5 hours. What was the train's average rate of speed in miles per hour?
  
• A block weighing #4 kg# is on a plane with an incline of #(pi)/2# and friction coefficient of #4/5#. How much force, if any, is necessary to keep the block from sliding down?
  
• What is the dot product of #<-1,4,7># and #<9,-7,5 > #?
  
• What is the average speed of an object that is still at #t=0# and accelerates at a rate of #a(t) =2t^2-3t-3# from #t in [2, 4]#?
  
• A charge of #16 C# is passing through points A and B on a circuit. If the charge's electric potential changes from #38 J# to #12 J#, what is the voltage between points A and B?
  
• A projectile is shot from the ground at a velocity of #1 m/s# at an angle of #(5pi)/12#. How long will it take for the projectile to land?
  
• A balanced lever has two weights on it, the first with mass #15 kg # and the second with mass #14 kg#. If the first weight is # 7 m# from the fulcrum, how far is the second weight from the fulcrum?
  
• How do you solve #Log 378 = x#?
  
• How do you evaluate the integral of #int (dt)/(t-4)^2# from 1 to 5?
  
• How do you find the slope of (-2, 5) and (-2, 8)?
  
• What is the projection of #<5,0,-2 ># onto #<1,-1,0 >#?
  
• What is the projection of #<-2,3,7 ># onto #<1,6,1 >#?
  
• What is the distance between #(1 ,( pi)/4 )# and #(-4 , ( 3 pi )/2 )#?
  
• How do you integrate #int (x+1)/(x^2 + 6x)# using partial fractions?
  
• If an object with a mass of #5 kg # changes speed from #12m/s# to # 8m/s#, by how much does its kinetic energy change?
  
• How do you solve # 5x^3 - 320 x = 0#?
  
• An object is thrown vertically at a height of #14 m# at #1 m/s#. How long will it take for the object to hit the ground?
  
• Objects A and B are at the origin. If object A moves to #(9 ,-7 )# and object B moves to #(-8 ,6 )# over #3 s#, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.
  
• A ball with a mass of #9 kg# moving at #15 m/s# hits a still ball with a mass of #2 kg#. If the first ball stops moving, how fast is the second ball moving?
  
• If #A = {2,-7 ,5}#, #B = {5,-7,4}# and #C = A - B#, what is the angle between A and C?
  
• A balanced lever has two weights on it, the first with mass #72 kg # and the second with mass #9 kg#. If the first weight is # 2 m# from the fulcrum, how far is the second weight from the fulcrum?
  
• An object, previously at rest, slides #15 m# down a ramp, with an incline of #pi/3 #, and then slides horizontally on the floor for another #12 m#. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?
  
• If #A = <-6 ,2 ,5 >#, #B = <-8 ,3 ,4 ># and #C=A-B#, what is the angle between A and C?
  
• Objects A and B are at the origin. If object A moves to #(5 ,-7 )# and object B moves to #(7 ,4 )# over #3 s#, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.
  
• An object with a mass of # 3 kg# is traveling in a circular path of a radius of #15 m#. If the object's angular velocity changes from # 5 Hz# to # 3Hz# in # 5 s#, what torque was applied to the object?
  
• A ball with a mass of # 5 kg# is rolling at #8 m/s# and elastically collides with a resting ball with a mass of #2 kg#. What are the post-collision velocities of the balls?
  
• How do you solve the following system: #6x+2y=-4, 3x - 4y = -10#?
  
• (a) With what speed must a ball be thrown vertically from ground level to rise to a maximum height of ? (b) How long will it be in the air ?
  
• An object with a mass of # 8 kg# is traveling in a circular path of a radius of #12 m#. If the object's angular velocity changes from # 15 Hz# to # 7 Hz# in # 6 s#, what torque was applied to the object?
  
• Two charges of # -2 C # and # 3 C# are positioned on a line at points # 5 # and # -6 #, respectively. What is the net force on a charge of # -1 C# at # 0 #?
  
• How do you solve #sqrt(3x)+8=x+2#?
  
• Objects A and B are at the origin. If object A moves to #(3 ,-4 )# and object B moves to #(2 ,-6 )# over #4 s#, what is the relative velocity of object B from the perspective of object A?
  
• How do you normalize #(- 7 i -j +25k)#?
  
• A ball with a mass of #2 kg# is rolling at #9 m/s# and elastically collides with a resting ball with a mass of #1 kg#. What are the post-collision velocities of the balls?
  
• Objects A and B are at the origin. If object A moves to #(6 ,-2 )# and object B moves to #(2 ,9 )# over #5 s#, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.
  
• What is the cross product of #<-3,0, 2># and #<-1, -2, 9 >#?
  
• Objects A and B are at the origin. If object A moves to #(8 ,5 )# and object B moves to #(9 ,-2 )# over #2 s#, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.
  
• A ball with a mass of #480 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #16 (kg)/s^2# and was compressed by #4/5 m# when the ball was released. How high will the ball go?
  
• An object with a mass of #4 kg# is hanging from a spring with a constant of #8 (kg)/s^2#. If the spring is stretched by #8 m#, what is the net force on the object?
  
• The velocity of an object with a mass of #2 kg# is given by #v(t)= sin 5 t + cos 6 t #. What is the impulse applied to the object at #t= pi /4 #?
  
• A ball with a mass of # 5 kg# is rolling at #3 m/s# and elastically collides with a resting ball with a mass of #2 kg#. What are the post-collision velocities of the balls?
  
• Two charges of # 2 C # and # 8 C# are positioned on a line at points # -3 # and # 6 #, respectively. What is the net force on a charge of # -3 C# at # -2 #?
  
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