Answers edited by Yonas Yohannes

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• How do you differentiate #f(x)= (3x^2-4 )/ (3x +1 )# using the quotient rule?
  
• A line segment has endpoints at #(4 ,9 )# and #(5 ,2)#. If the line segment is rotated about the origin by #pi #, translated vertically by #-4 #, and reflected about the x-axis, what will the line segment's new endpoints be?
  
• How do you find all the real and complex roots of #x^5 - 32 = 0#?
  
• If a #12 kg# object is constantly accelerated from #0m/s# to #4 m/s# over 7 s, how much power musy be applied at #t=1 #?
  
• What is the vertex form of #y=4x^2-17x+60 #?
  
• What is meant by a linearly independent set of vectors in #RR^n#? Explain?
  
• 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?
  
• How does Calcium Hypochlorite disinfect water?
  
• A ball with a mass of #9 kg# moving at #3 m/s# hits a still ball with a mass of #21 kg#. If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?
  
• What is the net area between #f(x) = cscx -xsinx# and the x-axis over #x in [pi/6, (5pi)/8 ]#?
  
• Who gained control of the Congo region after King Leopold ll was deposed for human rights violations?
  
• How do you find all the real and complex roots of #x^5 - 32 = 0#?
  
• What is meant by a linearly independent set of vectors in #RR^n#? Explain?
  
• What is the dot product of #<-7,2,-1 ># and #<0,8,-27 >#?
  
• Molly kicks a soccer ball into the air with an initial velocity of 15 m/s. It lands 20 meters from where she kicked it. At what angle did Molly launch the ball?
  
• How do you use the amplitude and period to graph #f(x) = 3 Sin x + 4 Cos x#?
  
• What are the extrema of #f(x)=f(x)= x^2 -4x +3#?
  
• What does alpha and beta signify in portfolio analysis?
  
• Who are the Allied Powers? What is their war plan? Why are they aligned politically? What are their goals in the war?
  
• How much work would it take to push a # 1 kg # weight up a # 9 m # plane that is at an incline of # (5pi) / 12 #?
  
• A triangle has corners at #(8 , 4 )#, ( 4 , 3)#, and #( 6 , 5 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors?
  
• How do you divide # (4-8i)/(9+i) # in trigonometric form?
  
• If a projectile is shot at an angle of #pi/3# and at a velocity of #6 m/s#, when will it reach its maximum height??
  
• A cone has a height of #6 cm# and its base has a radius of #6 cm#. If the cone is horizontally cut into two segments #3 cm# from the base, what would the surface area of the bottom segment be?
  
• A triangle has corners A, B, and C located at #(7 ,3 )#, #(4 ,8 )#, and #(3 , 4 )#, respectively. What are the endpoints and length of the altitude going through corner C?
  
• If a current of #4 A# passing through a circuit generates #80 W# of power, what is the resistance of the circuit?
  
• In an election contested by two parties, Party D secured 12% of the total votes more than Party R. If party R got 132,000 votes, by how many votes did it lose the election?
  
• Show that all Polygonal sequences generated by the Series of Arithmetic sequence with common difference #d, d in ZZ# are polygonal sequences that can be generated by #a_n = an^2+bn+c#?
  
• How do you graph #(x^3-6x+5)/(x^2-3)#?
  
• Constructing the angle 75°?
  
• What is the arc length of the polar curve #f(theta) = cos(3theta-pi/2) +thetacsc(-theta) # over #theta in [pi/12, pi/8] #?
  
• The force applied against an object moving horizontally on a linear path is described by #F(x)=x^3+ 3 #. By how much does the object's kinetic energy change as the object moves from # x in [ 3, 5 ]#?
  
• How do you solve the system of equations #8x-5y = -17# and #-2x + y = 6#?
  
• How do you solve # 10 + x - 2x^2 <0#? c) #-2 + 7x - 3x^2<0#
  
• How do you find the slope and intercept of # f(x)=-4x-8#?
  
• What is the electron dot structure for #PCl_3#?
  
• A triangle has corners at #(-3 ,5 )#, #(7 ,6 )#, and #(1 ,-4 )#. If the triangle is dilated by a factor of #2/3 # about point #(-3 ,4 ), how far will its centroid move?
  
• What is the orthocenter of a triangle with corners at #(4 ,1 )#, #(7 ,4 )#, and (3 ,6 )#?
  
• The base of a triangular pyramid is a triangle with corners at #(8 ,5 )#, #(2 ,7 )#, and #(3 ,1 )#. If the pyramid has a height of #8 #, what is the pyramid's volume?
  
• A triangle has vertices A, B, and C. Vertex A has an angle of #pi/12 #, vertex B has an angle of #pi/12 #, and the triangle's area is #8 #. What is the area of the triangle's incircle?
  
• What reforms did Mao Tse Tung make?
  
• A line segment has endpoints at #(5 ,9 )# and #(8 ,7 )#. If the line segment is rotated about the origin by #( pi)/2 #, translated vertically by #-8 #, and reflected about the y-axis, what will the line segment's new endpoints be?
  
• An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= < 6 N , -2 N># and the second is #F_2 = < -3 N, 3 N>#. What is the object's rate and direction of acceleration?
  
• A cone has a height of #8 cm# and its base has a radius of #6 cm#. If the cone is horizontally cut into two segments #4 cm# from the base, what would the surface area of the bottom segment be?
  
• Let #a_n# be a sequence given by: #{1, 6, 15, 28, 45,66,..., f(n)}#. Show that the generating function #f(n)# is of the form # an^2 + bn + c#. Find the formula by computing the coefficients #a, b, c#?
  
• How do you long divide # (x^3 + 9x^2 + 7x + 3 ) div (x+2) #?
  
• What is the orthocenter of the triangle formed by the intersection of the lines #x = 4# , #y = 1/2x + 7# , and# y = -x + 1#?
  
• A line segment with endpoints at #(-1 , 2 )# and #(-4, 1 )# is rotated clockwise by #pi #. What are the new endpoints of the line segment?
  
• An object with a mass of #4 g# is dropped into #650 mL# of water at #0^@C#. If the object cools by #12 ^@C# and the water warms by #30 ^@C#, what is the specific heat of the material that the object is made of?
  
• Question #b3589
  
• An object with a mass of # 25 kg# is lying still on a surface and is compressing a horizontal spring by #5/2 m#. If the spring's constant is # 4 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?
  
• An electron is released from rest in a uniform electric of magnitude 2.00×104 N/C. Calculate the acceleration of the electron (Ignore gravitation)?
  
• How do you use the rational roots theorem to find all possible zeros of # p(x)= 2x^5+7x^3+6x^2-15#?
  
• Let X and Y have joint density given by f(x,y) = 6(1-y) for 0 ≤ x ≤ y ≤ 1. What is Cov(X,Y)?
  
• Some very hot rocks have a temperature of #420 ^o C# and a specific heat of #210 J/(Kg*K)#. The rocks are bathed in #45 L# of boiling water. If the heat of the rocks completely vaporizes the water, what is the minimum combined mass of the rocks?
  
• Two rhombuses have sides with lengths of #2 #. If one rhombus has a corner with an angle of #pi/3 # and the other has a corner with an angle of #(5pi)/8 #, what is the difference between the areas of the rhombuses?
  
• Curtis wants to build a model of a 180-meter tall building. He will be using a scale of 1.5 centimeters = 3.5 meters. How tall will the model be?
  
• Why did Charles V summon Martin Luther to trial?
  
• How do you graph the circle #x^2+y^2+3x+4y+4=0#?
  
• How do you find the inverse of # f(x)=log(x+15)#?
  
• How does a star life cycle begin?
  
• A line passes through #(5 ,0 )# and #(7 ,3 )#. A second line passes through #(3 ,6 )#. What is one other point that the second line may pass through if it is parallel to the first line?
  
• What formula is used to calculate the age of the universe?
  
• Find the four digit numbers #abcd# that satisfy, #2(abcd)+1000=dcba#?
  
• Two corners of an isosceles triangle are at #(4 ,9 )# and #(9 ,3 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?