Answers edited by Yonas Yohannes

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• Who gained control of the Congo region after King Leopold ll was deposed for human rights violations?
  
• Constructing the angle 75°?
  
• How do you use the rational roots theorem to find all possible zeros of `p(x)= 2x^5+7x^3+6x^2-15`?
  
• 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?
  
• How do you use the amplitude and period to graph `f(x) = 3 Sin x + 4 Cos x`?
  
• 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?
  
• What is the dot product of `<-7,2,-1 >` and `<0,8,-27 >`?
  
• What is the electron dot structure for `PCl_3`?
  
• 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?
  
• 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?
  
• Question #b3589
  
• If a current of `4 A` passing through a circuit generates `80 W` of power, what is the resistance of the circuit?
  
• 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?
  
• 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?
  
• How do you solve the system of equations `8x-5y = -17` and `-2x + y = 6`?
  
• 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?
  
• 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?
  
• How do you divide `(4-8i)/(9+i)` in trigonometric form?
  
• What is the vertex form of `y=4x^2-17x+60`?
  
• How does Calcium Hypochlorite disinfect water?
  
• 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 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?
  
• 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?
  
• How do you graph the circle `x^2+y^2+3x+4y+4=0`?
  
• 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?
  
• 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 long divide `(x^3 + 9x^2 + 7x + 3 ) div (x+2)`?
  
• What is meant by a linearly independent set of vectors in `RR^n`? Explain?
  
• 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)?
  
• 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?
  
• 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?
  
• Find the four digit numbers `abcd` that satisfy, `2(abcd)+1000=dcba`?
  
• What is the net area between `f(x) = cscx -xsinx` and the x-axis over `x in [pi/6, (5pi)/8 ]`?
  
• 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?
  
• 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?
  
• 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)?
  
• 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?
  
• 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 ]`?
  
• What formula is used to calculate the age of the universe?
  
• A triangle has corners at `(8 , 4 )`, ( 4 , 3)`, and`( 6 , 5 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors?
  
• What are the extrema of `f(x)=f(x)= x^2 -4x +3`?
  
• What is meant by a linearly independent set of vectors in `RR^n`? Explain?
  
• 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 find the slope and intercept of `f(x)=-4x-8`?
  
• How does a star life cycle begin?
  
• 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`?
  
• How do you find all the real and complex roots of `x^5 - 32 = 0`?
  
• 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?
  
• Why did Charles V summon Martin Luther to trial?
  
• How do you find the inverse of `f(x)=log(x+15)`?
  
• 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`?
  
• 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?
  
• How do you solve `10 + x - 2x^2 <0`? c) `-2 + 7x - 3x^2<0`
  
• What does alpha and beta signify in portfolio analysis?
  
• How do you graph `(x^3-6x+5)/(x^2-3)`?
  
• 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?
  
• What is the orthocenter of a triangle with corners at `(4 ,1 )`, `(7 ,4 )`, and (3 ,6 )#?
  
• What is the orthocenter of the triangle formed by the intersection of the lines `x = 4` , `y = 1/2x + 7` , and`y = -x + 1`?
  
• Who are the Allied Powers? What is their war plan? Why are they aligned politically? What are their goals in the war?
  
• What reforms did Mao Tse Tung make?
  
• 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?
  
• What is the arc length of the polar curve `f(theta) = cos(3theta-pi/2) +thetacsc(-theta)` over `theta in [pi/12, pi/8]`?
  
• How do you differentiate `f(x)= (3x^2-4 )/ (3x +1 )` using the quotient rule?