Answers created by Narad T.

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• How do I graph the hyperbola with the equation #4x^2−y^2+4y−20=0?#?
  
• Solve the following systems of simultaneous equations using the inverse matrix of Gauss Jordan X1+2x2+3x3=3? 2x1+4x2+5x3=4? 3x1+5x2+6x3=8?
  
• How do you divide #(-18a+3a^3+9+6a^2)div(-3+3a)# using synthetic division?
  
• How do you evaluate # e^( ( pi)/4 i) - e^( ( 11 pi)/8 i)# using trigonometric functions?
  
• How to express this series in summation notation? 27+18+12+8
  
• A balloon filled with a lighter gas occupies a volume of 1500 cu metre. Its mass (mass of material of balloon + mass of gas in it) is 1650 kg. Its tied with a rope and floating in air of density 1.3 kg/cubic metre. The pull on the rope is ?
  
• A ball with a mass of #1 kg # and velocity of #2 m/s# collides with a second ball with a mass of #3 kg# and velocity of #- 4 m/s#. If #20%# of the kinetic energy is lost, what are the final velocities of the balls?
  
• Prove that the diagonals of a rhombus are at right angles when O is origin c ( α ,β) B ( α + h ,β) A (h, 0)?
  
• An object with a mass of #12 kg# is on a surface with a kinetic friction coefficient of # 2 #. How much force is necessary to accelerate the object horizontally at # 3 m/s^2#?
  
• How do you find the dimensions of the rectangle with largest area that can be inscribed in a semicircle of radius #r# ?
  
• How do you find the domain and range of #sqrt ( x- (3x^2))#?
  
• If an object is moving at #50 m/s# over a surface with a kinetic friction coefficient of #u_k=2 /g#, how far will the object continue to move?
  
• Find the value of c and state the amplitude and period of f (?)
  
• How much power is produced if a voltage of #7 V# is applied to a circuit with a resistance of #98 Omega#?
  
• How do you evaluate #\frac{4x^{4}-5x^{2}+2x-10}{2x-3}#?
  
• A projectile is shot from the ground at a velocity of #27 m/s# at an angle of #(5pi)/12#. How long will it take for the projectile to land?
  
• A box with an initial speed of #4 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #5/4 # and an incline of #(3 pi )/4 #. How far along the ramp will the box go?
  
• Two Train speeds?
  
• If #z+1/z=1#, find #z^3#, and then #z^1000+1/z^1000#?
  
• An aeroplane flying horizontally 750m above the ground lo an elevation of 60° . After 5 second the elevation is observed 30° . What is the speed of the aeroplane in km per hour?
  
• A force 6i+3j+k displaces an object from A(0,3,2) to B(5,1,6) what is the work done?
  
• A particle is projected at a definite angle #alpha# to the horizontal passes through the points #(a,b)# and #(b,a)#, referred to horizontal and vertical axes through the point of projection?
  
• What is the frequency of an x-ray that has a wavelength of #1.5*10^-10# m?
  
• The sum of two vector A and B is 5i+j and their difference is 3i-2j the vector then is?
  
• When 0.5 kg of aluminum is heated using a 1.5kw heater, the mass of aluminum changes completely into a liquid in 2.1 minutes. During this time its temperature remains constant at 660 Celsius. What is the specific latent heat of fusion of aluminum?
  
• How do you find #abs( 5+12i )#?
  
• A projectile is shot at an angle of #pi/8 # and a velocity of # 7 m/s#. How far away will the projectile land?
  
• Can someone solve this? IGCSE MATH, SEQUENCES QUESTION Book answer= (n-8)
  
• A container has a volume of #6 L# and holds #5 mol# of gas. If the container is compressed such that its new volume is #12 L#, how many moles of gas must be released to maintain a constant temperature and pressure?
  
• How much work would it take to push a # 2 kg # weight up a # 7 m # plane that is at an incline of # (5pi) / 12 #?
  
• How do you solve #13^(3x)-1=91#?
  
• Joy is preparing 13 liters of a 20% saline solution. She only has 30% and 10% solution in her lab. How many liters of the 30% and how many liters of the 10% should she mix to make the 20% solution?
  
• How do you find the center and radius for #x^2+y^2-6x-6y+14=0#?
  
• How do you graph #\frac { ( x - 3) ^ { 2} } { 9} + \frac { ( y - 5) ^ { 2} } { 25} = 1#?
  
• An ellipsoid has radii with lengths of #3 #, #6 #, and #5 #. A portion the size of a hemisphere with a radius of #3 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?
  
• Two vans leave a campground at the same time. One is traveling north at a speed that is 10 mi/hr faster than the other, which is traveling south. After 2.5 hours, the vans are 255 miles apart. What is the speed iof the van traveling south?
  
• How do you express #(x^2-2x+1)/(x-2)^3# in partial fractions?
  
• The rotational inertia of a disk about its axis is 0.70kgm2. When a 2kg mass is added to its rim ,0.40m what will be its rotational inertia?
  
• A particle is moving in a straight line.its displacement at time t is given by s (in m) =-4t^2+2t,then its velocity and acceleration at time t=1/2 second are..???
  
• Trig expression help?
  
• How do you solve #|-4x + 10| ≤ 46#?
  
• How do you use the ratio test to test the convergence of the series #∑(n!)/(n^n)# from n=1 to infinity?
  
• What is the kinetic energy of a #6 kg# object moving at #4/3 m/s#?
  
• How do I find the indefinite integral of #sin(3x)cos(3x)#?
  
• When the length of simple pendulum is dubuled ; find the ratio of new frequency to old frequency?
  
• What are the asymptote(s) and hole(s), if any, of # f(x) = tanx*cscx#?
  
• How do you solve #(2x)/(x-5)>=3#?
  
• What is the equation of a parabola with a focus at #(3, 2)# and a directrix at #y=-4#?
  
• How do I determine the vector projection of a vector?
  
• How can you use trigonometric functions to simplify # 15 e^( ( 17 pi)/12 i ) # into a non-exponential complex number?
  
• How do you solve #3^(x+4)=2^(1-3x)#?
  
• A container has a volume of #12 L# and holds #8 mol# of gas. If the container is compressed such that its new volume is #4 L#, how many moles of gas must be released from the container to maintain a constant temperature and pressure?
  
• Places A and B are 80 km apart from each other.A car starts from A and other from B at the same time.If they move in the same direction,they meet in 8 hours and if they move in opposite direction they meet in 1 hour and 20 minutes.find speed ?
  
• How do you solve #5x - 5y + 10z = -11#, #10x + 5y - 5z = 1# and #15x - 15y -10z = -1# using matrices?
  
• A model train with a mass of #9 kg# is moving along a track at #18 (cm)/s#. If the curvature of the track changes from a radius of #36 cm# to #42 cm#, by how much must the centripetal force applied by the tracks change?
  
• What is the period of #f(t)=sin( t / 30 )+ cos( (t)/ 42) #?
  
• If #2costheta=x+1/x# then prove that the value of the #x^n+1/(x^n), ninN# is #2cosntheta#?
  
• How do you find the domain and range of #f(x) = ln(-x + 5) + 8#?
  
• How do you verify #tanh(x + y) = (tanh x + tanh y)/(1 + tanh x + tanh y)#?
  
• A balloon is being filled with helium at the rate if #4"ft"^3/"min"#. What is the rate, in #"ft"^2/"min"#, at which the surface area is increasing when the volume is #(32pi)/3"ft"^3#?
  
• A ball with a mass of #3 kg# moving at #8 m/s# hits a still ball with a mass of #4 kg#. If the first ball stops moving, how fast is the second ball moving?
  
• How do you graph and list the amplitude, period, phase shift for #y=2cos4x#?
  
• How do you find the domain and range of #tan^-1(x)#?
  
• How much power is produced if a voltage of #2 V# is applied to a circuit with a resistance of #10 Omega#?
  
• The inverse of symmetric matrix is??
  
• How do you take the derivative of #tan^-1(x)#?
  
• How do you cube a matrix #([2, -1], [3, 1])#?
  
• How to find the final form of augmented matrix when solving for the inverse of this system of equations? #2x+3y=4# #4x+5y=5#
  
• How do you find all the critical points to graph #(x + 2)^2/4 - (y - 5)^2/25 = 1 # including vertices, foci and asymptotes?
  
• A sample of gas occupies 10.0 L at 100.0 torr and 27.0C. Calculate the pressure if the temperature is changed to 127C while the volume remains constant?(133torr)
  
• A ball with a mass of #9 kg # and velocity of #2 m/s# collides with a second ball with a mass of #3 kg# and velocity of #- 5 m/s#. If #10%# of the kinetic energy is lost, what are the final velocities of the balls?
  
• What is the projection of #(8i + 12j + 14k)# onto # (3i – 4j + 4k)#?
  
• How do you divide #(2x^4 -x^3 - 9x^2 - x + 5)/ (5x^2 - 2) # using polynomial long division?
  
• A container of rocks with a mass of 65 kilograms is is brought back from the Moon's surface where the acceleration due to gravity is 1.62 meters per second? What is the weight of the container of rocks on Earth's surface?
  
• How do you graph, find the intercepts and state the domain and range of #f(x)=1/2(2^x-8)#?
  
• If #xy+yz+zx=12-x^2=15-y^2=20-z^2# then #x+y+z=?#
  
• The price of a stock, A(x), over a 12-month period decreased and then increased according to the equation... ?
  
• Find curl F for the vector field at the given point. F(x, y, z) = x2zi − 2xzj + yzk; (7, −9, 3)?
  
• What is #int ln(2x)^2dx#?
  
• The curve with equation #y=x(3-x)^(1/2)# together with line segment OA.!) what are the coordinates of B and A; 2)what is the Area of the shaded region bounded by the line segment AO, x axis and the arc of AB curve?
  
• What is the frequency of #f(theta)= sin 24 t - cos 42 t #?
  
• Identify an equation in standard form for a hyperbola with center (0, 0), vertex (0, 7), and focus (0, 11). ?
  
• How do you find the standard form of the equation of the ellipse given the properties foci #(0,+-5)#, vertices #(0, +-8)#?
  
• A ball with a mass of #4 kg# moving at #3 m/s# hits a still ball with a mass of #26 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 unit vector that is normal to the plane containing #(3i + 4j - k)# and #(2i+ j - 3k)#?
  
• A mass of 0.2kg is whirled in a horizontal circle of radius 0.5m by a string inclined at 30° to the vertical. Calculate the tension in the string and the speed of the mass in the horizontal circle?
  
• How do you find the sum of the infinite geometric series 4/5+4/15+4/45...?
  
• How do you solve #log_x(1/256)=-4#?
  
• Using elementary row and coloumn transformation compute rank of following matrices: #((25,31,17,43),(75,94,53,132),(75,94,54,134),(25,32,20,48))# ?
  
• How do you find the amplitude, period, phase shift for #y=sin2(x+(3pi)/4)#?
  
• How do you find the center and radius for #x^2 - 3x + y^2 - 3y - 20 = 0#?
  
• If a projectile is shot at a velocity of #4 m/s# and an angle of #pi/6#, how far will the projectile travel before landing?
  
• What is #Cos(arcsin(5/13) - arccos(7/25))#?
  
• What is the correct option?
  
• How do you solve this system of equation: #x + 3y = 1 and - 3x - 3y = - 15#?
  
• How do you prove #(Sec x/Sin x)-(Sin x/Cos x)=Cot x#?
  
• What is the solution set of the equation #|3-2x| = 5#?
  
• Calculus Question?
  
• How do you find and classify local maxima, local minima, and all critical points of #f(x) = x^3+x^2-4x-4#?
  
• What is the residue of (2x^4+7x^3-3x^2-5x-9)÷(x+3)?
  
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