Answers edited by Harish Chandra Rajpoot

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• What is the distance between the following polar coordinates?: # (6,(19pi)/12), (3,(15pi)/8) #
  
• A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is #5 #, its base has sides of length #8 #, and its base has a corner with an angle of #(2 pi)/3 #. What is the pyramid's surface area?
  
• Three times a number increased by less than -62. What is the number?
  
• Find the centre,vertices foci,lengths of latera recta and the eccencivity of ellipse whose equation is? 49x²+144y²-196x-720y-668=0
  
• How do you find #int 1/sqrt(-x^2-4x)#?
  
• Two springs are in a series combination and are attached to a block of mass 'm' which is in equilibrium. Spring constants:k and k’ Extensions:x and x’ respectively. Find the force exerted by spring on the block?
  
• B) A force of 90 N is used to pull a truck 200 m along a horizontal floor. Determine the work done and the increase in K. E if there is no energy loss due to friction. ?
  
• Two charges of # 3 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 #?
  
• A solid disk, spinning counter-clockwise, has a mass of #5 kg# and a radius of #8 m#. If a point on the edge of the disk is moving at #6 m/s# in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?
  
• How do you integrate #int 1/sqrt(4x^2+16x+13) # using trigonometric substitution?
  
• How do you evaluate # log_16 57.2#?
  
• How do you solve the following linear system: # 2x+ 3y=-1 , 5x+y=8 #?
  
• A gear of radius 4 inches turns at 8 rpm. What is the linear velocity of a tooth of the gear in feet per minute to the nearest tenth?
  
• What is the slope and y-intercept of the line #x=2#?
  
• A ball with a mass of #5 kg# moving at #2 m/s# hits a still ball with a mass of #3 kg#. If the first ball stops moving, how fast is the second ball moving?
  
• Whats the answer to log(x-1) = -1 ?
  
• How do you solve #-3( x - 3) \geq 9- 3x#?
  
• What is the surface area of the solid created by revolving #f(x) =e^(4x)-x^2e^(2x) , x in [1,2]# around the x axis?
  
• How do you solve #cos^2x=3/4#? Which solution is correct?
  
• Solve the equation (2xy − 3)dx + (x 2 + 4y)dy = 0 given that y(2) = 5.??
  
• How about this?
  
• How do you solve: #x^3/2=125#?
  
• Please Help :) Lim (Ln(1+9X)+cos(4X)-1)/X X=0 ???
  
• How to find the standard form of the equation of the specified circle given that it Is tangent to line x+y =2 at point (4,-2) and the center is on the x-axis?
  
• How do you find the integral of #dx/(x(sqrt(3 + x^2)))#?
  
• How do you evaluate #(6\times 10^ { 3} ) \cdot ( 4.6\times 10^ { 5} ) \cdot ( 2\times 10^ { - 2} )#?
  
• A race car has a centripetal acceleration of 13.33 #m##/##s^2# as it goes around a curve. If the curve is a circle wilh radius 30 m, what is the speed of the car?
  
• If an object with a mass of #12 kg # changes speed from #3 m/s# to #1m/s#, by how much does its kinetic energy change?
  
• Eight drops of water.each radius 2mm are falling through air at a terminal velocity of 8cm/sec If they coalesce to form a single drop the terminal velocity of the combined drop will be?
  
• A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is #6 #, its base's sides have lengths of #5 #, and its base has a corner with an angle of #( pi)/6 #. What is the pyramid's surface area?
  
• How do you find the first and second derivative of #y=1/(1+e^x)#?
  
• A point moves in #x-y# plane according to #vec r=3cos(4t)veci +3(1-sin4t) vecj#. What is the distance travelled by the particle in 0.5 sec ?
  
• How do you multiply #\sqrt { 2} \cdot - 3\sqrt { 3}#?
  
• How do you find the cube root of #-125/2(1+sqrt3i)#?
  
• When working in decimal radians, how do you find sin^-1(-1/6)?
  
• What would the formula for the nth term be given 0.3, -0.06, 0.012, -0.0024, 0.00048, ...?
  
• How do you find the equation of the circle passing through (7,5) and (3,7), and with center on x-3y+3=0?
  
• The velocity of particle moving along a straight line increases according to the law#v=v_0+Kx# , where K is a positive constant,then options are below?
  
• How do you convert #(-4, 3pi)# from polar to cartesian coordinates?
  
• What is #int 1/(t^3sqrt( t^2 - 1))dt#?
  
• Cups A and B are cone shaped and have heights of #35 cm# and #21 cm# and openings with radii of #12 cm# and #11 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?
  
• How do you multiply #(4y + 8)/ (y^2 - 2y)*(y - 2)/(y+2)#?
  
• A 30 kg weight is positioned 2 m from a fulcrum. At what distance from the fulcrum must a 40 kg weight be positioned to keep the scale balanced?
  
• How do you solve #2b ^ { 2} - 20b - 5= 0#?
  
• How do solve the following linear system?: # y=-6x-9 , -x+3y=-5 #?
  
• How do you graph and label the vertex and axis of symmetry of #y=2(x+1)^2+1#?
  
• Find the standard form of the equation of the parabola with the given characteristics?
  
• If the half-life of iodine-131 is 8 days, how much of a 5-g sample is left after 32 days?
  
• How do you determine circle, parabola, ellipse, or hyperbola from equation #4x^2 + 9y^2 - 16x +18y -11 = 0#?
  
• What is the orthocenter of a triangle with corners at #(2 ,8 )#, #(3 ,4 )#, and (6 ,3 )#?
  
• How do you find the implicit differentiation of #1+lnxy=3^(x-y)#?
  
• Two circles have the following equations #(x -1 )^2+(y -4 )^2= 36 # and #(x +5 )^2+(y -7 )^2= 49 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?
  
• How do you solve #8^{3x}=154#?
  
• How do you divide #( -7i-5) / ( 9 i -2 )# in trigonometric form?
  
• A 0.78 kg block is attached to a horizontal spring of force constant 256 kg/s2, resting atop a frictionless surface. The block is pulled back 30 cm and then released. What is the period of the oscillations of the block? Maximum speed of the oscillation?
  
• Sally’ s tomato plants grow 11 tomatoes each week. Sally has 5 tomatoes. How many weeks will it take to grow 38 tomatoes?
  
• Is #f(x)=cos^2x+sin2x# increasing or decreasing at #x=pi/6#?
  
• What is the surface area of a 7cm cube?
  
• How do you find the derivative of f(x) = -2sqrt(x) by the limit process?
  
• Solve the following differential equation X(dy/dx)+2y=(x^2)logx?
  
• What is the derivative of #f(x) = (x)(6^(-2x))#?
  
• A stack of bricks has 61 bricks in the bottom layer, 58 bricks in the second layer, 55 bricks in the third layer,and so on until there are 10 bricks in the last layer. How many bricks are there all together?
  
• An object with a mass of #14 kg# is on a plane with an incline of # -(5 pi)/12 #. If it takes #12 N# to start pushing the object down the plane and #7 N# to keep pushing it, what are the coefficients of static and kinetic friction?
  
• At what time after 7:00 pm will the hands of the clock be opposite to each other?
  
• Why does the location of the center of gravity depend on how an object’s mass is distributed?
  
• What are the critical values of #f(x)=( (x-2)(x+3))/(x^2#?
  
• Given #int e^x(tanx + 1 )secx dx = e^xf(x)+C#.Write f(x)satisfying above.How can you solve it ?
  
• Two cars are 175m apart, facing each other. At that instant, the first car is traveling at 9.0 km/h [W] and is accelerating at 3.6m/s^2 [W]. The second car is traveling at a constant velocity of 21.5 m/s [E].?
  
• How do you find the coordinates of the vertices, foci, and the equation of the asymptotes for the hyperbola #(y-4)^2/16-(x+2)^2/9=1#?
  
• What is the slope of the tangent line of # (xy^2-3xy)/(sqrt(yx)-xy) =C #, where C is an arbitrary constant, at #(2,5)#?
  
• Solve the inequality 30/x-1 < x+2?
  
• How do you identify the important parts of #y = x^2 − 36# to graph it?
  
• How do you find all solutions to sin (2x + 1) = 0.2?
  
• How do you solve #cos^2 theta=2cos^2 (theta/2)# in the domain #0<=theta<=360#?
  
• The current through a wire depends on the time as, i=(10+4t) . Here, i is in ampere t in seconds. find the charge crossed through a section in time interval between t=0 to t=10 sec ?
  
• If you say 5000 at 85% interest rate for 10 years compounded annually how much will you have at the end of the 10th year?
  
• A ball with a mass of #5kg# moving at #2 m/s# hits a still ball with a mass of #9 kg#. If the first ball stops moving, how fast is the second ball moving?
  
• How do you simplify #log_3 5 + 5log_3 2#?
  
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