Answers edited by Harish Chandra Rajpoot

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• What is the derivative of #f(x) = (x)(6^(-2x))#?
  
• How do you find the first and second derivative of #y=1/(1+e^x)#?
  
• 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 #cos^2 theta=2cos^2 (theta/2)# in the domain #0<=theta<=360#?
  
• 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?
  
• When working in decimal radians, how do you find sin^-1(-1/6)?
  
• How do you simplify #log_3 5 + 5log_3 2#?
  
• Find the centre,vertices foci,lengths of latera recta and the eccencivity of ellipse whose equation is? 49x²+144y²-196x-720y-668=0
  
• 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 #?
  
• 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 evaluate # log_16 57.2#?
  
• 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?
  
• Given #int e^x(tanx + 1 )secx dx = e^xf(x)+C#.Write f(x)satisfying above.How can you solve it ?
  
• 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?
  
• How do you solve: #x^3/2=125#?
  
• What are the critical values of #f(x)=( (x-2)(x+3))/(x^2#?
  
• 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 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?
  
• What is the distance between the following polar coordinates?: # (6,(19pi)/12), (3,(15pi)/8) #
  
• 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 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?
  
• How do you find the equation of the circle passing through (7,5) and (3,7), and with center on x-3y+3=0?
  
• Find the standard form of the equation of the parabola with the given characteristics?
  
• 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?
  
• 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?
  
• 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 graph and label the vertex and axis of symmetry of #y=2(x+1)^2+1#?
  
• How do you find the cube root of #-125/2(1+sqrt3i)#?
  
• How do you divide #( -7i-5) / ( 9 i -2 )# in trigonometric form?
  
• How do you find all solutions to sin (2x + 1) = 0.2?
  
• How do you convert #(-4, 3pi)# from polar to cartesian coordinates?
  
• How do you solve the following linear system: # 2x+ 3y=-1 , 5x+y=8 #?
  
• What is #int 1/(t^3sqrt( t^2 - 1))dt#?
  
• Solve the inequality 30/x-1 < x+2?
  
• How do you solve #-3( x - 3) \geq 9- 3x#?
  
• How do you identify the important parts of #y = x^2 − 36# to graph it?
  
• 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. ?
  
• How about this?
  
• 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#?
  
• 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 ?
  
• How do you determine circle, parabola, ellipse, or hyperbola from equation #4x^2 + 9y^2 - 16x +18y -11 = 0#?
  
• 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 surface area of a 7cm cube?
  
• How do you integrate #int 1/sqrt(4x^2+16x+13) # using trigonometric substitution?
  
• Three times a number increased by less than -62. What is the number?
  
• 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?
  
• 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)#?
  
• 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?
  
• 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?
  
• How do solve the following linear system?: # y=-6x-9 , -x+3y=-5 #?
  
• 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 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?
  
• 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?
  
• Solve the equation (2xy − 3)dx + (x 2 + 4y)dy = 0 given that y(2) = 5.??
  
• Solve the following differential equation X(dy/dx)+2y=(x^2)logx?
  
• 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?
  
• What is the slope and y-intercept of the line #x=2#?
  
• Why does the location of the center of gravity depend on how an object’s mass is distributed?
  
• At what time after 7:00 pm will the hands of the clock be opposite to each other?
  
• How do you multiply #\sqrt { 2} \cdot - 3\sqrt { 3}#?
  
• Please Help :) Lim (Ln(1+9X)+cos(4X)-1)/X X=0 ???
  
• How do you multiply #(4y + 8)/ (y^2 - 2y)*(y - 2)/(y+2)#?
  
• How do you solve #8^{3x}=154#?
  
• Whats the answer to log(x-1) = -1 ?
  
• How do you find the derivative of f(x) = -2sqrt(x) by the limit process?
  
• How do you find the implicit differentiation of #1+lnxy=3^(x-y)#?
  
• 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?
  
• If the half-life of iodine-131 is 8 days, how much of a 5-g sample is left after 32 days?
  
• 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?
  
• 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].?
  
• What would the formula for the nth term be given 0.3, -0.06, 0.012, -0.0024, 0.00048, ...?
  
• How do you solve #2b ^ { 2} - 20b - 5= 0#?
  
• How do you solve #cos^2x=3/4#? Which solution is correct?
  
• How do you find #int 1/sqrt(-x^2-4x)#?
  
• What is the orthocenter of a triangle with corners at #(2 ,8 )#, #(3 ,4 )#, and (6 ,3 )#?
  
• 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?
  
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