Answers edited by Ananda Dasgupta

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• How do you factor the expression #-6 a^2 - ab + 7 b^2#?
  
• I cut a triangle ABC out of a piece of paper. I found out that sinA+sinB+sinC=5/2 and a/sinA=16. What is the triangle’s perimeter?
  
• Find two numbers whose sum is 12 such that the sum of the square of one plus 4 times the other is a maximum?
  
• Find the sum of the infinite series #-ne^(1-n)# from #n=1# to #oo#?
  
• When a load is connected to a voltage divider, will the total resistance of the circuit increase or decrease?
  
• What is the arclength of #(1/t^2,1/t)# on #t in [1,2]#?
  
• #int sqrt(x^2+5/x)=#?
  
• An object moves along a curve has an acceleration of 5 m/s^2 at 30° with its velocity of 5 m/s at some instant . The radius of curvature of the path at that instant is ? a) 10 m b) 20 m c) 5 m d)15 m
  
• If the area under the curve of f(x) = 25 – x2 from x = –4 to x = 0 is estimated using four approximating rectangles and left endpoints, will the estimate be an underestimate or overestimate?
  
• Question #265f1
  
• Find the required limit algebrically, if it exists. lim (x+3)/(x-3) if x approaches 4 ?
  
• An amount Q of heat is added to a mono atomic ideal gas in a process in which the gas performs a work Q/2 on its surrounding .find equation of the process?
  
• Integrate. What is the next step ?
  
• How to derive 1st of motion from second law of motion?
  
• How do you prove [(sinx-cosx)/(secx-cscx)]=[(sin2x)/2]?
  
• When #a-1/a=1#, #a^5-1/a^5 =#? how to solve....
  
• Find # i# for #t>0 # if the circuit is in steady state at # t=0# ?
  
• What is the answer please?
  
• What is the area of the shaded segment?
  
• A circular loop wire with current I1=I∘π and a V shaped wire with current I2 are arranged in a plane as shown in diagram. If magnetic field at O is zero, value of I2 is ? (a)#(13aI_@)/35r# (b)#(12aI_@)/17r# (c)#(aI_@)/r# (d)#(12aI_@)/35r#
  
• Integral Ln|x|/(1+x)^2 dx Answer Guys ???
  
• How do you solve #sin(x/2)-1=0# between the interval #0<=x<8pi#?
  
• Please solve with a detailed explanation?
  
• A particle begins to move with a tangential acceleration of constant magnitude #0.6m/s^2# in a circular path. If it slips when it's total acceleration becomes #1m/s^2#, then the angle through which it has turned before slipping is?
  
• What is the antiderivative of # ln(x^2 + 2x + 2)#?
  
• A frequency of variation of kinetic energy of a simple harmonic motion of frequency n is?
  
• 17!/(5!*12!) ?
  
• How do you evaluate the integral #int sqrtxsqrt(4-x)#?
  
• Show that the line integral #int_{-1,2}^{3,1}(y^(2)+2xy)dx+(x^(2)+2xy)dy# is independent of path and evaluate it?
  
• How many solutions are there to the following system of equations 4x – 8y = 0 and –3x + 8y = –7?
  
• Let #'f'# be an even periodic function with period '4' such that #f(x) = 2^x-1#, #0<=x<=2#. The number of solutions of the equation #f(x) = 1# in #[-10,20]# are?
  
• The number of solution of the equation 3^(sin2x+2cos2x)+ 3^(1-sin2x+2sin2x)=28 in [0,2π]?
  
• Find the Taylor series expansion formula of #f(x)=\lnx# at #a=3#?
  
• A particle moves in the x-y plane with velocity #v_x#=#8t-2# and #v_y#=2.If it passes through the points #x=14# and #y#=4 at #t#=2,what is the equation of the path?
  
• What is the derivative of #f(x)=sqrt(1+log_3(x)# ?
  
• How do you solve the inequality #x^2+3x-28<0#?
  
• Three rods each of mass M and length L, are joined together to form an equilateral triangle. What is the moment of inertia of a system about an Axis passing through its centre of mass and perpendicular to the plane of the triangle?
  
• A parellel plate capacitor with plate speration d is charged with a battery so that energy stored is #"U"#. If a plate of dielectric #"K"# and thickness d is placed betweeen the plates of capacitor and battery remains connected. The work by battery is?
  
• In a garden a boy is swinging in the standing position how will the time period of the swing be affected if the boy sites down on the swing?
  
• What are the local extrema of #f(x)= xlnx-xe^x#?
  
• A circle touches two perpendicular lines #2x-3y=15# and #3x+2y=3# at the points #A(6,-1)#, #B(1,0)# respectively. Find the equation of the circle?
  
• What is the solution to the integral of 2cosx + 3sinx / cosx + sinx? Thanks
  
• F(x)=e^0.5x when x<=0 and f(x)=-(x-h)2+k when x>0 find h and k such that f(x) is both continuous and smooth at x=0?
  
• The answer is?
  
• A radioactive isotope #""_Z^XA# decay and emits one alpha particle and two beta particles consecutively. How to write the formula for the nuclides produced?
  
• A town's January high temperatures average 36°F with a standard deviation of 10°, while in July the mean high temperature is 74° and the standard deviation is 8°. In which month is it more unusual to have a day with a high temperature of 55°?
  
• How to integrate 1/(64x^2+100)?
  
• What is the integration of #(dx)/(x.sqrt(x^3+4))#??
  
• How to find result ?
  
• #y=f(x)# is given. Graph, #y=f(3x)-2# and #y=-f(x-1)#?
  
• How do you solve for x given #|\frac{2x}{7}+9 | > frac{5}{7}#?
  
• #psi_A(x,0) = sqrt(1/6)phi_0(x) + sqrt(1/3)phi_1(x) + sqrt(1/2)phi_2(x)# Calculate the expectation value #<E># at any later time t=#t_1#, #phi_n# are energy eigenfunctions of the infinite potential well .Write the answer in terms of #E_0#?
  
• How to complete this electrical current table?
  
• A projectile is shot from the ground at an angle of #( pi)/3 # and a speed of #9 m/s#. Factoring in both horizontal and vertical movement, what will the projectile's distance from the starting point be when it reaches its maximum height?
  
• A particle of mass #m# moving with speed #v# hits elastically another stationary particle of mass #2m# inside a smooth horizontal circular tube of radius #r#. The time after which the second collision will happen?
  
• How to define a, b, c, d, e that are integer between 1-9 so that matrix is a symmetry matrix?
  
• If the AM and GM for 10 observations are both 15 then the value of harmonic mean......?
  
• What are the range of initial values using the Newton-Raphson method for #(x-9)/(x^2+1)=0# for it to converge to 9?
  
• Integrate #x^3/sqrt((x^2+16))# dx using trig substitution?
  
• #intint_Asqrt(xy-y^2)dxdyquadquadA={(x,y)inRR^2; 0<=y<=3, x/10<=y<=x}# Would anyone help me?
  
• Total resistance of the circuit ?
  
• Triangle A has an area of #15 # and two sides of lengths #4 # and #9 #. Triangle B is similar to triangle A and has a side of length #12 #. What are the maximum and minimum possible areas of triangle B?