Questions asked by AJ

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• Chemical reaction takes place when iron dust is added into copper sulphate solution but no reaction takes place when copper dust is added into ferrous sulphate solution, why?
  
• How many atoms of Chlorine are present in 0.072g of FeCl3?
  
• Please explain about the way to calculate the number of atoms of a certain element in a given mass of a compound?
  
• In what ratio is the line joining the points (1,3) and (2,7) divided by the line 3x+y=9?
  
• A hill station has a road that has road slope grade of 6% or 6÷100. If a vehicle drives 200 miles through that road,how much vertical distance is he covering?
  
• A right angled triangle is formed in first quadrant by a line passing through (2,1) at the X-intercept (a,0) and Y-intercept (0,b). Calculate the area of the triangle as function of "x"?
  
• If a projectile was shot from a building with a initial velocity of #60m/s# at an angle of#30^o# and took 3 sec to reach the ground,find the height of the building?
  
• Solve the following two linear equation by substitution and elimination method: #ax+by=(a-b) , bx-ay=(a-b)# ?
  
• Solve the following two linear equation by substitution and elimination method: #ax+by=(a-b) , bx-ay=(a+b)# ?
  
• How to solve for x and y if the equations are: #(5/(x+y))-(2/(x-y))+1=0# and #(15/(x+y))+(7/(x-y))-10=0# ?
  
• A ball is thrown off a building of height 2 metres at the horizontal velocity of 10m/s. If a boy is 10 m away from the bottom of the building. Would that ball hit him?
  
• If A is a number of degree and B is the number of grades of any angle, prove that: #B=A+(A/9)# ?
  
• How to solve for x if #x^2+(2/3)x-1/3=0# ?
  
• How to solve for #x# if #x^(2/3)-5x^(1/3)+6=0# ?
  
• Given #f(x)=|x|# and #g(x)=5x+1# Find #f(g(x))# and domain and range?
  
• How to evaluate #(sqrt (-20))^2# step by step?
  
• How to solve using quadratic formula: #(b/(x-a))+(a/(x-b)=2# ?
  
• How to solve by quadratic formula: #(p-q)x+(2q)/x=(p+q)# ?
  
• What is #sqrt (25)#? Is it #+5# or #-5# ?
  
• If G,D and C are grade, degree and radian of an angle respectively, prove that #(G-D)pi=20C# ?
  
• Calculate the area of a parallelogram bounded by y-axis, the line #x=3#,a line #y=2x+1# and a line parallel to that line passing through #(2,7)?
  
• Find the dimensions of the rectangular corral split into #2# pens of the same size producing the greatest possible enclosed area given #300# feet of fencing?
  
• Find a polynomial function if Y-intercept is #(0,1)# .If there are no X-intercepts . Degree is #4# and End behaviour is #xrarr-oo,f(x)rarr oo# and #xrarr oo,f(x)rarr oo# ?
  
• Find a polynomial function if Y-intercept is #(0,-4)#. The X-intercepts are #(-2,0)# and #(2,0)#. Degree is #2#. End behaviour is #xrarr-oo,f(x)rarroo# and #xrarroo,f(x)rarroo# ?
  
• In a circle of diameter #40# cm, the length of a chord is #20# cm. Find the length of minor arc of the chord?
  
• When a discount of #15%# is allowed on the marked price of a article,it is sold for #4250$# . If the marked price is #25%# above the cost price of the article. Calculate gain or loss percentage?
  
• If tanA+sinA=p and tanA-sinA=q. Then proove that #p^2-q^2=4sqrt (pq)# ?
  
• A spring attached to a ceiling is pulled down #20# cm. After #3# seconds, wherein it completes 6 full periods, the amplitude is #15# cm. Find a sinusoidal function modelling it's position #t# seconds after released?
  
• A spotlight on the ground 3 feet away from a 5 feet tall man cast a 15 feet shadow on a wall 6 feet away from the man. Find the angle in which light is placed?
  
• Prove that the line #xcosA+ysinA=p# is tangent to ellipse #(x^2/a^2)+(y^2/b^2)=1# if #p^2=a^2cos^2A+b^2sin^2A# ?
  
• What is the derivative of the function #f (x)=ln (ln ((x+4)/ln (x^2+4)# ?
  
• Prove that limit does not exist using epsilon delta proof : #lim_ (x->0) |x|/x# ? Please show the scratch work too.
  
• Evaluate #int_0^1 (t/(1+t^3))dt#?
  
• Prove that: if #A+B+C=180°# #cot(A/2)×cot (B/2)×cot (C/2)=cot(A/2)+cot (B/2)+cot (C/2)#?
  
• If #cosA+cosB+cosC=0# Then prove that #cos3A+cos3B+cos3C=12cosAcosBcosC# ?
  
• How to get surface area of a cone using integral calculus?
  
• How to derive power reducing formula for #int(sec^nx)dx# and #int (tan^nx)dx# for integration?
  
• How to integrate #int (secx)dx# and #int (cscx)dx# ?
  
• Proove that: #int _a^b f (x)dx= int_a^b f (a+b-x)dx# ?
  
• Are there any method apart from integration by parts , u substituting, trig substitution or partial decomposition for difficult integrals?
  
• How to evaluate : #int (1+sinx)/[cosx (1+cosx)]# ?
  
• How to integrate question of types: #int (asinx+bcosx)/(csinx+dcosx) dx# where a,b,c, d are coefficients by several methods?
  
• How to decompose into partial fractions: #(3x)/((x+3)sqrt (x^2+1))# ?
  
• What is the integral of #int x^(1/3)/[x^(1/3)+x^(1/4)]# ?
  
• If two circles #x^2+y^2+2ax+c^2=0# and #x^2+y^2+2by+c^2=0# touch each other externally then prove that #1/(a^2)+1/(b^2)=1/(c^4)# ?
  
• Prove that #cosec(x/4)+cosec (x/2)+cosecx=cot(x/8)-cotx# ?
  
• If #2tanA=3tanB# then prove that: #cos2A=(13cos2B-5)/(13-5cos2B)# ?
  
• Identify whether the infinite series converge absolutely conditionally or dont #sum_(n=1)^oo (-1)^(n+1) (n (arctan(n+1)-arctan (n))# (Apply Mean Value theorem to conclude)?