Answers created by P dilip_k

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• If the cosines of the two of the angles of a triangle are proportional to the oppsite sides show that the trangle is right angled.?
  
• If #x=a+b,y=aw+bw^2,z=aw^2+bw# then find #x^2+y^2+z^2 and xyz#?
  
• 3.x articles are produced at a total cost of (2x^2+30x+20)naira and each is sold for (x/3+100) naira. Find the of x which gives the greatest profit?
  
• Location 1. Times- 11.30am, 5:42pm, 11:55pm, and 6:07am. Tide heights- 0.6, 4.8, 0.6, and 4.8. Location 2. Times- 4:46pm, 10:59pm, 5:11am, and 11:24am. Tide height- -2.4, 3.3, -2.4, and 3.3. Find period and amplitude?
  
• When does the equation pH=(1/2)(pKa1+pKa2) used?
  
• If #logx/(a^2+ab+b^2)=log y/(b^2+bc+c^2)=log z/(c^2+ca+a^2)# then find #x^(a-b)* y^(b-c)*z^(c-a)=#?
  
• What is the value of x in the equation (a/b)^(2x-3) = (b^3/a^3)^(x+4)?
  
• Prove that the straight lines joining the origin to the point of intersection of #kx+hy=2hk# and the curve #(x-h)^2+(y-k)^2=a^2# are perpendicular if #h^2+k^2=a^2# ?
  
• The value of # (cos (pi/12)-sin (pi/12))(tan (pi/12)+cos( pi/12) )#??
  
• A bullet hits a solid target lying on a frictionless surface and gets embeded in it.what is conserved(kinetic energy, momentum,both or none)?
  
• Prove that the straight lines #ax^2+2hxy+by^2+lambda(x^2+y^2)=0# have the same pair of bisectors for every value of #lambda#?
  
• If w is a complex cube root of unity then show that #(2-w)(2-w^2)(2-w^10)(2-w^11)=49#?
  
• Find the square root of 4-3i?
  
• A proton with velocity v completes a circle with radius r in uniform magnetic field.what should be the velocity of alpha particle so that it completes a circle with same radius under the influence of the same magnetic field?
  
• A particle moves in a circle of radius 25cm covering 2 revolutions per second what will be the radial acceleration of that particle?
  
• Find the equation to the straight line drawn at right angle to the straight line #x/a-y/b=1# through the point where it meets x-axis?
  
• Show that the line y=mx bisects the angle between lines #ax^2-2hxy+by^2=0# if #h(1-m^2)+m(a-b)=0#?
  
• Find the condition that one of the straight lines given by the equation #ax^2+2hxy+by^2=0# may coincide with one of those given by the equation #a_1x^2+2h_1xy+b_1y^2#?
  
• Prove that the product of the length of perpendiculars from #(alpha,beta)# to the lines given by #ax^2+2hxy+by^2=0# is #(alpha^2+2halphabeta+b*beta^2)/(sqrt((a-b)^2+4h^2))#?
  
• Show that the two straight lines #x^2(tan^2theta+cos^2theta)-2xytantheta+y^2sin^2theta=0# makes angles with the x-axis such that the difference of their tangents is 2.?
  
• A vertical pole is divided by any point in the ratio 9:1. If both the segments subtend equal angles to each other at a point 20m away from the foot of the pole , find the height of the pole?
  
• Find #K_c# for the reaction below (see details)?
  
• If #0<(alpha),(beta),(gamma)<(pi)/2# prove that #sin(alpha)+sin(beta)+sin(gamma)>sin(alpha+beta+gamma)#?
  
• If in triangle ABC #sin^(2)A+sin^(2)B+sin^(2)C=2# then the triangle is options are below?
  
• What will be the answer?
  
• Find the volume, Vcm3, of the box in terms of x? (See details below for description of problem)
  
• A pendulum Makes an arc of length of 18 in. on its first swing. On Each suceeding Swing,The length of the arc is one-third the lenght of the preceding swing.How far does the Tip of the pendulum move before it comes to rest?
  
• A Pingpong Ball dropped from a height of 128 m rebounds on each bounce one-half the distance from which it fell.How far will it travel before coming to rest?
  
• The number of common integers for two arithmetic progressions 1,8,15,22,...2003 and 2,13,24,35,...2004 is?
  
• If #2costheta=x+1/x# then prove that the value of the #x^n+1/(x^n), ninN# is #2cosntheta#?
  
• The value of x satisfying #2log_9(2(1/2)^x-1)=log_27((1/4)^x-4)^3# is?
  
• Hot water of mass 10 kg at 90°C is cooled forr taking bath by mixing 20kg of water at 20°C. What will be the final temperature of the water neglecting the heat taken by bucket ?
  
• If a line parallel but nont identical with x-axis cuts the graph of the curve #y=(x-1)/((x-2)(x-3))# at #x=a,x=b# then (a,b)=?
  
• Let #a=1^2/1+2^2/3+3^2/5+....1001^2/2001, b=1^2/3+2^2/5+3^2/7+...+1001^2/2003# then #a-b=#?
  
• Let P be a point in an equilateral triangle with each side of length '1'. Let #h_1,h_2,h_3# be the length of perpendicular distance from 'P' to the 3 sides of the triangle. What is the possible value of #h_1+h_2+h_3#?
  
• #((2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)+1)/(2^33)#=?
  
• Minimum vertical distance between graph of #y=2+sinx and y=cosx# is ?
  
• If #a,b,c# are real numbers such that #a^2+2b=7, b^2+4c=-7,c^2+6a=-14# then the value of #a^2+b^2+c^2#=?
  
• How do I simplify sqrt((1-cos110º)/(cos110º+1)?
  
• The sum #1/(sin46sin47)+1/(sin47sin48)+1/(sin48sin49)+cdots+1/(sin133sin134)=# ?
  
• A square and an equilateral triangle have the same perimeter. Let A be the area of the circle circumscribed about the square and B be the area of the circle cicumscribed about the triangle. Then #A/B=?#
  
• How do you factorize #xy(x^2-y^2)+yz(y^2-z^2)+zx(z^2-x^2)# ?
  
• If #xy+yz+zx=12-x^2=15-y^2=20-z^2# then #x+y+z=?#
  
• #n# is the smallest positive integer such that (2001+n) is the sum of the cubes of the first 'm' natural numbers. Then (m,n)=?
  
• How many right triangles, whose sides are all positive whole numbers, have the property that the area is numerically equal to perimeter?
  
• The number of ordered triples (x,y,z) satisfy #3x^2+3y^2+z^2-2xy+2yz=0# is?
  
• If α,β are the roots of x²-x+1=0,then the quadratic equation whose roots are α²⁰¹⁵,β²⁰¹⁵ is ?
  
• Prove that #1^99+2^99+3^99+4^99+5^99# is divisble by 5.?
  
• The number of integer pairs (x,y) satisfy the equation #x(x+1)=2^y# is?
  
• The slope of a line with a positive rational slope l, which passes through the point (6,0) and at a distance of 5 from (1,3). Write the slope in the form #a/b# where a and b are relatively prime. Then the sum of a and b is?
  
• The area of triangle ABC is equal to #a^2+b^2-c^2#. If angle C is acute then find the numerical vaue of secant where a,b,c are positive real numbers?
  
• There exists integer #x,y,z# satisfying #28x+30y+31z=365# then the value of #z-2x# for some such triplet is?
  
• Prove that #tan20+tan80+tan140=3sqrt3#?
  
• Prove that #tan20+tan80+tan140=3sqrt3#?
  
• The maximum value of #f(x)=(3sinx-4cosx-10)(3sinx+4cosx-10)# is?
  
• If #loga/(b-c)=logb/(c-a)=logc/(a-b)# then the numerical value of #a^a*b^b*c^c=?#
  
• The minimum value of #f(x,y)=x^2+13y^2-6xy-4y-2# is?
  
• The value of x such that #4(1+y)x^2-4xy+1-y=0# is?
  
• Given that there exists a triangle whose sides are a,b,c. Then prove that there exists a triangle whose #sqrta,sqrtb,sqrtc#?
  
• The sides of triangle are 6,7,x. Then the largest value of area of #Delta# is?
  
• In IUPAC nomenclature, which bond is given more priority?
  
• What is #(2h^4-h^3+h^2 +h-3)-:(h^2- 1)#?
  
• Prove that if lengths of 2 medians of a triangle are equal then the triangle is isosceles ?
  
• If #i^2=-1# then the sum of #cos45+icos135+…i^n*cos(45+90n)+…i^40*cos3645=#?
  
• The value of the series #(1+2-3-4+5+6-7-8+9+10-11-12+…-99-100=?#
  
• If #2*sqrt(3(2/4)*(3/5)*(4/6)...(x/y))=1# then (x,y)=?
  
• If #theta# is eliminated from the equation #x=acos(theta-alpha)# and #y=bcos(theta-beta)# then prove that #(x/a)^2+(y/b)^2-(2xy)/(ab)cos(alpha-beta)=sin^2(alpha-beta#)?
  
• Solve for #x# in #(a+b-x)/c+(a+c-x)/b+(c+b-x)/a+(4x)/(a+b+c)=1#?
  
• What is the particle's displacement from r1 to r2?
  
• What is the length between PO, PQ, OQ have to be when the points form a equilateral triangle?
  
• 2kg disc of radius 1m moment of inertia 0.5kgm^2 is released from top of 2m long incline having inclination 30degree. Find it’s velocity just before reaching the ground .??
  
• Exterior angle of a regular polygon measures #10alpha# degrees.Then, prove that #alpha in ZZ# and there are precisely 7 such alpha#?
  
• The product of #(1-1/(2^2))*(1-1/(3^2))....(1-1/(9^2))*(1-1/(10^2))=a/b# then find a and b without full simplification?
  
• In a #DeltaABC#, prove that the value of #cosA/(sinBsinC)+cosB/(sinCsinA)+cosC/(sinAsinB)# is a prime?
  
• The value of expression #(2(sin1+sin2+...+sin89))/(2(cos1+cos2+...+cos44)+1)=csctheta, theta in (0,pi/2)# then find #costheta and tantheta#?
  
• Find the value of x in # sqrt(1+log_x(27))*log_3(x)+1=0#?
  
• Aaconverging lens of focal length 15 mm is used as a magnifying glass for inspecting stamp. A rectangular stamp which is 20mm 40mm is placed 30mm from the lens find the length of the image of the 20mm side of the stamp?
  
• Nathan cut an isosceles triangle from felt to make a spirit banner. Two sides of his banner had the following measures : 15 inches and 7 inches. Which could be the measure of the third side of Nathan’s banner ?
  
• If #log_10x+log_10y.>=2# the minimum value of #x+y=#?
  
• The value of #x# satisfying the equation?
  
• If #alpha and beta # are the roots of the equation #x^2-p(x+1)-c=0# then the numerical value of #(alpha^2+2alpha+1)/(alpha^2+2alpha+c)+(beta^2+2beta+1)/(beta^2+2beta+c)#=?
  
• Prove each of the following identities (a) sec x + tan x =cos x/1 − sin x (b) tan^2 x/tan^2 x + 1= sin^2 x?
  
• Let S be a square of unit area. Consider any quadrilateral which has one vertex on each side of S. If #a,b,c and d# denote the lengths of sides of the quadrilateral, prove that #2<=a^2+b^2+c^2+d^2<=4#?
  
• The fourth power of the common difference of an arithmetic progression is with integer entries is added to the product of any four consecutive terms of it. Prove that the resulting sum is the square of an integer?
  
• A mixture containing 22.4 g of ice (at exactly 0.00 ∘C) and 78.7 g of water (at 62.1 ∘C) is placed in an insulated container. Assuming no loss of heat to the surroundings, what is the final temperature of the mixture?
  
• Which one is greater of #99^50+100^50 and 101^50#?
  
• Angelica starts on a walk at 5 kilometres an hour. Three hours later, on the same route, Janelle starts riding her bicycle at 11 kilometres an hour. When will Janelle overtake Angelica?
  
• The leopard is capable of jumping to a height of 1.9 m in hunting for food. Determine the take off speed of the leopard. ?
  
• The question is below?
  
• The question is below?
  
• If a, b& c are three non zero vectors then the expression a.(b.c) is ? a)scalar triple product b)volume of parallelepiped c)meaning less d) dot product
  
• We have #ABC# a scalene triangle, and a point #M# in plane of this triangle. How to prove that #vec(AB)*vec(CM)+vec(AC)*vec(MB)+vec(AM)*vec(BC) = 0#?
  
• If # alpha +beta -gamma =pi# Prove that #(sin^2alpha + sin^2beta - sin^2gamma)=#2sin alpha ×2sin beta ×2 cos gamma#?
  
• C) A boat is in dry dock and water is allowed in until it floats. The volume of water allowed in is metered and found to be 3450 m3. The dry dock is a rectangular shape 80m long and 20 m wide. ............rest of the question in the picture? plz help
  
• A block of mass m=2kg is kept in position on the wall by applying an oblique force 'F' at 60° to the vertical as shown . calculate the minimum value of 'F'(the coafficient of friction between the wall and the block = 0.9) (Take 'g'=10ms^-2)?
  
• If O be a inner point of a triangle ABC Then prove that OA+OB+OC < AB+BC+CA ?
  
• How to solve Cos(3x)-Cos(2x)+Cos(x)=0 ?
  
• How do you evaluate #int# #dx/(x^2sqrt(x^2 - 9))# with x = 3sec(#theta#)?
  
• How to solve the ecuation Arctan((x-1)/(x-2))+Arctan((x+1)/(x+2))=(Pi/4) ?
  
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