Questions asked by Criss G.

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• (1-cosx)/sinx =tanx/2,can u help me to prove that?
  
• #cos 4x=8cos^4(x)-8cos^2x + 1 # and #cos 4x=8sin^4(x)-8sin^2x + 1#,can u prove it?
  
• Given cos 40=m and sin 10=n,can u please express sin 50 in terms of m and n?
  
• Given A is an obtuse angle and cos A=-(√5)/3.without using calculator, can u please help me to find cos 3A and also find cos 4A?
  
• Can u tell me how can cos 3x = 4cos³x-3cos x?
  
• Given that tan a=-(√5)/2 where a is an obtuse angle, can u please help me to find the value of sin(a/2) without using a calculator?
  
• If A,B and C are angles of a triangle, can u help me to prove sin (A+B)=sin c?
  
• Can u prove tan 67.5= (√2)+1? Also, how can -tan(A+B)=(tan A+ tan B)/tanAtanB-1?
  
• Can u prove that # (cosa + 2cos3a + cos5a)/(cosa - 2cos3a + cos5a) = -cot²a# ?
  
• Given (0<x<360),can u please prove 3(sin x + cos x)= 2cos x for answer correct to the nearest 0.1?
  
• By using method of differences, how can we get f(n)-f(0) but y not f(1)-f(n-1), from ∑f(r)-f(r-1)?
  
• Summation of series(method of differences),When we use #∑f(r)-f(r+1#),how can we know it is #f(1)-f(n+1)#, but not #f(n)-f(1+1)#? Also, how can we know it is #f(n+1)-f(1)# but not #f(1+1)-f(n)# when we use #∑f(r+1)-f(r)#?
  
• A stationary uranium nucleus (238U) decay with emission of alpha particle and total kinetic energy. 238/92U ↣234/90Th+ 4/2a what is Kinetic energy of patricle?
  
• A metal sphere falls with terminal velocity through cylinder filled with oil.If sphere experiences a viscous force of kv(k is constant), what is the kinetic energy of the sphere(express in m,g,k form)?
  
• Can u please solve sin3x=4sin²x for 0<x<360?
  
• Can anyone help me to solve# 4sin(x-pi)cos(x-pi)=√3 " for " 0<x<2pi#?
  
• Can anyone help me to solve sinx=cos(x+(π/6)) for -π<x<π?
  
• How to solve cos2x<3sinx + 2 for (-π<x<π)?
  
• In an arithmetic progression of n terms, the common differences is d and the last terms is l. How to find first two terms of the A.P in terms of d, l and n?
  
• If 5² x 5∧4 x 5∧6 x...x 5∧2p = (0.04)∧-28,can anyone help me to find value of p?
  
• Given the sum of the first n terms of a series is given by Sn =n²+2n for n ＞1. how to determine an expression for the rth term , Ur?
  
• How to use formula to find the sum of the series 20²-19²+18²-17²+16²-15²+...+2²-1²?
  
• A sequence of numbers formed by adding together corresponding terms of an A.Proression and G.Progresion with(common ratio=2).The 1st term =48,2nd term=73,3rd term=128.How to find fourth term? How to write expression (in term n),for nth term of sequence?
  
• The first three terms of 4 integers are in Arithmetic P.and the last three terms are in Geometric.P.How to find these 4 numbers?Given (1st +last term=37) and (the sum of the two integers at middle is 36)
  
• The 2nd, 6th and 8th terms of an Arithmetic progression are three successive terms of a Geometric.P. How to find the common ratio of G.P and obtain an expression for nth term of the G.P?
  
• If the pth, qth and rth terms of a G.P.are in geometric progression. How to show,that p, q, and r are successive terms of an Arithmetic progression?
  
• The 3rd,6th,and 12th terms of an Arithmetic progression are successive terms of a Geometric progression.How to show that the 4th,8th,and 16th terms of the A.P are also successive terms of a G.P?
  
• Given that ∑Ur =5/6 - (1/n+2) - (1/n+3).i found that sum of infinity of ∞∑Ur is 5/6....but how to find sum of infinity of ∞∑ (Ur+1 + 1/(2∧r))?the answer given is (19/12)?
  
• If #f(r)=cos2rtheta# ,by simplifying f(r+1)-f(r).How to use the result to find the sum of first n terms of the series #sin3theta + sin5theta + sin7theta +...#?
  
• The first three terms in binomial expansion of (p-q)∧m, in ascending power of q, are denoted by a, b, and c.How to show that b∧2/ac = 2m/m-1?
  
• Tin ore is extracted from mine,At first year production,8000kg of tin was obtained,but then each year, it show decrease of 10％ on the previous years,How to find the maximum amount of tin which could be probably extracted?
  
• THE gravitational field strength at two different points X and Y are 9.0Nkg∧-1 and 4.0Nkg∧-1 respectively .how to determine the ratio (gravitational potential at X/gravitational potential at Y)?
  
• How to expand (3-x)∧-2 in ascending powers of 1/x , stating the first four non-zero terms and the value of x for which the expansion is valid?
  
• Given matrix B= A + #3A∧3# + #5A∧5#+...+#99A∧99#, How to find matrix B, given answer is 2500A, how to do it?
  
• How to obtain a quadratic equation, with integer coefficient, having roots 2+i√5 and 2-i√5 ?
  
• ABCD is a square with the letters in the anticlockwise order.The points A and B represents 2+3i and 6+i,respectively.How to find the complex numbers represented by C and D?
  
• A and C are two points in,an argand diagram representing the complex numbers -5+2i and 1+i respectively. Given that the AC the diagonal of the square ABCD, How to find the complex numbers represented by the points B and D?
  
• This is a complex number question, how to show that -√2 +√2 is a root of x∧4+16=0?
  
• How to use de moivre's theorem to express #(sin 6theta)/sin theta# as a polynomial in #cos theta#?
  
• How to show that #y>(9/10)# from equation #y=(9+x^2)/(x^2+2x+1)#?
  
• Given z=2cosθ+i(1-2sinθ) ,How to prove that the real part of #1/(z+2-i)# is a constant for -180<θ<180?
  
• Given that #3^(4-2x)# = #5^(3y+x)# and #3^(x-y)×25^(2y-1)#= 1. How to show #x^2-3y^2-6xy+4x+16y-8=0# ?
  
• How to prove that #(2sin(4theta)-sin(6theta)-sin(2theta))/(2sin(4theta)+sin(6theta)+sin(2theta)) = tan^2(theta)# ?
  
• How to find z in terms of x+yi if #(z+1)/(z+2-i)# = 1 ?
  
• How to show that #S_oo- S_n= (-1/3)^n# ,given, #S_oo=9/4# and #S_n=9/4(1-(-1/3)^n)#?
  
• The voltage of a certain thermocouple as a function of the temperature is given by E = 2.800T + 0.006#(T∧2)#. If the temperature is increasing at the rate of 1.00°C/min,how fast is the voltage increasing when T=100°C?
  
• A rectangular piece canvass with dimensions 10m by 6m is used to make a pool.Equal sizes squares are to be cut from each corner and remaining will folded up around some plastic tubing.what is the dimension of the pool so the water volume is maximum?
  
• In the presence of sodium fluoride, #25cm^3# of 0.4moldm-3 aqueous iron(‖)sulphate requires #25cm^3# of 0.10moldm-3 aqueous potassium manganate(Ⅶ)for complete reaction.What is the final oxidation state of manganese?
  
• Two faraday of electric charge produces 30g of any element X(A=45) at the cathode.What is the formula of the ion of X? the answer is X with +3 charge, any explanation pls?
  
• How to find the general solution of differential equation #(3y)(x)dy/dx = e^x# when #x=2# and #y= 1# ?
  
• A certain quantity of electric charge produces 5.0g of silver from an aqueous solution of silver nitrate. When the same amount of charge is passed through an aqueous solution containing the #X^n+# ions , 3.02g of X is produced.,What is the value of n?
  
• A particle is released from rest at point O at time t= 0 and it falls vertically that its acceleration at is given g-kv,where k is positive constant, g is gravity,v is instantaneous velocity at time t.Express v in terms of g,k and t?
  
• If x is very small such that the terms in #x^4# and higher can be neglected, how to find sin2xln(1+x) in first three terms by using maclaurin series?
  
• Magnesium is used in extraction of titanium from titanium(IV) chloride. How to calculate the mass of magnesium required to react with 1000kg of titanium (IV) chloride?
  
• How to integrate #1/(1+cosx)# ?
  
• How to differentiate ln#x/2# and ln(#√(1-#1/x#)#) respect to x?
  
• How to differentiate #y=x^tanx# with respect to x?
  
• A and B plays a game by flipping a fair coin where the first person to obtain a head wins.If A flip first and the probability A wins is equal to the probability B wins, how to show the coin is biased and determine the probability of obtaining head?
  
• L denotes student is late and M denotes student misses the bus.Given P(M)=0.9 , P(L|M)=0.9 and P(L|M')=0.1 How to find the values of P(L),and P(M|L)?
  
• In a certain region, 46% of the population is female.It is known that 5% of males and 2% of females are left-handed.A person is chosen at random and found to be left-handed.What is the probability that this person is a male?
  
• P(n)is the product of two digits in the integer n.For example, P(18)=1x8=18 ,P(99)=9x9=81.How to find the value of P(10)+P(11)+P(12)+..+P(99)?
  
• How many even numbers can be formed if the digits of the number 112433 are rearranged?
  
• In a speaking contest, there are six finalist.One winner is to be selected for the first prize, two winners for second prize and three winners for third prize.What is the number of ways the prizes can be awarded?
  
• If these numbers(112233)are arranged to form six-digit numbers in ascending order,how to find the 30th number? and the median?
  
• A boy wishes to buy exactly six marbles.There are 4 different colours of marbles available.In how many ways can he buy six marbles?
  
• Three candidates are selected from a certain number of interviewees.If the order is not taken into account, then number of ways the candidates can be chosen is 35.How many ways are there if the order is taken into account?
  
• Five points lie on the diameter of a semicircle and another 4 points lie om the circumference.How many number lines that can be drawn by joining these points?
  
• Find the number of different sums that can be obtained by using one,some or all of the numbers in the set{1,2,4,8}.Then, how about from {#2^0,2^1,2^2,..,2^n#}?
  
• In arranging a 10-day examination time-table involving 10 subjects and one subject per day, how many ways are possible when mathematics, physics and chemistry all separated by at least one day?
  
• Three fair cubical dice are rolled.What is the probability that exactly two dice have the same score?Suppose the three dice are rolled one after another.If two dice have different scores,what is the probability that two of three dice have the same score?