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  1. chwala

    Solve for x in this inequality problem

    ##7x+12≥3x## ##7x−3x≥−12## ##4x≥−12## → ##x≥−3## or ## 12/x≥-4## but by substituting say## x=−4## we see that it also satisfies the equation implying that my solution may not be correct. Note I was not able to use the inequality sign at the original problem, kindly insert for me...
  2. chwala

    How do you find the LCM and HCF?

    as per my thinking, lcm of ##1## and ##0.5## is 1. And lcm of therefore, ##1## and ##0.75## should be ##0.75## from research, lcm= lcm(numerator)/hcf(denominator) = 3/1 hcf=hcf(numerator)/lcm(denominator)= 1/4 i would appreciate more insight on this...
  3. chwala

    Simultaneous equations: Do these have (i) a unique solution, (ii) many solutions, or (iii) no solution?

    ...##2y-2z-2mz=6## ## 2y-2z-2mz= mx+8y+5z## i then let, ##-2z-2mz=5z## ##m=-7/2## ##→2y=mx+8y## ##7x=12y##
  4. chwala

    Reverse substitution to find the inverse of modular arithmetic

    ##132,289≡1973* 67 + 98## ##1973≡98*20+13## ##98≡13*7+7## ##13≡7*1+6## ##7≡6*1+1## now in reverse my attempt is as follows, ##1≡7-6## ## 1≡7-(13-7)## ##1≡2*7-(1973-20*132,289+1340*1973)## ##1≡2*7-(1341*1973-20*132,289## which is correct but my interest is in finding the inverse of 1973 help?
  5. chwala

    Modular arithmetic

    ok this is a bit confusing to me, long since i did this things...-10/3=quotient -3+ remainder -1. How is the remainder 2?
  6. chwala

    Solve the linear Diophantine equation

    ##259x+581y=7## ##581=259.2+63## ##259=63.4+7## ##63=7.9+0## therefore by reversing... ##7=0.63+1.7## ##7=1.259-4.63### ##x=1## ##y=-4## is this correct? Bingo
  7. chwala

    Basic algebra question grade 1

    attempt 1. 6 /2×3 = 3×3=3×3=9 attempt 2 6/2(3)= 6 divide 6 = 1. sorry i cannot see the divide symbol.
  8. chwala

    How to explain collision theory?

    What activities can one use in explaining collision theory to secondary level students?
  9. chwala

    What is the color of chromium Cr##^{3+}##?

    kindly clarify on the color of chromium ##cr^{3+}##. Is it green or grey-green? There is a conflict in my textbook i.e Roger Norris IGCSE Chemistry and the cie syllabus content 2019. regards,
  10. chwala

    Find the area of the shaded region as a ratio to the area of the square

    1. Homework Statement find the area of the shaded region as a ratio to the area of the square (kindly see attached diagram) 2. Homework Equations 3. The Attempt at a Solution ##A= \frac 1 2####b×h## ##A= \frac 1 2####×2x × 3x##
  11. chwala

    Probability generating function when x is even

    1. Homework Statement A random variable x has a probability function ##G(t)##. Show that the probability that ##x## takes an even value is ## \frac 1 2 ( 1+G(-1))## 2. Homework Equations 3. The Attempt at a Solution ##G(t)= \sum_{k=0}^\infty p_k t^k ##... ## 1=P(X=even)+...
  12. chwala

    Solving a first order ODE using the Adomian Decomposition method

    1. Homework Statement how do we solve the ode ## y'+y^2=-2, y(0)=0## using adomian decomposition method? 2. Homework Equations 3. The Attempt at a Solution ##Ly = -2-y^2## ## y= 0 + L^{-1}[-2-y^2]## ##y_{0}= -2t## ##y_{1}= -L^{-1}[4t^2] = -4t^3/3## are my steps correct so far in trying to...
  13. chwala

    Failure of uniqueness for this first-order differential equation

    1. Homework Statement how do we establish failure of uniqueness on this first order differential equation ## y(x)= x y'+(y')^2## 2. Homework Equations 3. The Attempt at a Solution general solutions are ## y= cx^2+c^2## where c = constant and ## y= -0.25x^2## ## -0.25x^2+cx+4c^2=0## ##x=...
  14. chwala

    Probability: Cumulative distribution table for the number of heads when the four coins are tossed

    1. Homework Statement (i) Construct the cumulative distribution table for the number of heads when the four coins are tossed. Coins are fair. (ii) Find the Median. 2. Homework Equations 3. The Attempt at a Solution (i) x 0 1 2...
  15. chwala

    Finding the inverse of ##y=2^{x}##

    1. Homework Statement find the inverse of the function ##y=2^{x}## ok i know the steps but why is this question awarded 1 mark... 2. Homework Equations 3. The Attempt at a Solution ## y= 2^{x}## →## ln y= xln 2## →## x= ln y/ln 2##
  16. chwala

    Quartic polynomials

    1. Homework Statement Given ## x^4+x^3+Ax^2+4x-2=0## and giben that the roots are ## 1/Φ, 1/Ψ, 1/ξ ,1/φ## find A 2. Homework Equations 3. The Attempt at a Solution ## (x-a)(x-b)(x-c)(x-d)=0## where a,b,c and d are the roots
  17. chwala

    Tangent/Parabola question

    1. Homework Statement If the tangent at the point ##P## to the parabola ## y^2=4ax## meets the parabola ## y^2=4a(x+b)## at points ##Q## and ##R##. Prove that ##P## is the midpoint of ##QR## 2. Homework Equations 3. The Attempt at a Solution We know that the tangent equation to the...
  18. chwala

    Convergence of a series

    1. Homework Statement Determine whether the series ## \frac {(n^3+3n)^{1/2}} {5n^3+3n^2+2 sin (n)}## converges or not 2. Homework Equations 3. The Attempt at a Solution looking at ## 1/sin (n) ## by comparison, ##1/n^2=1+1/4+1/9+1/16+...## converges for ##n≥1## for ##n≥1 ## implying that...
  19. chwala

    Cauchy-Riemann condition

    1. Homework Statement Verify ## f(z)= z^3-5iz+√7## satisfies cauchy riemann equations. 2. Homework Equations 3. The Attempt at a Solution seeking alternative method ## f(z)= (x^3+5y-3xy^2+√7)+ (3x^2y-y^3-5x)i## ##∂u/∂x = 3x^2-3y^2 = ∂v/∂y## ##∂v/∂x=6xy-5= -∂u/dy## hence satisfies.
  20. chwala

    Trigonometry identities

    1. Homework Statement Show that ## {(tan φ+sec φ-1)/(tan φ-sec φ+1)}≡ {(1+sin φ)/cos φ}## 2. Homework Equations 3. The Attempt at a Solution ## (sin φ+1-cos φ)/(sin φ+cos φ-1)##
  21. chwala

    Finding the convergence of a binomial expansion

    1. Homework Statement Expand ##(1+3x-4x^2)^{0.5}/(1-2x)^2## find its convergence value 2. Homework Equations 3. The Attempt at a Solution on expansion ##(1+3/2x-3.125x^2+4.6875x^3+...)(1+4x+12x^2+32x^3+...)## ##1+5.5x+14.875x^2+42.1875x^3+... ## how do i prove for convergence here?
  22. chwala

    How do we solve this cubic equation

    1. Homework Statement solve ## x^2/y + y^2/x=9, 1/x+1/y=3/4## 2. Homework Equations 3. The Attempt at a Solution ##9x^3+9y^3=81xy## ## 4x+4y-3xy=0## ##x^3+y^3-9xy=0, 12x+12y-9xy=0## ##x^3-12x+y^3-12y=0##
  23. chwala

    Atomic symbol notation question

    considering the symbol of an element, under the cambridge curriculum , is the nucleon number written on top or at the bottom on the left side of the element?
  24. chwala

    Statistics: probability distribution problem

    1. Homework Statement two indepedent observations ##X_1## and ##X_2## are made up of the continous random variable having the probability density function ## f(x)= 1/k##, and ## 0≤x≤k## find a. the cumulative distribution of ##X## b. Find the probability distribution of M, the...
  25. chwala

    Solving four variable simultaneous equations

    1. Homework Statement given ##mx + ny =7## ##mx^2 + ny^2=49## ##mx^3+ny^3=133## ##mx^4+ny^4=406## find ##2014(x+y-xy)-100(m+n)## 2. Homework Equations 3. The Attempt at a Solution ##(mx+ny)(mx-ny)=7(mx-ny)## ##m^2x^2-n^2y^2=7(mx-ny)## ##mx^2+ny^2=49##
  26. chwala

    Solve three simultaneous polynomial equations in three variables...

    1. Homework Statement ## x^2 +xy + y^2 = 3## ## y^2+yz+z^2=1## ##z^2+zx+x^2=4## 2. Homework Equations 3. The Attempt at a Solution ##yz^2-xz^2+yx^2-xy^2=4y-x## ##z^2(y-x)-xy(y-x)=4(y-x)## thus ##z^2-xy=4## or ##z^2=4+xy## ..........................on working out i end up with ##...
  27. chwala

    Complex numbers problem

    1. Homework Statement if ## x + iy## = ## \frac a {b+ cos ∅ + i sin ∅} ## then show that ##(b^2-1)(x^2+y^2)+a^2 = 2abx## 2. Homework Equations 3. The Attempt at a Solution i let ## ... ##x + iy = ## \ a(b+cos ∅ - i sin ∅)##/ ##(b + cos ∅)^2 + sin^2∅ ##.......got stuck here...
  28. chwala

    Integration question

    1. Homework Statement if ## f(x)= \int_x^3 \sqrt {1+t^{16}} dt ## find f'(x) 2. Homework Equations 3. The Attempt at a Solution let ## x = 1+t^{16},## → ##\frac {dx}{dt},= 16t^{15},## ## y= x^{1/2} ## →##\frac {dy} {dx},= 0.5x^{-0.5}##
  29. chwala

    Exponential proof

    1. Homework Statement they say 1. ##e^{ln x}= x ## and 2.##e^-{ln(x+1)}= \frac 1 {x+1}## how can we prove this ##e^{ln x}= x ## and also ##e^-{ln(x+1)}= \frac 1 {x+1}##? 2. Homework Equations 3. The Attempt at a Solution let ## ln x = a## then ##e^a= x, ## a ln e= x,## →a= x, where ##...
  30. chwala

    Integration problem

    1. Homework Statement given ## tan 2θ-tan θ≡ tan θ sec 2θ## show that ##∫ tan θ sec θ dθ = (1/2 )ln (3/2)## limits are from θ= 0 to θ=π/6 2. Homework Equations 3. The Attempt at a Solution ##∫ tan 2θ-tan θ dθ ## → -(1/2 )ln cos 2θ + ln cos θ → ##-1/2 ln 1/2 + ln √3/2## ##=...
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