# Search results

1. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### How to explain collision theory?

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

14. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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 $(mx+ny)(mx-ny)=7(mx-ny)$ $m^2x^2-n^2y^2=7(mx-ny)$ $mx^2+ny^2=49$