Christopher

For a 0.1mol/L of monoprotic weak acid (HA) at a certain temperature, the ratio between the unionized and ionized molecules is 50:2, find the value of ionization constant (Ka) for the acid, HA.

(i) (a-1)^3 -8 + (a+1)^3 +6(a²-1)

(ii) x²-y²-2z²+zx+3yz

given answer: (6x-7) /5

A saturated calcium hydroxide solution is prepared. 25mL of this solution is titrated with 0.05mol/L hydrochloric acid and 23.75mL are required for completed neutralization. Calculate the solubility product of calcium hydroxide.

Given that O is te origin , and the polar coordinates of A and B are (-3, 7π/6) and (5, -π/2) respectively. Find the area of 🔺OAB.

The answer provided = (15√3)/4

lim (x→∞) [√(16x²+5x-x)/2x]

given answer -7 or 2

Given that z is an imaginary root of the equation x⁵=1 and z≠1, find the value of z+z^2+z^3+z^4.

given answer is -1

A circle with center on the x-axis passes through point A(-1,1) and B(1,3). Find the equation of this circle.

Show that the curve of the equation=3/(2sinθ-cosθ) is a straight line

If the formula of sulfate of a metal is Rn(SO₄)m. What is the formula of the chloride of R?

Find the principal values of am(4+3i)^(1/3)

(am is amplitude)

A wire of length 6m is cut to form 15 squares and arranged in order of increasing size. Suppose the difference between the perimeters of any two consecutive squares is 4cm, find the length in cm of the side of the smallest square.

x^8=1, one root is α=cosπ/4+i sinπ/4. Prove that the roots can be expressed as 1+α+α²+α³+......+α⁷ if can also represent them on Argand diagram .Prove that also 1+α+α²+α³+......+α⁷=0