Express \(\frac{3}{3 - √6}\) in the form \(x + m√y\)
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2023
\(Differentiate f (x) = \frac{1}{(1 - x^2)^5}\) with respect to \(x\).
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2023
Consider the statements:
x: The school bus arrived late
y: The student walked down to school
Which of the following can be represented by y ⇒ x?
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2023
Given that P = {x : 2 ≤ x ≤ 8} and Q = {x : 4 < x ≤ 12} are subsets of the universal set μ = {x : x ∈ R}, find (P ⋂ Q\(^1\)).
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2023
Find the fifth term in the binomial expansion of \((q + x)^7\).
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2023
A particle began to move at \(27 ms^{-1}\) along a straight line with constant retardation of \(9 ms^{-2}\). Calculate the time it took the particle to come to a stop.
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2023
Given that M is the midpoint of T (2, 4) and Q (-8, 6), find the length of MQ .
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2023
Find the radius of the circle \(2x^2 + 2y^2 - 4x + 5y + 1 = 0\)
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2023
The table shows the operation * on the set {x, y, z, w}.
*
X
Y
Z
W
X
Y
Z
X
W
Y
Z
W
Y
X
Z
X
Y
Z
W
W
W
X
W
Z
Find the identity of the element.
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2023
If\((\frac{1}{9})^{2x-1} = (\frac{1}{81})^{2-3x}\)find the value of x
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2023
Given that \(sin x = \frac{4}{5}\) and \(cos y = \frac{12}{13}\), where x is an obtuse angle and y is an acute angle, find the value of sin (x - y).
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2023
Evaluate \(\int^1_0 x(x^2-2)^2 dx\)
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2023
The distance S metres moved by a body in t seconds is given by \(S = 5t^3 - \frac{19}{2} t^2 + 6t - 4\). Calculate the acceleration of the body after 2 seconds
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2023
Find the equation of the normal to the curve y = \(3x^2 + 2\) at point (1, 5).
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2023
Calculate, correct to one decimal place, the angle between 5 i + 12 j and -2 i + 3 j