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Questions and Answers
What is the slope of line AC?
What is the slope of line AC?
- $rac{3}{2}$
- $rac{1}{3}$
- $2$
- $rac{1}{2}$ (correct)
What is the slope of line PD?
What is the slope of line PD?
- $1$
- $2$
- $rac{1}{2}$
- $0$ (correct)
What is the slope of line BC?
What is the slope of line BC?
- $rac{1}{2}$
- $1$
- $2$
- $-rac{1}{2}$ (correct)
What is the slope of line EP?
What is the slope of line EP?
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What is the equation of line AP?
What is the equation of line AP?
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What is the equation of line BC?
What is the equation of line BC?
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What is the value of $k$ in the given matrix equation?
What is the value of $k$ in the given matrix equation?
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What is the value of $p$ and $q$ in the given equation?
What is the value of $p$ and $q$ in the given equation?
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What is the value of $27 \sec 2 - 8 \csc 2$?
What is the value of $27 \sec 2 - 8 \csc 2$?
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What is the value of $5 \sin 2 - 2$?
What is the value of $5 \sin 2 - 2$?
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What is the value of $4 \cos 2 - 1$?
What is the value of $4 \cos 2 - 1$?
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What is the intersection of the sets $S_1$ and $S_2$?
What is the intersection of the sets $S_1$ and $S_2$?
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What is the value of $x$ in the equation $x^2 - 3x + 2 = 0$?
What is the value of $x$ in the equation $x^2 - 3x + 2 = 0$?
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Study Notes
Analytical Geometry
- Slope of AC is infinity, and slope of PD is 0.
- Point D is (2, 2), and point C is (-3, -1).
- Equation of AP is x + 2y = 3, and equation of BC is 3x - y + 8 = 0.
Algebra
- The number of real solutions of the equation e^4x + 4e^3x - 58e^2x + 4ex + 1 = 0 is 2.
- Equation 25sin^4α + 10(1 - sin^2α) = 6 is equivalent to 25sin^2α - 10sin^2α - 10sin^2α + 4 = 0.
- The equation 2^15sin4α + 10(1 - sin^2α) = 6 has solution sin^2α = 4/5.
Inequalities
- Let S1 = {x ∈ R - {1, 2} : (x + 2)(x^2 + 3x + 5) ≥ 0}, and S2 = {x ∈ R : 32x - 3x + 1 - 3x + 2 + 27 ≤ 0}.
- S1 ∪ S2 is equal to (-∞, -2] ∪ [1, 2].
Matrices
- If PQ = kI, then P is an invertible matrix, and Q = kP^(-1).
- adj(P) = k, and Q = kP^(-1)I.
Complex Numbers
- If α is a 7th root of unity, then 1 + α + α^2 + ... + α^6 = 0.
- The equation x^2 + x + 2 = 0 has solutions p and q, where p = α + α^2 + α^3, and q = α^4 + α^5 + α^6.
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