A graph of a cumulative frequency distribution is called
A graph of a cumulative frequency distribution is called an ogive.
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Find the unit vector perpendicular to each of the vectors 6i + 2j + 3k and 3i – 2k.
A vector is a quantity that has both magnitude, as well as direction. A vector that has a magnitude of... View Article
The formula to find the slant height of the cone is
The slant height of the cone of height h and radius r is given by l = √h2 + r2.
Can two obtuse angles be supplementary?
No, two obtuse angles cannot be supplementary angles.
The diagonal AC of a parallelogram ABCD bisects angle A. Show that it bisects angle C also.
Given a parallelogram ABCD. ∠1 = ∠2 —- (1) To show that AC bisects ∠C that is ∠3 = ∠4.... View Article
Given that kx (x – 2) + 6 = 0 has real and equal roots, the root is
The given expression is \(\begin{array}{l}\mathrm{kx}(\mathrm{x}-2)+6=0 \\ \mathbf{k} \mathbf{x}^{\mathbf{2}}-\mathbf{2 k x}+\mathbf{6}=\mathbf{0}\\ \mathbf{a}=\mathbf{k}, \mathbf{b}=-\mathbf{2 k}, \mathbf{c}=\mathbf{6}\\ b^{2}-4 a c=0\\ (-2 \mathbf{k})^{2}-4 \mathbf{k}(6)=\mathbf{0}\\... View Article
Without actually calculating the cubes, find the value of the following: ((- 12)3 + (7)3 + (5)3).
The given expression is \(\begin{array}{l}\begin{array}{l} \begin{array}{l} (-12)^{3}+(7)^{3}+(5)^{3} \\ \mathbf{a}=-\mathbf{1 2}, \mathbf{b}=\mathbf{7}, \mathbf{c}=\mathbf{5} \end{array}\\ \mathbf{a}+\mathbf{b}+\mathbf{c}=(-\mathbf{1 2})+\mathbf{7}+\mathbf{5}=\mathbf{0}\\ \begin{array}{l} \mathbf{a}^{3}+\mathbf{b}^{3}+\mathbf{c}^{3}=\mathbf{3 a b c},... View Article
The smallest rational number is
The smallest rational number doesn’t exist.
The value of tan 30 tan 60 is
tan 30 tan 60 = (1 / √3) √3 = 1
If sec α and cosec α are the roots of the equation x2 – px + q = 0, then prove that p2 = q (q + 2).
The given equation is x2 – px + q = 0 sec α and cosec α are the roots of the equation.... View Article
The harmonic mean of the roots of the equation (5 + √2) x2 – (4 + √5) x + 8 + 2 √5 = 0 is
Let \(\begin{array}{l} \alpha, \ \beta \end{array} \) be the roots of given quadratic equation. \(\begin{array}{l} \alpha+\beta=(4+\sqrt{5}) /(5+\sqrt{2})\\ \alpha \beta=\frac{8+2 \sqrt{5}}{5+\sqrt{2}}\\... View Article
Simplify a (a2 + a + 1) + 5 and find its value for a = 1.
Consider \(\begin{array}{l}\mathbf{a}\left(\mathbf{a}^{2}+\mathbf{a}+\mathbf{1}\right)+\mathbf{5} \\ =\mathbf{a}^{3}+\mathbf{a}^{2}+\mathbf{a}+\mathbf{5} \\ \text { At } \mathbf{a}=\mathbf{1} \\ =\mathbf{1}^{3}+\mathbf{1}^{2}+\mathbf{1}+\mathbf{5} \\ =\mathbf{1}+\mathbf{1}+\mathbf{1}+\mathbf{5} \\ =\mathbf{8} \end{array} \)
Find the multiplicative inverse of (2 – √3) / (2 + √3).
To find the multiplicative inverse of the given expression. \(\begin{array}{l}\begin{array}{l} \frac{2-\sqrt{3}}{2+\sqrt{3}} \times \frac{1}{\frac{2-\sqrt{3}}{2+\sqrt{3}}}=\frac{2-\sqrt{3}}{2+\sqrt{3}} \times \frac{2+\sqrt{3}}{2-\sqrt{3}}=1\\ \text { Hence, the multiplicative... View Article
Solve 4z + 3 = 6 + 2z for the value of z.
4z + 3 = 6 + 2z 4z – 2z = 6 – 3 2z = 3 z = 3... View Article
Two supplementary angles differ by 48 degrees. Find the angles.
The two supplementary angles are differed by 48 degrees. Let the angle measured is x degrees. Its supplementary angle will... View Article
If 2x + 3 = x – 4 then the value of x is
2x + 3 = x – 4 ⇒ 2x – x = – 4 – 3 ⇒ x = –... View Article
If nC8 = nC2 find nC2.
The given expression is of the form of \(\begin{array}{l}\begin{array} { }^{\mathrm{n}} \mathrm{C}_{\mathrm{a}}={ }^{\mathrm{n}} \mathbf{C}_{\mathrm{b}} \Rightarrow \mathbf{a}=\mathbf{b} \text { or }... View Article
How many lines of symmetry does an octagon have?
A regular octagon has 8 lines of symmetry.
Explain the scalar product of two vectors.
The dot product/scalar product of two vectors is the product of the magnitude of 1 vector and the magnitude of... View Article
The standard form of 192 / – 168 is
192 / – 168 = – 192 / 168 = – [2 * 3 * 4 * 8] / [2... View Article
