theorem 7

Use the rational zero theorem to list all the possible rational zeros for f ( x ) = x 4 + 8 x 3 - x 2 - 6. =>± 1; ± 2; ± 4 or ± 1; ± 2; ± 5; ± 10 or ± 1; ± 2; ± 3; ± 6 or ± 1; ± 7..

Use the fundamental theorem of calculus, to evaluate ∫ 2 5 1 4 x 2 - 9 dx . => 1 12 [ ln 7 + ln 13 ] or 1 12 (ln 13) or 1 6 (ln 7) or 1 12 [ 2 ln 7 + ln 13 ] or 1 12 [ 2 ln 7 - ln 13 ]..

+ 90 + m ∠ N = 180. Step 5: Solving gives m ∠ N = 0. Step 6: This means that there is no ΔLMN, which contradicts the given statement. Step 7: So the assumption that ∠ L and ∠ M are both right angles must b => Angle addition postulate or Triangle angle - sum theo..

Question: Solve the following equation: Answer: 4x + 7 = -3 (2x + 1) (By cross-multiplication) 4x+7=-6x-3 4x+6x=-3-7 10x=-10 x=-..

Question: Solve the following equation: 7x+5=3x-25 Answer: ..

Fundamentals of Equations Algebraic and transcendental equations; If f(x) is a polynomial in x, then f(x) =0 is an algebraic equation. Example; x 7 + 5x - 2=0. If f(x) contains algebraic and non algebraic functions namely exponential, logarithmic, trigonometric and inverse trigo..

Question: Given D ABC and DE||BC. [2 Mark] AD = 4x - 3 DB = 3x - 1 AE = 8x - 7 EC = 5x - 3 Find the value of x. Answer: Since DE||BC, using Basic Proportionality Theorem, we get ..

Degrees of Freedom and Molar Specific Heats - Molecule Example Degrees of Freedom Predicted Molar Specific heats Translational Rotational Total (f) Cv Cp = Cv + R Monatomic He 3 0 3 3/2 R 5/2 R Diatomic O 2 3 2 5 5/2 R 7/2 R Polyatomic CH4 3 3 6 3 R 4 R The above table shows the predictio..

to q is the side AB. The hypotenuse of the D ABC is the side AC. Now, let us write down the trigonometrical ratios with the help of the above triangles: (i) Sine q : It is defined as the ratio of the side opposite to q and the hypotenuse. i.e., In short we write sin (ii) Cosine q : It is defined as..