theorem 7

Question: Find the equation of two lines passing through the point (4,5) Answer: The equation of the line through (4,5) with slope m is y - 5 = m(x - 4) The slope of line 2x - y + 7 = 0 is 2. ..

Question: D ABC is a right angled triangle at B, and P is the mid-point of parallel to BC, meeting AB in Q). Answer: Given: D ABC is right angled triangle at B. P is the mid-point of AC. To prove: Construction: Through P, draw a line parallel to BC, meeting AB at Q. Pro..

Question: Prove the converse of mid-point theorem using Basic Proportionality Theorem. That is, prove that the line drawn from the mid-point of one side of a triangle, parallel to the second side, bisects the third side. [2 Mark] Answer: Given: ABC is a triangle..

Question: Answer: Expanding by binomial theorem, we get ..

Using the fundamental theorem of calculus, evaluate ∫ 5 7 3 (x - 3) 2 d x . => - 3 4 or 4 3 or - 4 3 or 3 4..

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

Use Rolle's Theorem to determine the value of c such that f ′ ( c ) = 0, if f ( x ) = x 2 - 15 x + 56 in the interval [7, 8]. => 7 or 0 or 2 15 or 15 2 or 8..

Use Pythagorean theorem to find the length of AC ‾ . => 3 7 units or 6 units or 12 units or 6 2 units..

Use binomial theorem to write the expansion of (2 x + 3 y ) 3 => 8 x 3 + 3 6 x 2 y + 5 4 x y 2 + 2 7 y 3 or 8 x 3 + 2 7 3 or x 3 + 1 8 x 2 y + 1 8 x y 2 + y 3 or 8 x 3 + 3 6 x 2 y + 3 6 x y 2 + 2 7 y 3..

Find the value in the interval, which satisfies the Mean Value Theorem for the function f ( x ) = x ( x 2 - 2 x - 3) on [- 1, 2]. => 2 + 7 3 , 2 - 7 3 or 2 + 7 , 2 - 7 or 3, 1 or 0, - 6 or 4, 1..