a2 +b2=?
Question
A fruit vendor bought 60 kg of mangoes at 48 per kg he sold 70% of mangoes at 60per kg and the remaining mangoes at 35per kg find fruit vendor's gain or loss per centon the whole transaction
Maths
Nov. 22, 2019, 11:01 p.m.
Answer
1) Show that 𝑥2 + 𝑥𝑦 − 6𝑦2 − 𝑥 − 8𝑦 − 2 = 0 represent a line pair and calculate their angle of intersection.
2) Show that the line pair through the origin respectively perpendicular to the line pair 𝑎𝑥2 + 2ℎ𝑥𝑦 + 𝑏𝑦2 = 0 is given by 𝑏𝑥2 − 2ℎ𝑥𝑦 + 𝑎𝑦2 = 0.
3) The straight line 𝑙𝑥 + 𝑚𝑦 + 𝑛 = 0 cuts the distinct pair of straight lines
𝑎𝑥2 + 2ℎ𝑥𝑦 + 𝑏𝑦2 = 0 at the points P and Q. If the angle OPQ equals the angle OQP,O being the origin. Show that ℎ(𝑙2− 𝑚2)= 𝑙𝑚(𝑎 − 𝑏).
4) Translate to the parallel axes through (4,-2) and hence simplify
16𝑥2 + 25𝑦2− 128𝑥 + 100𝑦 − 44 = 0.
5) Rotate axes for each of the following through the angle indicated.
I. 𝑥2 + 4𝑥𝑦 + 𝑦2 = 2 ; 450
II. 𝑥𝑦 + 𝑥 + 𝑦 = 0 ; 450
III. 4𝑥2 + 4𝑦2 = 17𝑥𝑦 ; 450
Maths
Nov. 22, 2019, 10:31 p.m.
Answer
The position vectors of the points A, B, C, D are 2𝒊 + 4𝒋 + 2𝒌, 𝒊 + 2𝒋 + 𝒌,
4𝒊 + 3𝒋 − 2𝒌, 3𝒊 + 𝒋 − 3𝒌. Show that AB is parallel to CD and that ABCD is a
parallelogram.
Maths
Nov. 22, 2019, 9:06 p.m.
Answer