Question

(TUSDAY 22ND JUNE, 2021) Find r, if 6r78 = 5119 (A) 6 (B) 5 (C) 3 (D) 2 2. If p + 1, 2p - 10, 1-4p² are the three consecutiv terms of an arithmetic progression, find the possib values of p (A) -4, 2 (B) -3, 4/11 (C)-11/4, 2 (D) 5, -3 A train moves from P to Q at an average speed 90km/h and immediately returns from Q to P throu the same route at an average speed of 45km/h. F the average speed for the entire journey (A) 55 km/h (B) 60.00km/h (C) 67.50km/h (D) 75.00km/h When a polynomial f(x) is divided by (2x -3), quotient is (x2 - x + 2), the remainder is -1. find (A) 2x³ - 5x² + 7x-5 (B) 2x³ - 5x² + 7x - 7 (C) 2x³ 3x + 7 (D) 2x³-5x² - 7x-7 A line perpendicular to the line of gradient 3/2 gh the point (), () find the equation​

Answer 1

Hello,

Explanation:

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2)

If p + 1, 2p - 10, 1-4p² are the three consecutiv terms of an arithmetic progression, find the possib values of p

(A) -4, 2 (B) -3, 4/11 (C)-11/4, 2 (D) 5, -3

Let's say x the first term, a the commun difference.

`\left \{\begin {array} {ccc}x&=&p+1\\x+a&=&2p-10\\x+2a&=&1-4p^2\\\end {array} \right.\\\\----------------\\\left \{\begin {array} {ccc}x&=&p+1\\a&=&p-11\\p+1+2p-22&=&1-4p^2\\\end {array} \right.\\\\----------------\\4p^2+3p-22=0\\\Delta=3^2-4*4*(-22)=361=19^2\\\\p=(-3+19)/(8) =2\ or\ p=(-3-19)/(8) =(-11)/(4)\\\\Answer\ is\ \boxed{C}`

3)

A train moves from P to Q at an average speed 90km/h and immediately returns from Q to P through the same route at an average speed of 45km/h. F the average speed for the entire journey (A) 55 km/h (B) 60.00km/h (C) 67.50km/h (D) 75.00km/h

Let's say d the distance PQ, t1 the time going, t2 the time returning,

v the average speed:

`d=90*t_1\\d=45*t_2\\2d=90*t_1+45*t_2\\since\ 2d=v*(t_1+t_2)\\\\v=(2)/((1)/(90)+(1)/(45) ) =(2*90)/(3) =60\ (km/h)\\\\Answer\ is\ \boxed{C} \\`

4)

When a polynomial f(x) is divided by (2x -3), quotient is (x2 - x + 2), the remainder is -1. find

(A) 2x³ - 5x² + 7x-5 (B) 2x³ - 5x² + 7x - 7 (C) 2x³ 3x + 7 (D) 2x³-5x² - 7x-7

`f(x)=(2x-3)*(x^2-x+2)-1\\=2x^3-2x^2+4x - 3x^2+3x-6-1\\=2x^3-5x^2+7x-7\\\\Answer\ is\ \boxed{B}\\`