Mathematics: If x and y are two positive real numbers such that x 2 +4y 2 =17 and xy =2, then find the value of x- 2y. a. 3 b. 4 c. 8 d. 9

If x and y are two positive real numbers such - id7176968, maxwellirowa10oy9yaf

kprincess16r

30.01.2022

The value of x- 2y is a. $\pm 3$ .

Step-by-step explanation:

Given: x and y are two positive real numbers such that x^2+4y^2=17 and xy= 2 .

Consider $(x-2y)^2=x^2-2(x)(2y)+(2y)^2\ \ \ [(a+b)^2=(a^2-2ab+b^2)]$

=x^2-4xy+4y^2

=x^2+4y^2-4(xy)

Put x^2+4y^2=17 and xy= 2 , we get

(x-2y)^2=17-4(2)=17-8=9

$\Rightarrow\ (x-2y)^2=9$

Taking square root on both sides , we get'

$x-2y= \pm3$

Hence, the value of x- 2y is a. $\pm 3$ .

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dadnapper

04.06.2023

the time of fall of the stone is 15 s.

Step-by-step explanation:

Given;

height through which the stone was dropped, h = 3,600 ft

the initial velocity of the stone, u = 0

The time of fall of the stone is calculated using the following kinematic equation;

h = ut + ¹/₂gt²

h = 0 + ¹/₂gt²

h = ¹/₂gt²

where;

g is acceleration due to gravity = 32.17 ft/s²

$t = \sqrt{\frac{2h}{g} } \\\\t = \sqrt{\frac{2\times 3,600 \ ft}{32.17 \ ft/s^2} }\\\\t =14.96 \ s = 15 \ s$

Therefore, the time of fall of the stone is 15 s.

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