Question

y = A + B where A and B vary directly and inversely respectively with x; x = 1 when y = 11 and x = 2 when y = 13. The value of y when x = 3 is

Answer 1

Answer:

given

A varies directly w.r.t. x

A cx x

A = ax

B varies inversely w.r.t x

B cx 1/x

B = b/x

hence, y = ax + b/x

given, when x= 1, y = 11

11 = a + b, or

a + b = 11...........(1)

again when x= 2, y = 13

2a + b/2 = 13

4a + b = 26.........(2)

from (1) and (2)

3a = 15

a= 5

b = 26-4a = 26-20

b = 6

hence,

y = 5x + 6/x

when x = 3

y = 5*3 + 6/3

= 15 + 2

y = 17

Answer 2

The value of y when x = 3 is 17

Given, $y = A + B$

Also $A\propto x\ and\ B\propto \frac{1}{x}$

So, let $A=ax\ and\ B=\frac{b}{x}$

Where a and b are some constants

So, $y=ax+\frac{b}{x}$

Now, given x = 1 when y = 11

$11=a+b$ ..(1)

And, $13=2a+\frac{b}{2}$ ..(2)

Multiplying equation (2) and subtracting equation (1) from it

$13\times 2-11=2(2a+\frac{b}{2})-(a+b)\\\Rightarrow 26-11=4a+b-a-b\\\Rightarrow 15=3a\\\therefore a=\frac{15}{3}=5$

From equation (1),

$b=11-a\\\therefore b=6$

$\therefore y=5x+\frac{6}{x}$

Now, x=3

$\therefore y=3a+\frac{b}{3}\\\Rightarrow y=3\times 5+\frac{6}{3}\\\therefore y=15+2=17$

To learn more about linear equations from the given link

https://brainly.in/question/3145580

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