Question

x varies directly with y and inversely with the square of z for x= 2,y=3 the value of z is 8.find x for y is 6 and z is 2​

Answer 1

Answer:

160

Step-by-step explanation:

x=k.yz2

⇒10=k.414×4

∴k=490

Now, x=490×167×7=160

Answer 2

Answer:

Required value of x is 64

Step-by-step explanation:

Given, x varies directly with y

So, x varies y

It is also given that x varies inversely with the square of z

So,x varies $\frac{1}{ {z}^{2} }$

We can write,

x varies $\frac{y}{ {z}^{2} }$

Or,

$x = \frac{ky}{ {z}^{2} } .....(1)$

Again given,x= 2,y=3 the value of z is 8

So,

$2 = \frac{k \times 3}{ {8}^{2} } \\ 2 = \frac{3k}{64} \\ k = \frac{128}{3}$

Again,y is 6 and z is 2

So from equation (1),

$x = \frac{128}{3} \times \frac{6}{ {2}^{2} } \\ = \frac{128}{3} \times \frac{6}{4} \\ = 32 \times 2 \\ = 64$

This is a problem of Algebra.

Some important Algebra formulas,

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Know more about Algebra,

1) https://brainly.in/question/13024124

2) https://brainly.in/question/1169549

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