Suppose z varies inversely with t and that z=6 when t=8. What is the value of z when t=3?

Question

Suppose z varies inversely with t and that z=6 when t=8. What is the value of z when t=3?

1 Answer

Impact of this question

17873 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-18T04:54:28

$" "$
$z = 16$ $color(red)(z=16$

Explanation:

The general form of an Inverse Variation is given by

$y = \frac{k}{x}$ $color(blue)(y = k/x$ , where $k$ $color(blue)(k$ is an unknown constant with $x \neq 0 and k \neq 0$ $color(red)(x!=0 and k!= 0$

In the equation above, observe that when the value of $x$ $color(blue)x$ is getting larger and larger, $k$ $color(blue)(k$ being a constant, the value of $y$ $color(blue)(y$ will be getting smaller and smaller.

This the reason why it is called an Inverse Variation.

For the problem we are solving, the equation is written as

$z = \frac{k}{t}$ $color(brown)(z= k/t$ , with $k$ $color(brown)(k$ being the Constant of Proportionality

It is given that $z$ $color(brown)z$ varies inversely as $t$ $color(brown)(t$ .

Problem says that $z = 6$ $color(green)(z=6$ when $t = 8$ $color(green)(t=8$

Now you can find $k$ $color(brown)k$ , the constant of proportionality.

Use

$z = \frac{k}{t}$ $color(green)(z=k/t$

$\Rightarrow 6 = \frac{k}{8}$ $rArr 6=k/8$

Rewrite as

$\Rightarrow \frac{6}{1} = \frac{k}{8}$ $rArr 6/1=k/8$

Cross-multiply to solve for $k$ $color(green)(k$ .

$\Rightarrow k \cdot 1 = 6 \cdot 8$ $rArr k*1 =6*8$

$\Rightarrow k = 48$ $rArr k = 48$

Your inverse equation now becomes

$z = \frac{48}{t}$ $color(green)(z=48/t$

Next, we need to determine the value of $z$ $color(green)(z$ when $t = 3$ $color(green)(t=3$

$z = \frac{48}{3}$ $z= 48/3$ , as $t = 3$ $t= 3$

$\Rightarrow z = 16$ $rArr color(red)(z= 16$

which is the required answer.

Hope it helps.

Science

Math

Humanities

... and beyond

Suppose z varies inversely with t and that z=6 when t=8. What is the value of z when t=3?

1 Answer

Explanation:

Related questions

Impact of this question