Let's draw a cuboid

Algebra Level 1

Over the ranges

$\begin{aligned} -1 \leq & v & \leq 1 \\ -2 \leq & u & \leq -0.5 \\ -2 \leq & z & \leq -0.5 \\ \end{aligned}$

what is the range of $w = \frac {vz}{u}$ ?

[-2,-0.5]

[-0.5,2]

[-4,4]

[-4,2]

2 solutions

Chew-Seong Cheong
Sep 18, 2014

We need to find:

$w_{min} \le w \le w_{max} \Rightarrow \dfrac{(-1)(-2)}{-0.5} \le w \le \dfrac{(1)(-2)}{-0.5} \Rightarrow -4 \le w \le 4$ .

I understand we need to find $w_{min}$ and $w_{max}$ . However, unless I'm forgetting an elementary step, aren't the minimum values of z and u substituted incorrectly (and the maximum value of z, too)?

Hailey Levin - 5 years, 4 months ago

It is not about substitution of the actual maxima but the absolute values. The trick is to get $\pm \dfrac{|Max(vz)|}{|min(u)|}$ . Check the final results if you substitute the actual values.

Chew-Seong Cheong - 5 years, 4 months ago

Satyam Kumar
Jan 4, 2016

if v is 1, z is -0.5 and u is -0.1 then w becomes 5 and if we put u=0, w becomes infinity.......... the question is wrong.

But $u \le - 0.5$ and cannot be $-0.1$ .

Chew-Seong Cheong - 5 years, 4 months ago

Let's draw a cuboid

2 solutions

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