I need help with this please

Mathematics

1 answer:

Gnoma [55]3 years ago

4 0

Answer:

He started with 180.

Step-by-step explanation:

If 90 is 50% of what he started with, then the other 50% is 90

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1. A box without a top is to be made from a rectangular piece of cardboard, with dimensions 3 in. b)

Soloha48 [4]

Answer:

a) The volume of the box is represented by $V = 21\cdot x - 20\cdot x^{2}+4\cdot x^{3}$ .

b) A side length of 0.653 inches leads to the maximum volume of the box: 6.299 inches.

Step-by-step explanation:

a) The volume of the box ( $V$ ), in cubic inches, is modelled by the equation for the cuboid:

$V = (3-2\cdot x) \cdot (7-2\cdot x) \cdot x$ (1)

Where $x$ is the side length of the cutted square corners, in inches.

$V = (21 - 20\cdot x + 4\cdot x^{2})\cdot x$

$V = 21\cdot x - 20\cdot x^{2}+4\cdot x^{3}$

The volume of the box is represented by $V = 21\cdot x - 20\cdot x^{2}+4\cdot x^{3}$ .

b) The method consist in graphing the polynomial and looking for a relative maximum. We graph the equation found in a) by means of a graphic tool. We present the outcome in the image attached below. According to this, a side length of 0.653 inches leads to the maximum volume of the box: 6.299 inches.