Jean Monnet worksheet - Linear function

A perfume bottle has a pyramidal shape with a square base with a side of 5 cm and a height of h=6 cm. What is the volume of the bottle?[br]What is the volume of the bottle if its height is 5 cm? But8 cm? But 10 cm?[br]Describe the function that defines the volume of the bottle depending on its height.[br][br]

What is the maximum domain of definition of the function ?

The volume of the bottle with h=6 is[br][br][br]

45 30 40 50

The volume of the bottle with h=5 is[br][br][br]

125 [math]\frac{25\sqrt{3}}{3}[/math] 40 [math]\frac{125}{3}\simeq42[/math]

Is V a strictly increasing function?

True False

What is the image of the function [math]V:\left[5;10\right][/math]?

[math]\left[\frac{125}{3};\frac{250}{3}\right][/math] [math]\left[42;83\right][/math] R [math]\left[41;83\right][/math][

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