At lunch Claire is drinking her juice out of an aluminum can She claims that if the radius of the can is doubled, the volume of the can will be greater than if the height of the can is doubled

True

Step-by-step explanation:

Can is shaped in the form of a cylinder :

Volume, V of a cylinder = πr²h

Volume if radius is doubled and height remains the same :

r = 2r

V = π(2r)²h

V = 4πr²h

Volume if height is doubled and radius remains the same ;

V = πr²h

If h = 2h

V = 2πr²h

Radius doubled ; V = 4πr²h

Height doubled ; V = 2πr²h

Hence, volume of can is greater with Radius doubled than with height doubled.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

9 x 8 divided by (5-3)=36