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2 years ago

The equation y=2x represents a set of data. Which statement is not true?

Mathematics

2 answers:

TEA [102]2 years ago

8 0

D, the initial value is 2

Sonja [21]2 years ago

7 0

Answer:

Option D is correct

The initial value is 2

Step-by-step explanation:

The equation of line passes through the origin is represented by:

y = mx where m is the slope or unit rate .

Direct Proportionality says that:

if $y \propto x$ then the equation of the form is y = kx where k is the constant of proportionality.

Given the equation: $y = 2x$

Then by definition:

m = 2

⇒ Slope on the line is 2.

⇒ the unit rate is 2.

Also, the constant of proportionality is 2.

Therefore, the statement which is not true for the equation y=2x represents a set of data is: The initial value is 2

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A cardboard box without a lid is to have a volume of 16,384 cm3. Find the dimensions that minimize the amount of cardboard used.

Reika [66]

Answer:

The dimensions that minimize the amount of cardboard used is

x = 31 cm , y = 34 cm & Z = 15.54 cm

Step-by-step explanation:

Volume of the cardboard = 16,384 $cm^{3}$

The function that represents the area of the cardboard without a lid is given by

$f (x,y,z) = xy + 2xz + 2yz$ ------ (1)

Volume of the cardboard with sides x, y & z is

$xyz = 16384$

$z = \frac{16384}{xy}$

Put this value of z in equation (1) we get

$f (x,y,z) = xy + 2x(\frac{16384}{xy} ) + 2y(\frac{16384}{xy} )$

$f (x,y,z) = xy + \frac{32768}{y} + 2y(\frac{32768}{x} )$

Differentiate above equation with respect to x & y we get

$f_{x} = y - \frac{32768}{x^{2} }$

$f_{y} = x - \frac{32768}{y^{2} }$

Take $f_{x} = 0 \ and \ f_{y} = 0$

$y - \frac{32768}{x^{2} } = 0$

$y = 32768 \ x^{-2}$ ------ (2)

$x - \frac{32768}{y^{2} } = 0$

$x = 32768 \ y^{-2}$ ------- (3)

By solving equation (2) & (3) we get

$x^{3} = 32768$

x = 31 cm

From equation 2

$y = 32768 \ x^{-2}$

y = 32768 ( $31^{-2}$ )

y = 34 cm

$z = \frac{16384}{xy}$

$z = \frac{16384}{(34)(31)}$

Z = 15.54 cm

Thus the dimensions that minimize the amount of cardboard used is

x = 31 cm , y = 34 cm & Z = 15.54 cm

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Answer:

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Answer:

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