2 years ago

Max travels to see his brother's family by car. He drives 216 miles in 4 hours.

Mathematics

1 answer:

LUCKY_DIMON [66]2 years ago

3 0

Answer:

54 mph

Step-by-step explanation:

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Natasha is seeding her backyard. The backyard is square in shape and has an area of 4225 square feet. What is the length of one

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Answer:65ft

Step-by-step explanation:area of a square is =s^2

Therefore 4225=s^2

Find the square root of both sides

√4225=√s^2

Therefore s=65

Each side is 65ft

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2 years ago

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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2 years ago

Michael starts a new paper company. The function fff models the company's net worth (in thousands of dollars) as a function of t

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Answer:

is 0,14

Step-by-step explanation:

i promise

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2 years ago

The cost of a car is $15,570. You plan to make a down payment of $1,500, and a monthly payment of $338.08 for 60 months. What is

Helga [31]

Hi there
1) b
15,570−1,500
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2) a
338.08×60
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3)d
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4) c
338.08×60+1,500
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2 years ago

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