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2 years ago

12

Sarah needs 11 bottles of water from the store. sarah can only carry three at a time. what's the minimum number of trips sarah n

eeds to make to the store?

1 answer:

Ratling [72]2 years ago

5 0

11/3 = 3 2/3....so the minimum number of trips would be 4

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Y = mx + b
y - b = mx
(y - b) / x = m

so its : m = (y - b) / x.....or m = (y/x) - (b/x)

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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.

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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

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Answer:

Decreased.

Step-by-step explanation:

Decrease means to go down or take away, therefore in a mathematical equation, it would be represented by a negative integer.

Change could be positive or negative

each is a singular description word

and drastically is just describing how fast.

have a good day!

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2 years ago

When alice completes each level in her favorite video game she wins 3 extra lives and 6 gold coins

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The answer is 24. because you multiply 8 and 6 <span />

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The following situation can be modeled by a linear function. Write an equation for the linear function and use it to answer the

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Answer:

Part 1) Option B. The independent variable is time (t), in minutes, and the dependent variable is rental cost (r), in dollars. The linear function that models this situation is r equals to r=0.55x+8

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Step-by-step explanation:

Part 1)

Let

r ------> the rental cost (dependent variable)

t -----> the time in minutes (independent variable)

The linear equation that represent this problem is equal to

r=(5.50/10)t+8

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we have

r=0.55t+8

For r=$25

substitute and solve for t

25=0.55t+8

0.55t=25-8

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Round down

t=30 minutes

Note If you round up to 31 minutes the rental cost exceed $25

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2 years ago