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Rus_ich [418]
2 years ago
5

A truck's gas tank holds 50 gallons of gas. if one gallon takes 30 seconds to pump, how many minutes will it take to fill the em

pty tank?
Mathematics
1 answer:
umka2103 [35]2 years ago
7 0
To find how long it will take to fill the tank, you can use the idea that every 30 seconds will get you one gallon closer to being full.

This means to fill 50 gallons, you will need 50 groups of 30 seconds.  

50 x 30 = 1500 seconds

1500/60 = 25 minutes.

It will take 25 minutes.  

You could also think of it as filling 2 gallons every minute.  It would take 25 of these.
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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

6 0
2 years ago
A small cube with side length 6y is placed inside a larger cube with side length 4x^2. What is the difference in the volume of t
fomenos

the different volume is the numbers. 4*2*6=?


3 0
2 years ago
Read 2 more answers
The volume of a cylinder is given by the formula mc023-1.jpg, where r is the radius of the cylinder and h is the height. Suppose
Simora [160]
Volume of a cylinder = π r² h

Given:
radius = (x+8)
height (2x + 3)

Volume of a cylinder = π * (x+8)² * (2x + 3)

V = π * (x+8)(x+8) * (2x+3)
V = π * (x² + 8x + 8x + 64) * (2x + 3)
V = π * (x² + 16x + 64) * (2x + 3)
V = π * (2x³ + 32x² + 128x + 3x² + 48x + 192)
V = π * (2x³ + 32x² + 3x² + 128x + 48x + 192)
V = π * (2x³ + 35x² + 176x + 192)

5 0
2 years ago
For what values of m does the graph of y = 3x^2 + 7x + m have two x-intercepts? a) m>12/49 b) m<12/49 c) m<49/12 d) m&g
den301095 [7]

The quadratic formula, has a part we call the "discriminant" defined by the variables that are inside the square root, and is denotated by "delta":

<span>Δ=<span>b2</span>−4ac</span> Whenever we solve a quadratic equation that is complete and we analyze the discriminant, we can get 3 scenarios: <span>if→Δ>0<span>=></span>∃<span>x1</span>,<span>x2</span>/a<span>x2</span>+bx+c=0</span> This just means: "if the discriminant is greater than zero, there will exist two x-intercepts" And for the second scenario: <span>if→Δ=0→∃<span>xo</span>/a<span>x2</span>+bx+c=0</span> This means: "if the discriminant is equal to zero, there will be one and only one x-intercept" And for the last scenario: <span>if→Δ<0→∃x∉R/a<span>x2</span>+bx+c=0</span> This means that :"if the discriminant is less than zero, there will be no x-intercepts" So, if we take your excercise and analyze the the discriminant: <span>3<span>x2</span>+7x+m=y</span> we will find the values that satisfy y=0 : <span>3<span>x2</span>+7x+m=0</span> And we'll analyze the discriminant: <span>Δ=<span>72</span>−4(3)(m)</span> And we are only interested in the values that make the discriminant equal zero: <span><span>72</span>−4(3)(m)=0</span> All you have to do is solve for "m".

6 0
2 years ago
The cost of coffee is determined by the type of coffee beans that are mixed together. The cost of a local mix of Arabica and Rob
Andreyy89

Answer:

If a mixture contains 1000 pounds of Arabica beans, there should be <u>250 pounds of Robusta beans</u> in the mixture.

Step-by-step explanation:

700A+1,200R=1,000,000

700(1000) +1,200R=1,000,000 - First, plug in the A value and simplify .

700000+1,200R=1,000,000 - Then, subtract 700,000 from both sides.

1,200R=300,000 - Finally, divide by 1,200 on both sides of the equation.

R=250  - This is your value for R, or the Robusta beans.

<u>250 pounds of Robusta beans</u>

Hope this helps!

7 0
2 years ago
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