A 13.5-gasoline tank is 4 / 5 full how many gallons will it take to fill the tank

SashulF [63]

Volume = (1/3) * π * r² * h.
= (1/3) * π * 3² * 4.5.
= (1/3) * 127.23450247
= 42.41115 cm^3

7 0

3 years ago

A bin is constructed from sheet metal with a square base and 4 equal rectangular sides. if the bin is constructed from 48 square

kondaur [170]

This is a problem of maxima and minima using derivative.

In the figure shown below we have the representation of this problem, so we know that the base of this bin is square. We also know that there are four square rectangles sides. This bin is a cube, therefore the volume is:

V = length x width x height

That is:

$V = xxy = x^{2}y$

We also know that the <span>bin is constructed from 48 square feet of sheet metal, s</span>o:

Surface area of the square base = $x^{2}$

Surface area of the rectangular sides = $4xy$

Therefore, the total area of the cube is:

$A = 48 ft^{2} = x^{2} + 4xy$

Isolating the variable y in terms of x:

$y = \frac{48- x^{2} }{4x}$

Substituting this value in V:

$V = x^{2}( \frac{48- x^{2} }{x}) = 48x- x^{3}$

Getting the derivative and finding the maxima. This happens when the derivative is equal to zero:

$\frac{dv}{dx} = 48-3x^{2} =0$

Solving for x:

$x = \sqrt{\frac{48}{3}} = \sqrt{16} = 4$

Solving for y:

$y = \frac{48- 4^{2} }{(4)(4)} = 2$

Then, <span>the dimensions of the largest volume of such a bin is:
</span>
Length = 4 ft
Width = 4 ft
Height = 2 ft

And its volume is:

$V = (4^{2} )(2) = 32 ft^{3}$

8 0

3 years ago

There are between 90 and 115 cars in a parking lot. Exactly one-fourth of them are green. Exactly one-eighth of them have a stic

Schach [20]

There are 104 cars in the parking lot.

According to statement there are between 90 and 115 cars on the lot.

So, {X| 90 < x < 115} (This renders an infinite solution set finite)

AND exactly one eight of them have a sticker on the back, so the total number of cars must be evenly divisible by eight.

X ∈ {96, 104, 112,}

AND exactly one fourth of the cars are green, so the number of cars must be evenly divisible by 4. Here all above written numbers are divisible by 4. So, find the mean to calculate the number of cars in the parking lot.

x = (96+104+112)/3

x = 104

There are 104 cars in the parking lot.

Learn more about ELIMINATION METHOD here brainly.com/question/13729904

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5 0

2 years ago

Pleeeeeeeeeaaase help

Zinaida [17]

The correct answer is 110 degrees

The value of X is 115
If we substitute X, then the “equation” would be (115)-5=110 degrees :))))

5 0

4 years ago

What is the markup percent on a diamond for which the markup is $870 and the selling price is $2870?

ryzh [129]

Answer:

30.31%

Step-by-step explanation:

Mark up on selling price is given by markup*100%/selling price

In this case, markup is given as $870 while the selling price is $2870 hence the percentage of narkup to selling price will be given by $\frac {870\times 100}{2870}=30.313588850174\approx 30.31$

Therefore, the percentage of markup to selling price is approximately 30.31%

3 0

3 years ago