Find the value of x and then the angle measurements of angle 1 and angle 2.

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 bin is constructed from 48 square feet of sheet metal, so:

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, the dimensions of the largest volume of such a bin is:

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

A surveyor is measuring the distance across a canyon. He sets up two similar right triangles and finds that the length of CD = 1

Citrus2011 [14]

The length side AB is 64 ft , Option D is the correct answer.

<h3>What is a Right triangle ?</h3>

A triangle that has one angle 90 degree is called Right angled Triangle.

From the figure it can be seen that

The triangle CDE is a right Triangle

Applying Pythagoras theorem to find the length of CE

CE² = 12² + 16²

CE = 20 ft

As both the triangles are similar therefore the ratio of the sides will be equal

BC : CD = AC : CE

48 / 12 = AC / 20

AC = 80ft

As Triangle ABC is also a right angled triangle

Applying Pythagoras theorem to find the length of AB

AC² = BC² +AB²

6400 = 48² +AB²

AB² = 4096

AB = 64 ft

Therefore Option D is the correct answer.

To know more about Right Triangle

brainly.com/question/6322314

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3 0

2 years ago

Sadie has 8 quarts of lemon lime juice and 8 cups of orange juice how many more quarts of lemon lime juice will she use than ora

AnnZ [28]

Answer:

8-2=6 the answer is 6 because there are 4 cps in 1 quart

Step-by-step explanation:

4 0

3 years ago

Which of the following can be modeled with exponential function ? select all that apply.

Ainat [17]

Answer: Please include more information

Step-by-step explanation:

4 0

3 years ago

A tank contained 80 liters of water. The function “w” represents the relationship between “t”, time in minutes, and the amount o

Leni [432]

w(t) tells you the amount of water w at a given time t.

The inverse function tells you at which time t the tank contains an amount of water w.

To get the inverse function, solve the equation

w = 80 - 2.8t

for t :

w = 80 - 2.8t

2.8t = 80 - w

t = (80 - w) / 2.8

t ≈ 28.57 - 0.357 w

The graph of w(t) is a downward-sloping line. The graph of the inverse is also a downward-sloping line, but its intercept (28.57) and slope (-0.357) are both smaller than the intercept and slope of w(t).

8 0

2 years ago