Tell whether the angles are adjacent or vertical. Then find the value of x.

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

Let u = 14. What is the value of 4u?

77julia77 [94]

Answer: B 56

Step-by-step explanation:

3 0

4 years ago

Read 2 more answers

Pls answer attached question

BartSMP [9]

Answer:

It's a horizontal line passing through 4 on the y-axis.

Simply place a ruler at 4 and draw a straight line from left to right, which passing through the number 4.

6 0

3 years ago

Help me!!! Please and thank you!!!

Novay_Z [31]

Answer:

Third option is correct: 1 / (t+4)^2

Step-by-step explanation:

This equation can be written as the following:

(t+3)/(t+4)*(1/t^2+7t+12)

We know this because of the division of fractions. For example:

(1/y)/(1/x) = (1/y)*(x/1)

Now that we know this, we can advance.

Now we have to try to factor (t^2+7t+12)

We can make this into (t+3)(t+4)

Ah! Perfect! There is a t+3 in the denominator of the first fraction!

We can now cancel these out.

Now our equation looks like this:

(1 / t+4) * (1 / t+4)

This can also be written as 1^2 / (t+4)^2 = 1 / (t+4) ^2

So the correct option is the third one.

6 0

4 years ago

The function of f is defined as follows

Alborosie

Answer:

f(-121) = -5

f(31) = 3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Function Notation

Step-by-step explanation:

Step 1: Define

f(x) = ∛(x - 4)

f(-121) is x = -121

f(31) is x = 31

Step 2: Evaluate

f(-121)

Substitute in x: f(-121) = ∛(-121 - 4)
[Radical] Subtract: f(-121) = ∛(-125)
[Radical] Evaluate: f(-121) = -5

f(31)

Substitute in x: f(31) = ∛(31 - 4)
[Radical] Subtract: f(31) = ∛27
[Radical] Evaluate: f(31) = 3

7 0

3 years ago