Solve for y,6x+7=-14y

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

Although not so common now, consider a phone plan that does not have unlimited texting. Your base plan costs you $30 a month and

german

Answer:

The bill will be $26070.

Step-by-step explanation:

Your base plan costs you $30 a month

And each text sent or received is only 12 cents or $0.12.

Let the messages sent be = x

So, cost for messages become = $0.12x$

Let total bill cost be = y

Now, total bill will comprise of monthly plan charges plus message charges.

So, equation forms:

$y=30+0.12x$

Now, given is that In one month 217,000 messages were sent between two brothers in Philadelphia.

So, their approximate bill will be :

$y=30+0.12(217000)$

=> $y=30+26040$

=> y = 26070

Therefore, bill will be $26070.

5 0

3 years ago

Help me out pleasee!!!

Viefleur [7K]

T=sin⁻¹(36/85)=25.06

5 0

3 years ago

A store has clearance items that have been marked down by 60% they having a sale, advertising an additional 30% off clearance it

bagirrra123 [75]

The original price is 100% of the price. If the price is marked 60% off, then you pay 40% of the original price.

An item costs x dollars.

With the 60% off discount, it now costs 40% of x, or 0.4x.

Now you apply a 30% discount.

For the second discount, consider the price 0.4x to be the new original price. If the price is now discounted 30%, you will pay 70% of the new original price.

Start with 0.4x.

Now calculate 70% of 0.4x.

70% of 0.4x = 0.70 * 0.4x = 0.28x

After applying the 60% discount and the 30% discount, the item that originally cost x now costs 0.28x. 0.28x is the same as 28% of x. The amount you pay is 28% of the original price.

Answer: 28%

3 0

3 years ago

The table shows information about some children.

Sindrei [870]

Answer:

$P(Age\ 12) = \frac{2}{3}$