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2 years ago

How many ways can you make a 3 letter arrangements out of the letters in the word trapezoid

Mathematics

1 answer:

seropon [69]2 years ago

7 0

504

i just googled an old lesson i had done

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A rectangular storage container with an open top is to have a volume of 24 cubic meters. The length of its base is twice the wid

Mariana [72]

Answer:

419.25

Step-by-step explanation:

The calculation of the cost of materials for the cheapest such container is shown below:-

We assume

Width = x

Length = 2x

Height = h

where, length = $2 \times width$

Base area = lb

= $2x^2$

Side area = 2lh + 2bh

= 2(2x)h + 2(x)h

= 4xh + 2xh

Volume = 24 which is lbh = 24

$h = \frac{24}{2x^2} \\\\ h = \frac{12}{x^2}$

Now, cost is

$= 13(2x^2) + 9(4xh + 2xh)\\\\ = 13(2x^2) + 9(4x + 2x)\times \frac{12}{x^2} \\\\ = 26x^2 + \frac{648}{x}$

now we have to minimize C(x)

So, we need to compute the C'(x)

$= 52x - \frac{648}{x^2}$

C"(x) $= 52x - \frac{1,296}{x^3}$

now for the critical points, we will solve the equation C'(x) = 0

$= 52x - \frac{648}{x^2} = 0\\\\ x = \frac{648}{52}^{\frac{1}{3}}$

$C" = ((\frac{648}{52} ^{\frac{1}{3} } = 52 + \frac{1296}{(\frac{648}{52})^\frac{1}{3} )^3}\\\\ = 52 + \frac{1296}{\frac{648}{52} } >0$

So, x is a point of minima that is

= $(\frac{648}{52} )^\frac{1}{3}$

Now, Base material cost is

$= 13(2x^2)\\\\ = 26(\frac{648}{52} )^\frac{2}{3}$

= 139.75

Side material cost is

$= \frac{648}{x} \\\\ = \frac{648}{(\frac{648}{52})^\frac{1}{3} }$

= 279.50

and finally

Total cost is

= 139.75 + 279.50

= 419.25

4 0

2 years ago

What is 2s+(−4s) 2s+(−4s)?

algol13

It’s -4 because you need to like distribute then add like terms, etc.

3 0

2 years ago

Find the value of x. If necessary, you may learn with the markings on a figure indicate.

love history [14]

Answer:

112

Step-by-step explanation:

6 0

2 years ago

Determine the equation of the circle with radius 99 and center (-1,-8)(−1,−8).

kumpel [21]

<h2>Equations of Circles</h2>

Generally, you'd see the equation of a circle organized in the following format:

$(x-h)^2+(y-k)^2=r^2$

$(h,k)$ is the center
$r$ is the radius

To determine the equation given the center and the radius:

Plug both pieces of information into the general equation
Simplify

<h2>Solving the Question</h2>

We're given:

Radius: 99
Center: (-1,-8)

Plug the radius and center into the equation as r and (h,k):

$(x-(-1))^2+(y-(-8))^2=99^2\\(x+1)^2+(y+8)^2=9801$

<h2>Answer</h2>

$(x+1)^2+(y+8)^2=9801$

7 0

1 year ago

The volume of cube is 343 cubic centimeters.What is the suface area of the cube

Ann [662]

The cube root of 343 is 7.
One side has an area of 7*7 = 49 square cm
There are 6 sides to a cube
6 * 49 is the surface area = 294

7 0

2 years ago