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3 years ago

Evaluate if x = 1 , y = 3 , and z = 5 |5z - 2y|

Mathematics

1 answer:

Aleks04 [339]3 years ago

4 0

Answer:

Step-by-step explanation:

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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

3 years ago

the length of a rectangle is 50 feet less than its width. If the perimeter of the field is 840 feet, find the length of the fiel

LiRa [457]

$look\ at\ the\ picture\\\\2a+2(a-50)=840\\\\2a+2a-100=840\\\\4a-100=840\ \ \ /+100\\\\4a=940\ \ \ \ /:4\\\\a=235\ (ft)\\\\a-50=235-50=185\ (ft)\\\\Answer:lenght=185\ ft;\ width=235\ ft.$

8 0

2 years ago

HELPPPPPPPPP PLEASE!!! :(

erastovalidia [21]

Answer:

x = 25

Step-by-step explanation:

Given:

∠A = ∠B (Vertically opposite angles)
∠A = (7x - 8)°
∠B = (6x + 17)°

Since ∠A is equivalent to ∠B...

$\implies (7x - 8)= (6x + 17)$

Open the parenthesis:

$\implies 7x - 8= 6x + 17$

Add 8 both sides:

$\implies 7x - 8 + 8= 6x + 17 + 8$

Simplify both sides:

$\implies 7x = 6x + 25$

Subtract 6x both sides:

$\implies 7x - 6x = 6x - 6x + 25$

Simplify both sides:

$\implies x = 25$

7 0

2 years ago

Read 2 more answers

Suppose f(x)= 4x/3+5 and g(x) = x/3 +1. solve for x when f(x)=g(x)

yuradex [85]

$\bf \begin{cases}
f(x)=\cfrac{4x}{3}+5\\\\
g(x)=\cfrac{x}{3}+1
\end{cases}\qquad f(x)=g(x)\implies \cfrac{4x}{3}+5=\cfrac{x}{3}+1$

solve for "x" then

4 0

3 years ago

Solve for x:

slava [35]

Answer:

Step-by-step explanation:

Any value of x makes the equation true.

4 0

3 years ago