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3 years ago

The fan below has been stretched open as far as it will go to form a semi-circle.

Mathematics

1 answer:

Komok [63]3 years ago

5 0

Answer:

Area of each sector= $12.6cm^2$

Step-by-step explanation:

We are given that

Length of each wooden od that connects the center of the fan to its edge ,r=12 cm

Total number of sectors=18

We have to find the approximate area of each sector.

Area of semi-circle= $\frac{1}{2}\pi r^2$

Using the formula

Area of fan= $\frac{1}{2}\pi (12)^2=72 \pi cm^2$

Area of each sector= $\frac{area\;of\;fan}{Total\;number\;of\;sectors}$

Area of each sector= $\frac{72\pi}{18}=\frac{72\times 3.14}{18} cm^2$

Where $\pi=3.14$

Area of each sector= $12.56cm^2\approx 12.6 cm^2$

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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

Write an equation of the parabola that opens up whose vertex (−1, 2) is 3 units from the focus. (Vertex form or Parabola Form is

TEA [102]

Answer:

y2 = 4ax (opens right, a > 0)

y2 = -4ax (opens right, a > 0)

x2 = 4ay (opens up, a > 0)

x2 = -4ay (opens down, a > 0)

Vertex at (h, k) :

(y - k)2 = 4a(x - h) (opens right, a > 0)

(y - k)2 = -4a(x - h) (opens right, a > 0)

(x - h)2 = 4a(y - k) (opens up, a > 0)

(x - h)2 = -4a(y - k) (opens down, a > 0)

Equation of a Parabola in Vertex form

Vertex at Origin :

y = ax2 (opens up, a > 0)

y = -ax2 (opens down, a > 0)

x = ay2 (opens right, a > 0)

x = -ay2 (opens left, a > 0)

Vertex at (h, k) :

y = a(x - h)2 + k (opens up, a > 0)

y = -a(x - h)2 + k (opens down, a > 0)

x = a(y - k)2 + h (opens right, a > 0)

y = -a(y - k)2 + h (opens left, a > 0)

Step-by-step explanation:

7 0

3 years ago

If a day was a year, how many does it take to make a million years?

Tasya [4]

It would take 2,740 days to make a million years.

1,000,000 divided by 365.

6 0

3 years ago

Read 2 more answers

(ASAP)Someone help me out please

ludmilkaskok [199]

Answer:

Y= 1/3x + 4

Step-by-step explanation:

4 is the y intercept and it goes across one and down 3 for the get the slope of 1/3.

8 0

3 years ago

Determine if the triangles are congruent. If they are, state how you know.

hram777 [196]

Answer:

1 - SSS

Step-by-step explanation:

We need either two sides one angle, two angles one side, or three sides to prove congruency. In this case we have 3 sides so therefore this is congruent by the SSS theorem.

6 0

3 years ago

Read 2 more answers