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3 years ago

Please help me understand how to do this

Mathematics

1 answer:

kicyunya [14]3 years ago

4 0

Answer:

A) This can be shown using the equation of Arc length. Arc length = r x Theta where r is the radius of the circle in this case OA and Theta is the angle subtended by the arc, which is angle AOC. This angle can be found because we know the angle OAC which is π/3 rad and angle OCA is π/2 (right angle) so that makes angle AOC π - (π/2+π/3) because the total angles should add up to π, we will find that the angle AOC is π/6. So now we know the arc length so we can substitute in the equation the Theta and the arc length to get 5 = r x π/6

dividing both sides by π/6 we will get 5/(π/6) which is approximately 9.55 cm.

B) To find the perimeter we need to add up all sides of the shaded region, in this case the arc length that we have (5) and add it with AC and BC. So the goal is to find AC and BC. We found OA to be 9.55 cm. We have angles so we can use trigonometric functions to find the other sides. we have the hypotneus so we can use either sin or cos so sin will give us length of AC so sin(π/6) = AC/9.55 and you will find that AC is 4.75 and cos(π/6) = OC/9.55 and you will find OC is 8.27

so now we know the perimeter is 5 + 4.75 + BC well we still need to find BC well we know that the radius of the circle is 9.55 (OA) and that applies to OB as well so OB is 9.55. Since we have OC we can do 9.55-8.27 to get BC which is 1.28 cm. So the perimeter is 5 + 4.75 + 1.28 = 11.03 cm

C) The area of the sector can be found by the equation Area = 0.5 x r^2 x theta

substituting in will give us 0.5 x 9.55^2 x π/6 = 23.88 cm^2. The area of the triangle can be found by 0.5 x b x h where b is base and h is height, so 0.5 x 8.27 x 4.75 and you will get 19.64. To find the area of the shaded region that's the area of the whole sector minus the area of the triangle so 23.88 - 19.64 = 4.24 cm ^2. to express it as a precentage, divide it by the area of the whole sector and multiply by 100. So the final answer will be 4.24/23.88 x 100 = 17.75%

Hope I helped <3

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vesna_86 [32]

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3 years ago

A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the bar

Luba_88 [7]

The dimensions for the plot that would enclose the most area are a length and a width of 125 feet.

In this question we shall use the first and second derivative tests to determine the optimal dimensions of a rectangular plot of land. The perimeter ( $p$ ), in feet, and the area of the rectangular plot ( $A$ ), in square feet, of land are described below:

$p = 2\cdot (w+l)$ (1)

$A = w\cdot l$ (2)

Where:

$w$ - Width, in feet.
$l$ - Length, in feet.

In addition, the cost of fencing of the rectangular plot ( $C$ ), in monetary units, is:

$C = c\cdot p$ (3)

Where $c$ is the fencing unit cost, in monetary units per foot.

Now we apply (2) and (3) in (1):

$p = 2\cdot \left(\frac{A}{l}+l \right)$

$\frac{C}{c} = 2\cdot (\frac{A}{l}+l )$

$\frac{C\cdot l}{c} = 2\cdot (A+l^{2})$

$\frac{C\cdot l}{c}-2\cdot l^{2} = 2\cdot A$

$\frac{C\cdot l}{2\cdot c} - l^{2} = A$ (4)

We notice that fencing costs are directly proportional to the area to be fenced. Let suppose that cost is the maximum allowable and we proceed to perform the first and second derivative tests:

FDT

$\frac{C}{2\cdot c}-2\cdot l = 0$

$l = \frac{C}{4\cdot c}$

SDT

$A'' = -2$

Which means that length leads to a maximum area.

If we know that $c = 8$ and $C = 4000$ , then the dimensions of the rectangular plot of land are, respectively:

$l = \frac{4000}{4\cdot (8)}$

$l = 125\,ft$

$A = \frac{(4000)\cdot (125)}{2\cdot (8)} -125^{2}$

$A = 15625\,ft^{2}$

$w = \frac{15625\,ft^{2}}{125\,ft}$

$w = 125\,ft$

The dimensions for the plot that would enclose the most area are a length and a width of 125 feet.

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3 years ago

Fill in the table using this function rule. y = 24 - 4x x y 2 ? 3 ? 4 ? 6 ?

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3 years ago

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Can someone please answer all parts?? Extra points for this one!

Brilliant_brown [7]

a)
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Integrate:
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Integrate again:
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c) velocity = 10t

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d.

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Integrate again:

5t^2 + 5t

Solve
5t^2 + 5t = 450

Gives 9 seconds

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3 years ago

The first term of a geometric sequence is –2 and the common ratio is -1/4. What are the next three terms of the sequence?

Gelneren [198K]

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3 years ago

Please help me understand how to do this​

Please help me understand how to do this