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kobusy [5.1K]
3 years ago
15

Finding the length of arc and and sector area? Genuinely confused and will mark for brainliest.

Mathematics
2 answers:
SOVA2 [1]3 years ago
7 0

Answer:

Arc length = =\frac{5}{4} \pi \,km=1.25\ \pi\,\,km

Area=\frac{25}{8}\,  \pi\,\,km^2= 3.125\, \pi\,\,km^2

Step-by-step explanation:

For the length of an arc of circumference, you need to recall the formula:

arc = R * \theta

which is the product of the radius R times the angle, but only valid if the angle \theta is given in radians (not degrees). So we need to change the 45 degree angle into radians. we can do so by remembering that \pi radians is the same as 180°, and then the following proportion can be written to find what is the value (x) of 45° in radians:

\frac{45^o}{180^o} = \frac{x}\pi} \\x=\frac{45^o}{180^o} \,\pi\\x=\frac{\pi}{4}

Now we find the length of the arc using the formula given above:

arc = R * \theta\\arc=5\,km\,\frac{\pi}{4} \\arc=\frac{5}{4} \pi \,km

Now for the area of the sector, recall the formula:

Area = \frac{1}{2} R^2\,\theta

with the same condition for \theta of being expressed in radians (and not degrees). So the formula becomes:

Area = \frac{1}{2} R^2\,\theta\\Area= \frac{1}{2} (5\,km)^2\,\frac{\pi}{4} \\Area=\frac{25}{8}\,  \pi\,\,km^2

LiRa [457]3 years ago
5 0

Answer:

5 &x = 14

Step-by-step explanation:

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2 years ago
What is the equation of the line graphed below?
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Answer:

y=-7/2x - 2

Step-by-step explanation:

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Ad libitum [116K]

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3 years ago
You have 42 ft. of fencing (1 ft. segments) to make a rectangular garden. How much should each side be to maximize your total ar
Verizon [17]

Answer:

Length=10.5\ ft

Width=10.5\ ft

Area=110.25\ ft^{2}

Step-by-step explanation:

Let

x----> the length of the rectangular garden

y---> the width of the rectangular garden

we know that

The perimeter of the rectangle is equal to

P=2(x+y)

we have

P=42\ ft

so

42=2(x+y)

simplify

21=(x+y)

y=21-x------> equation A

Remember that the area of rectangle is equal to

A=xy ----> equation B

substitute equation A in equation B

A=x(21-x)

A=21x-x^{2}----> this is a vertical parabola open downward

The vertex is a maximum

The y-coordinate of the vertex is the maximum area

The x-coordinate of the vertex is the length side of the rectangle that maximize the area

using a graphing tool

The vertex is the point (10.5,110.25)

see the attached figure

so

x=10.5\ ft

Find the value of y

y=21-10.5=10.5\ ft

The garden is a square

the area is equal to

A=(10.5)(10.5)=110.25\ ft^{2} ----> is equal to the y-coordinate of the vertex is correct

6 0
3 years ago
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