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soldier1979 [14.2K]
3 years ago
11

How long is the arc intersected by a 2pi/3 radian central angle in a circle with radius 7 feet?

Mathematics
2 answers:
VashaNatasha [74]3 years ago
4 0

=\frac{43.96}{3}Formula to find the central angle is,

s= r\theta

Where, s = arc length

r = radius

\theta= central angle in radian.

According to the given problem,

r = 7 and \theta = \frac{2\pi}{3}.

First step is to plug in these values in the above formula. So,

s= 7*\frac{2\pi}{3}

=\frac{14\pi}{3} By simplifying.

=\frac{14*3.14}{3} Since \pi =3.14

=\frac{14*3.14}{3}

s=14.65

Hence, arc length iss 14.65 feet.

dangina [55]3 years ago
3 0

Answer:

14π/3 feet

Step-by-step explanation:

The next answer is 2.36 and the next is 21.24

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A dvd is marked down 15% the regular price is $12 what is the sale price?
mash [69]

15% off means the dvd is selling for 85% of the original price ( 100% - 15%=85%)

Multiply the original price by 85%

12 x 0.85 = 10.20

The price is $10.20

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2 years ago
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I need help with this im on a test
sergey [27]

Answer: A. 2

Step-by-step explanation:

add all 5 numbers together to get 40 then add one of the answer choices to the total and divide each one by 6 until you get 7.

42/6=7

7 0
2 years ago
HELP!!!! Position and label the triangle on the coordinate plane
Darya [45]

Answer:

Option (2).

Step-by-step explanation:

It is given in the question,

ΔLMN is a right triangle with base LM = 3a units

Hypotenuse MN = 5a

By applying Pythagoras theorem in ΔLMN,

MN² = LM² + NM²

(5a)² = (3a)² + MN²

25a² - 9a² = MN²

MN = √16a²

MN = 4a

Therefore, vertices of the triangle will be L(0, 0), M(3a, 0) and N(0, 4a).

Option (2) will be the answer.

4 0
2 years ago
Find the distance from the point (1,4) to the line y = 1/3x - 3
Troyanec [42]

Answer:

Step-by-step explanation:

If I'm not mistaken, and I very well could be, this is a calculus problem(?). In order to find the distance without calculus you'd need a point on the given line to use to find the distance in the distance formula. But you don't have a point on the given line, so we can find the shortest distance between the point (1, 4) and the given line using the derivative of the polynomial formed when using the distance formula.

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} and we have the x and y for x2 (or x1...it doesn't matter which you choose to fill in):

d=\sqrt{(1-x)^2+(4-y)^2}

but what we find is that we have too many unknowns here, namely, the distance, the x coordinate, and the y coordinate. So we can replace the y coordinate with what y is equal to in terms of the linear equation:

d=\sqrt{(1-x)^2+(4-\frac{1}{3}x-3)^2 } and simplify:

d=\sqrt{(1-x)^2+(7-\frac{1}{3}x)^2 }

. No we'll expand each binomial by squaring:

d=\sqrt{(1-2x+x^2)+(49-\frac{14}{3}x+\frac{1}{9}x^2)  }

.  Combining like terms gives us

d=\sqrt{\frac{10}{9}x^2-\frac{20}{3}x+50  }

The distance between the point (1, 4) and the given line will be at a minimum when the polynomial above is at a minimum. We find the value of x for which the polynomial is at a minimum by finding its derivative, setting the derivative equal to 0, and then solving for x. The derivative of the polynomial is

\frac{20}{9}x-\frac{20}{3}

Setting equal to 0 and getting rid of the denominators gives us

20x - 60 = 0

Solving for x gives us

20x = 60 and x = 3.

That's the value of x that gives us the shortest distance between (1, 4) and the line y = 1/3x - 3. Sub into the distance formula that x value to find the distance:

d=\sqrt{(\frac{10}{9})(3)^2-(\frac{20}{3})(3)+50   }

which simplifies down, finally, to

x ≈ 6.325 units

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Mrrafil [7]

The correct answer is B. Two out of every five people in the shopping center are in the clothing store.

Step-by-step explanation:

To establish this answer we have to know the total number of people that were in the Shopping Center. So, we have to add people from every store.

48+96+20+64+12=240

The result of this operation is 240 people.

Later we have to divide the total number in 5 and multiply by 2.

So, the operation is

240/5 = 48

48x2=96

According to the above, the correct answer is B. Two out of every five people in the shopping center are in the clothing store.

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