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3 years ago

Find the area of each shaded segment in nearest tenth.

Mathematics

1 answer:

shepuryov [24]3 years ago

7 0

Answer:

Denote the center of circle as O, the 2 endpoints of shaded segment as AB, then we have:

section OAB area = pi x radius^2 x (120/360) = pi x 6^2 x (1/3) = 37.7 (cm2)

Considering triangle OAB, we have OA = OB = radius, angle AOB = 120 deg. Denote OH as the height of triangle. H lies on AB.

=> Applying cosine and sine theorem in right triangle AHO:

OH = OA x cos 60 = 6 x (1/2) = 3 (cm)

AH = OA x sin 60 = 6 x (sqrt3)/2 = 5.2 (cm)

=> triangle AOB area:

A = triangle AOH area x 2

= AH x OH x (1/2) x 2 = 3 x 5.2 x (1/2) x 2 = 15.6 (cm2)

=> shaded segment area = section OAB area - triangle AOB

= 37.7 - 15.6 = ~21.1 (cm2)

Hope this helps!

You might be interested in

What is the multiplicative inverse of -27 and what is the multiplicative inverse for 7/9 and -9/16

liberstina [14]

The multiplicative inverse of a number is the number when you multiply it, it gives you the product of 1.

So for - 27, what number will give us 1 when we multiply it by -27

-27 * -1/27 = 1

So the multiplicative inverse of -27 = -1/27

7/9 * 9/7 = 1

-9/16 * -16/9 = 1

So in essence, just take the number and flip it

-27 = -1 / 27

7/9 = 9/7

-9/16 = -16/9

3 0

3 years ago

Y= 2x +2

Airida [17]

Answer:

The system has one solution, at a single point of intersection.

Step-by-step explanation:

I'm going to assume that g and y are the same thing here, on a normal xy-coordinate plane. If there is actually a third dimension, 'g', then I am probably wrong, and I apologize.

For a system of 2 linear equations, a 'solution' is a point of intersection for the two lines.

If the two lines are parallel, they will have no intersection. These two equations are in the form y = mx + b, where m is the slope. If their slopes are the same, then the lines are parallel. The first equation has a slope of 2. The second equation has a slope of 6. 2 ≠ 6, obviously. They are are not parallel, so there is at least one solution (intersection)

If two equations are 'equivalent', then they represent the same exact line and you cannot find a unique solution to the system because there is no single point where they intersect. They intersect at all points, so there are an infinite number of solutions. Two equations in the same format (like point-slope) will be equivalent if you see that one is just a multiple of the other. That is not the case here. They are not equivalent, so there are not an infinite number of solutions.

For the intersection of two lines in a plane, that intersection is no point, 1 point, or infinite points.

We have ruled out no point and we have ruled out infinite points.

There must be a solution of one point where the two lines intersect.

That would be consistent with answers B and E as shown in your Brainly question.

4 0

3 years ago

Read 2 more answers

50 POINTS!!! WILL MARK BRAINLIEST!!! CORRECT ANSWERS PLS 1 HOUR LEFT

Brut [27]

Answer:

○ 3

○ y + ½ = 3(x - 2)

○ Multiply both sides of the equation by 3. The Standard Form of the equation is 12x - 2y = 24.

○ 5x - 3y = 15

○ y = ½x + 5⁄2

Step-by-step explanation:

Find the rate of change [slope]:

-y₁ + y₂\-x₁ + x₂ = m → (-1, 1) and (-2, -2)

$\frac{2 + 1}{2 - 1} = 3$

__________________________________________________________

According to the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY CAREFUL inserting this coordinate into the formula with their CORRECT SIGNS:

(2, -½) → y + ½ = 3(x - 2)

__________________________________________________________

We do not want fractions in our Standard Equation, so multiply by the denominator to get rid of it:

-3[4x - ⅔y = 8] → -12x + 2y = -24

** They should have multiplied by -3 instead of 3 because that negative is hooked up to everything in the fraction, but since the exercise gave you 12x - 2y = 24, go with 12x - 2y = 24.

__________________________________________________________

If you would take a look at this graph real closely, you will see that this graph intersects the y-axis and x-axis at ENDPOINTS, so to find the x-intercept, you simply plug in zero for y: 5x = 15, and you will know right away that x is set to equal 3, which is what you see in the graph, (3, 0). Now, to find the y-intercept, you simply plug in zero for x: -3y = 15, and you will know right away that y is set to equal -5, which is what you see on the graph as well, (0, -5). With that being said, you have your answer.

__________________________________________________________

y - 3 = ½(x - 1)

y - 3 = ½x - ½

+ 3 + 3

_____________

y = ½x + 2½

* 2½ = 5⁄2

I am joyous to assist you anytime.

4 0

3 years ago

Sarah is investing $10,000 in a CD at a bank. If the bank uses simple interest, and the bank pays 2.75% in interest annually, ho

Leokris [45]

Answer: it would be worth $11925 when it matures after 7 years.

Step-by-step explanation:

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the loan.

P represents the principal or amount invested in the CD.

R represents interest rate on the amount invested in the CD.

T represents the duration of the investment in years.

From the information given,

P = $10,000

R = 2.75%

T = 7 years

I = (10000 × 2.75 × 7)/100

I = $1925

Therefore, the worth of the CD in total at the end of 7 years when the CD matures is

10000 + 1925 = $11925

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3 years ago

How many people live in the state of Tennessee?

DochEvi [55]

6.549 million in 2014 i hope this helps.

8 0

3 years ago

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