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Exercise 6
Use the x button on a calculator. You will need basic trigonometry (page 209).
1. The chord AB subtends an angle of 130° at the centre O.
The radius of the circle is 8 cm. Find:
a) the length of AB
b) the area of sector OAB
c) the area of triangle OAB
d) the area of the minor segment (shown shaded).
2. Find the shaded area when:
a) = 6 cm, 0 - 70°
b) r=14 cm, 0 = 104°
c) r=5 cm, 0 = 80
8 cm
1.
3. Find and hence the shaded area when:
a) AB = 10 cm, r= 10 cm
b) AB=8 cm, r = 5 cm
4. How far is a chord of length 8 cm from the centre of a circle of radius 5 cm?
5. How far is a chord of length 9 cm from the centre of a circle of radius 6 cm?

Answer:

2,457

Step-by-step explanation:

The thousands place is when you move four spaces to the left starting from the first number. In this case, that number was seven, and to round, you need to round it up or down depending if the number to the left of the 4th number is greater or less than 5. In this case, that number was 3, so that 3 and the rest of the remaining numbers turn into 0's, making the rounded number 2,457.

I hope this information was of any use to you.

Answer:

2,457,000

Hope that this helps!

Answer:

Step-by-step explanation:

20000000000+3000000000+900000000+60000+8000+400+7

Answer:

16π

Step-by-step explanation:

The circle touches the X-axis and center at (3,4), the coordinate is representing as (x, y), so the radio will be r = y (circle touches the X-axis), and the formula of circle area is π * r^2, so:

π * 4^2 is equal to 16π

Answer:

Height = 6000 m

Step-by-step explanation:

[tex]Volume = length \times breadth \times height \\\\480000 = 10 \times 8 \times height\\\\480000 = 80 \times height\\\\height = \frac{480000}{80} = 6000 \ m[/tex]

Answer:

The answer is 3y - 10x - 27

6,000 + 700 + 30 + 8 is the expanded from.

Answer:

True

Step-by-step explanation:

A system of equations can be solved by Translating the system of equations into a matrix by following theses steps

write out the resulting answer in form of equations.

Answer with Step-by-step explanation:

We are given that

[tex]g(x)=(x^2-3x-10)(x^2+2x^2-5x+4)[/tex]

x=-1

Using property of limit

[tex]\lim_{x\rightarrow -1}g(x)=\lim_{x\rightarrow -1}(x^2-3x-10)(3x^2-5x+4)[/tex]

=[tex](1+3-10)(3+5+4)[/tex]

=[tex](-6)(12)[/tex]

=[tex]-72[/tex]

[tex]g(-1)=(1+3-10)(1+2+5+4)[/tex]

[tex]g(-1)=(-6)(12)=-72[/tex]

[tex]\lim_{x\rightarrow -1}g(x)=g(-1)[/tex]

Hence, the function is continuous at x=-1

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Answer:

3(3x - 10)(9x² + 30x + 100)

Step-by-step explanation:

Given

81x³ - 3000 ← factor out 3 from each term

= 3(27x³ - 1000 )← a difference of cubes which factors in general as

a³ - b³ = (a - b)(a² + ab + b²) , then

27x³ - 1000

= (3x)³ - 10³

= (3x - 10)((3x)² + (3x)(10) + 10²)

= (3x - 10)(9x² + 30x + 100)

Then

81x³ - 3000 = 3(3x - 10)(9x² + 30x + 100) ← in factored form

Answer:

Step-by-step explanation:

1)

9:10

+ 0:45

9:55      

so at 9:55 she finished her eating.

2)

  10:25

- 2:15

8:10

so test started at 8:10

3)

9:15

-7:30

2:15    

si games duration was 2;15

4)

2:40

+25

3:05

 se reached home at 3:05

Answer:

8

Step-by-step explanation:

count the number of solid-black lines.

perimeter = length plus

breadth

8cm +7cm + 5cm

= 20

Answer:

Set 2

Step-by-step explanation:

First find the median of each set (the median being the number in the middle):

(1) { 4,7,10,13,16} = 10

(2) {8,9,10,18,19} = 10

(3) {8,9,10,11,12} = 10

(4) {1,2,10,11, 12} = 10

Then find the mean of each set (the mean being average of all the numbers, to find the average add up all the numbers and divide by the amount of numbers):

(1) { 4,7,10,13,16} = 10

(2) {8,9,10,18,19} = 12.8

(3) {8,9,10,11,12} = 10

(4) {1,2,10,11, 12} = 7.2

the answer being 12.8 since 12.8 is greater than 10

(4) {1,2,10,11, 12}

Answer:

Solution given:

1:

{ 4,7,10,13,16}

n=5

median={n+1)/2th term=6/2=3th term=10

mean=sum/n={ 4+7+10+13+16}/{5}=10

(2)

{8,9,10,18,19}

n=5

median={n+1)/2th term=6/2=3th term=10

mean=sum/n={8+9+10+18+19}/{5}=12.8

3) {8,9,10,11,12}

n=5

median={n+1)/2th term=6/2=3th term=10

mean=sum/n={8+9+10+11+12}/{5}=10

(4) {1,2,10,11, 12}

n=5

median={n+1)/2th term=6/2=3th term=10

mean=sum/n={1+2+10+11+13}/{5}=7.4

In above

1: mean=median

2:mean>median

3:mean=median

4:mean<median

so median is greater than mean is in 4th one.

(4) {1,2,10,11, 12}

Answer:

300

Step-by-step explanation:

to find volume u will have to multiply the length x width x breadth which is 5x5x12=300

Answer:

Find the answers below

Step-by-step explanation:

Using m<X as the reference angle

Opposite YZ = 7

Adjacent  XY = 10

Hypotenuse XZ = √149

Using the SOH CAH TOA identity

sinX = opp/hyp

sinX =YZ/XZ

sinX = 7/√149

For cos X

cos X = adj/hyp

cos X =10/√149

Using m<Z as reference angle;

Opposite XY = 10

Adjacent  YZ = 7

Hypotenuse XZ = √149

Using the SOH CAH TOA identity

sinZ = opp/hyp

sinZ =10/√149

sinZ = 7/√149

For cos Z

cosZ = 7/√149

Answer:

5 loaves

Step-by-step explanation:

13 1/3 divided by 2 2/3 is 5 so the answer is 5 loaves.

Rewrite the fractions as improper fractions then divide the total amount used by the amount per loaf:

13 1/3 = 40/3

2 2/3 = 8/3

40/3 / 8/3

When dividing by a fraction flip the fraction over and multiply

40/3 x 3/8 = (40 x3) /( 3 x 8) = 120/24 = 5

She made 5 loaves of bread.

Answer:

B

Step-by-step explanation:

An experiment is a study carried out in a controlled environment where the person undertaking the research hopes to understand cause and effect between the independent and dependent variables. An example of a experiment is the palovian experiment

The independent variable is the variable that the person carrying out an experiment changes or manipulates. the independent variable usually have a direct effect on the dependent variable

The dependent variable is the variable that is being measured in an experiment. It is usually affected by the independent variable

Observational study is the study where the researcher observes and measures cause and effect between independent and dependent variables without trying  to control or influence the population

Answer:

6/5

Step-by-step explanation:

2x+3=ky

ky=2x+3

y=(2x+3)/k

y=2x/k + 3/k - > equation 1

y=mx + c - >equation 2

Comparing equation 1 and 2,

2/k=m

2/k=5/3

6/5=k

k=6/5

Answer:

b.

[tex]V = \pi \cdot \int\limits^a_b {\left([f(x)]^2 - [g(x)]^2} \right) \, dx[/tex]

(c)

[tex]V = \pi \cdot \int\limits^3_1 {\left([arcos(y - 2)]^2 - [arcsine(x)]^2 - (-1)^2} \right) \, dx[/tex]

Step-by-step explanation:

b. The volume of solid formed is given by the washers formula as follows;

[tex]V = \pi \cdot \int\limits^a_b {\left([f(x)]^2 - [g(x)]^2} \right) \, dx[/tex]

Therefore, we have, the integral expression whose solution is the volume formed by rotating 'R', about the equations y = 2 + cos(x) and y = csc(x) in the first quadrant on the interval, 0 ≤ x ≤ π, V is given as follows;

[tex]V = \pi \cdot \int\limits^\pi_0 {\left([2 + cox(x)]^2 - [csc(x)]^2} \right) \, dx[/tex]

(c)  We have;

x = arcos(y - 2), x = arcsin(1/y)

At x = 0, y = 2 + cos(0) = 3

csc(0) = ∞

At x = π, y = 2 + cos(π) = 2 + -1 = 1

csc(π) = ∞

Therefore, we get;

[tex]V = \pi \cdot \int\limits^3_1 {\left([arcos(y - 2)]^2 - [arcsine(x)]^2 - (-1)^2} \right) \, dx[/tex]

B) An equation that involves integral expressions whose solution is the volume of the solid generated when R is revolved around the x-axis is;

[tex]V = \pi \int\limits^\pi _0 ({[2 + cos(x)]^{2} - [csc(x)]^{2}}) \, dx[/tex]

C) An equation involving integral expressions whose solution is the volume of the solid generated when R is revolved around the line x= -1 is;

[tex]V = \pi \int\limits^\pi _0 ({[cos^{-1} (y - 2)]^{2} - [sin^{-1}(x)]^{2} - (-1)^{2} }) \, dx[/tex]

B) The volume of solid formed is gotten from applying the washers formula;

[tex]V = \pi \int\limits^a_b ({[f(x)]^{2} - [g(x)]^{2}}) \, dx[/tex]

This means that the integral expression whose solution is the volume formed by rotating R about the equations y = 2 + cos(x) and y = csc(x) in the first quadrant on the interval, 0 ≤ x ≤ π, V is expressed as;

[tex]V = \pi \int\limits^\pi _0 ({[2 + cos(x)]^{2} - [csc(x)]^{2}}) \, dx[/tex]

C) From answer above, we have;

x = cos⁻¹(y - 2), x = sin⁻¹(1/y)

Now,

At x = 0; y = 2 + cos(0) = 3

csc(0) = 1/0 = ∞

Also,

At x = π; y = 2 + cos(π)

y = 2 + (-1)

y = 1

Also, csc(π) = ∞

Thus, we have;

[tex]V = \pi \int\limits^\pi _0 ({[cos^{-1} (y - 2)]^{2} - [sin^{-1}(x)]^{2} - (-1)^{2} }) \, dx[/tex]

Read more about finding the integral volume of solid at; https://brainly.com/question/21036176

Answer:

1/2

Step-by-step explanation:

These two triangles are similar, so there is a scale factor. The heights and the bottom sides of each triangle are similar, figure A has a bottom length of 6, and figure B has a bottom length of 3. To get from A to B, you multiply by 1/2. So the scale factor is 1/2.

Answer:

A. i think

Step-by-step explanation:

Answer:

4, -16, 64, -256

the common ratio is -4

Step-by-step explanation:

Answer:

it is 12

Step-by-step explanation:

for n= 36 divided by 3.

Answer:

9

Step-by-step explanation:

a^2 +b

Let a = -2 and b = 5

(-2)^2 +5

Exponents first

4 +5

Then add

9

Answer:

9

Step-by-step explanation:

Here, we have to observe that a^2 = a×a =-2 × -2 = 4

hence, a^2 + b = 4 + 5 = 9.

Step-by-step explanation:

everything can be found in the picture

Answer:

5/7 is the answer to your question

Step-by-step explanation:

The area of a circle = pi r^2

d = 2r Divide by 2 to get the radius

r = d/2

The diameter = 2.8 cm

r = d/2

r = 2.8/2

r = 1.4

The area of the circle = pi * r^1

The area of the circle = 3.14 * 1.4^2

The area of the circle = 6.1544

But you are working with a semic circle

The area of a semicircle is 1/2 that of a circle

Area of semicircle = 1/2 6.1544 = 3.0772 =3.08 when rounded

Answer:

Y=7

Step-by-step explanation:

the 7 is the y value. the y value is = 7 when x =2

Answer:

19,000

Step-by-step explanation:

because for 1 year its 19,000 just for that year so it would be 19,000