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3 years ago

13

What is the area of a sector with a central angle of 2π9 radians and a diameter of 20.6 mm? Use 3.14 for π and round your answer

to the nearest hundredth.

1 answer:

sleet_krkn [62]3 years ago

7 0

The answer to this is 37.01

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X^2+4x+y^2-10y+20=30 find the center of the circle by completing the square

swat32

Answer:

a). Center of the circle = (-2, 5)

b). Equation of the line ⇒ y = $-\frac{4}{5}x+\frac{58}{5}$

Step-by-step explanation:

Equation of the circle is,

x² + 4x + y²- 10y + 20 = 30

a). [x² + 2(2)x + 4 - 4] + [y²- 2(5)y + 25] - 25 + 20 = 30

[x² + 2(2)x + 4] - 4 + [y² - 2(5)y + 25] - 25 + 20 = 30

(x + 2)² + (y - 5)²- 29 + 20 = 30

(x + 2)² + (y - 5)²- 9 = 30

(x + 2)² + (y - 5)² = 39

By comparing this equation with the standard equation of a circle,

Center of the circle is (-2, 5).

b). A point (2, 10) lies on this circle.

Slope of the line joining this point to the center (-2, 5),

$m_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

= $\frac{10-5}{2+2}$

= $\frac{5}{4}$

Let the slope of the tangent which is perpendicular to this line is ' $m_{2}$ '

Then by the property of perpendicular lines,

$m_{1}\times m_{2}=-1$

$\frac{5}{4}\times m_{2}=-1$

$m_{2}=-\frac{4}{5}$

Now the equation of the line passing though (2, 10) having slope $m_{2}=-\frac{4}{5}$

y - y' = $m_{2}(x-x')$

y - 10 = $-\frac{4}{5}(x-2)$

y - 10 = $-\frac{4}{5}x+\frac{8}{5}$

y = $-\frac{4}{5}x+\frac{8}{5}+10$

y = $-\frac{4}{5}x+\frac{58}{5}$

Therefore, equation of the line will be, y = $-\frac{4}{5}x+\frac{58}{5}$

7 0

3 years ago

Mr. Lawrence used 100 tiles when he put a new floor in the kitchen 34 tiles are squares and 16 tiles are rectangles write the to

Oliga [24]

<h3>Fraction of square tiles = $(\frac{4}{25}) = 0.16$ </h3><h3>Fraction of rectangle tiles = $(\frac{17}{50}) = 0.34$ </h3>

Step-by-step explanation:

Total number of tiles to be used in the kitchen = 100

The total number of square tiles = 34

The total number of rectangle tiles = 16

Now, calculating the total fraction of square tiles:

The fraction of square tiles = $\frac{\textrm{Total number of square tiles}}{\textrm{Total number of tiles}} = \frac{16}{100} = \frac{4}{25}$

Also, solving the fraction, we get $\frac{4}{25} = 0.16$

So, the decimal value of square tiles = 0.6

Calculating the total fraction of rectangle tiles:

The fraction of rectangle tiles = $\frac{\textrm{Total number of rectangle tiles}}{\textrm{Total number of tiles}} = \frac{34}{100} = \frac{17}{50}$

Also, solving the fraction, we get $\frac{17}{50} = 0.34$

So, the decimal value of rectangle tiles = 0.34

4 0

3 years ago

HELP PLEASE! Drag the tiles to match each measurement with an equivalent measurement.

Sunny_sXe [5.5K]

Answer:

8 fluid ounces

Step-by-step explanation:

I just got it right on my quiz.

3 0

3 years ago

Enrollment in a photography class increased from 25 to 35 students. What was the percent of increase in enrollment?

DaniilM [7]

About 29%.
35 - 25 = 10, or the amount of change
10 / 35 = .285, or the amount of change over total

3 0

4 years ago

Sally has 16 marbles in her collection. John has only 7 marbles. Sally gives John 8 of her marbles. How much marbles does John h

Sati [7]

Answer:

The answer is 15

Step-by-step explanation:

hope this helps

5 0

3 years ago