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3 years ago

Find the area of the region enclosed by the graph of $x^2 + y^2 = 2x - 6y + 6$

Mathematics

1 answer:

Luda [366]3 years ago

7 0

Answer:

16π ≈ 50.27 square units

Step-by-step explanation:

The equation is that of a circle of radius 4. The area of a circle is given by ...

A = πr²

A = π(4²) = 16π ≈ 50.27 . . . . square units

_____

The equation can be put into the standard form for a circle to find its radius.

(x^2 -2x) +(y^2 +6y) = 6 . . . . collect variable terms on the left

(x^2 -2x +1) +(y^2 +6y +9) = 6 + 1 + 9 = 16 . . . . . complete the squares

(x -1)^2 +(y +3)^2 = 4^2 . . . . . the radius is 4

Compare to the form ...

(x -h)^2 +(y -k)^2 = r^2 . . . . circle of radius r centered at (h, k)

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the diagram shows a door that has a window in it the front faces the door and window are similar rectangles that have the dimens

Vaselesa [24]

Answer:

The correct answer is B. 150 cm.

Correct statement, question and diagram:

The diagram shows a door that has a window in it. The front faces of the door and window are similar rectangles that have the dimensions shown. What is h, the height of the window in centimeters?

A. 66 cm

B. 150 cm

C. 186 cm

D. Not here.

Source:

Question that can be found at quizizz

Step-by-step explanation:

Let's recall that if the door and the window in it are similar rectangles, then we have:

60/84 = h/210

84 * h = 210 * 60

84h = 12,600

h = 12,600/

h = 150 cm

The correct answer is B. 150 cm.

3 0

3 years ago

Read 2 more answers

Find the area of the of just the trench

Effectus [21]

Answer:

0.5m^2

Step-by-step explanation:

3 1/2- 2 1/2 =1/2

3m-2m=1

1/2 × 1 = 0.5m^2

3 0

3 years ago

Ms. Benjamin puts $1,200 in Virtue bank. The interest rate is 6% per year. a. How much interest will she get in after one year?

Mazyrski [523]

Answer:

the answer is 1

Step-by-step explanation:

3 0

3 years ago

According to industry sources, online banking is expected to take off in the near future. The projected number of households (in

Airida [17]

Answer:

(a) The least-square regression line is: $y=4.662+2.709x$ .

(b) The number of households using online banking at the beginning of 2007 is 31.8.

Step-by-step explanation:

The general form of a least square regression line is:

$y=\alpha +\beta x$

Here,

y = dependent variable

x = independent variable

α = intercept

β = slope

(a)

The formula to compute intercept and slope is:

$\begin{aligned} \alpha &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \\\beta &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \end{aligned}$

The values of ∑X, ∑Y, ∑XY and ∑X² are computed in the table below.

Compute the value of intercept and slope as follows:

$\begin{aligned} \alpha &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 68.6 \cdot 55 - 15 \cdot 218.9}{ 6 \cdot 55 - 15^2} \approx 4.662 \\ \\\beta &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 6 \cdot 218.9 - 15 \cdot 68.6 }{ 6 \cdot 55 - \left( 15 \right)^2} \approx 2.709\end{aligned}$