i really don't get this can someone pls i'd appreciate it a lot

  (a) center: (1, -2); radius √10

  (b) distance from (4, -1) to center is √10, so is on the circle

  (c) work shown below

  (d) y = -1/3x +5/3

Step-by-step explanation:

It is well you should have difficulty, as point B is not defined. If we assume it is (0, -5), then we can proceed as follows.

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(a) The center of the circle will be the midpoint of AB, so will be the average of their coordinates.

  C = (A+B)/2 = ((2, 1) +(0, -5))/2 = (2, -4)/2

  C = (1, -2) . . . . the center of the circle

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The radius of the circle is the distance between the center and either end of the diameter. (It can also be figured as half the diameter.)

Here, we choose ...

  r = ║A-C║ = ║(2, 1) -(1, -2)║ = ║(1, 3)║

  r = √(1² +3²)

  r = √10 . . . . the radius of the circle

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(b) There are a couple of ways to show (4, -1) is a point on the circle. One of them is to show that its distance from the center is the same as the radius. That distance is ...

  ║(4, -1) -(1, -2)║ = ║(3, 1)║ = √(3² +1²) = √10 . . . . same as the radius

  (4, -1) is on the circle

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(c) The standard form equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

To get to the desired general form, we need to eliminate parentheses and subtract r². Filling in the values (h, k) = (1, -2) and r = √10, we have ...

  (x -1)² +(y +2)² = 10

  x² -2x +1 + y² +4y +4 = 10 . . . . . eliminate parentheses

  x² +y² -2x +4y -5 = 0 . . . . . . . . subtract 10 and put in appropriate order

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(d) We can write the equation of the tangent at point A starting with a point-slope form of the equation for the line, then rearranging it to slope-intercept form.

You know the tangent to a circle is perpendicular to the radius at the point of tangency. You know from the work in part (a) that the segment from C to A has a rise of 3 and a run of 1, so a slope of 3/1 = 3. The tangent is perpendicular, so its slope is the negative reciprocal of that, or -1/3.

Now we know the slope of the tangent and the point of tangency (A), so we can write the equation as ...

  y -1 = (-1/3)(x -2)

Adding 1 and eliminating parentheses, we get ...

  y = -1/3x +2/3 +1

  y = -1/3x +5/3

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Comment on notation above

We have used the notation ║(a, b)║ to refer to the length of a segment with components (a, b). It is fully equivalent to √(a²+b²) in this context.

a) centre: (1,-2)

radius = sqrt(10)

b) distance from the centre = radius

c) x² + y² - 2x + 4y - 5 = 0

d) y = (-1/3)x + (5/3)

Step-by-step explanation:

Centre is the midpoint of the diameter:

(h,k) = (2+0)/2, (1-5)/2

(h,k) = (1,-2)

radius is ½ times length of the diameter:

½ sqrt[(-5-1)² + (0-2)²]

½ sqrt(40)

½ × 2 sqrt(10)

radius = sqrt(10) units

Find the distance between the centre and (4,-1)

sqrt[(4-1)² + (-1--2)²]

sqrt(9 + 1)

sqrt(10) = radius

Therefore on the circle

Equation:

(x - h)² + (y - k)² = r²

(x - 1)² + (y + 2)² = 10

x² - 2x + 1 + y² + 4y + 4 - 10 = 0

x² + y² - 2x + 4y - 5 = 0

Tangent at (2,1)

Slope would be -ve reciprocal of the slope from A to the centre

m = (-2-1)/(1-2) = 3

Slope of the tangent = - ⅓

y - 1 = -⅓(x - 2)

y = (-⅓)x + ⅔ + 1

y = (-1/3)x + (5/3)

b). 4320 have a nice day

both the histogram and the stem and leaf plot will visually show how many shoppers were of various ages within each range of data.   the histogram does not give us the specific ages of these shoppers unlike the stem and leaf plot.a histogram does not give us a true range of the data because we do not know exactly how old the shoppers were. a stem and leaf plot will give exact ages, so we can determine the exact range along with all measures of center and the others measures of center.   with the histogram, we cannot find any of these.

step-by-step explanation: