[TQ] is a tangent at A to a circle, centre O, /AB/ is a chord. if <BAT=y, show that <BOA=2y​

[tex]f(-2) = -4[/tex] for the given piecewise function by using the equation [tex]f(x) = x - 2[/tex]  if   [tex]x < 3.[/tex]

A piecewise function is a mathematical function that is defined differently on different parts of its domain.

Instead of having a single formula that applies to the entire domain, a piecewise function has multiple formulas, each applying to a specific interval or subset of the domain.

To find f(-2) for the given piecewise function, we need to determine which piece applies to the input value o  [tex]f -2[/tex], which is less than 3. Therefore, we use the first piece of the function, which is[tex]f(x) = x - 2 if x < 3.[/tex]

Substituting x = -2 into this piece, we get:

[tex]f(-2) = (-2) - 2 = -4[/tex]

Therefore, f(-2) = -4 for the given piecewise function.

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Increasing [tex]\frac{15}{16}[/tex] by [tex]\frac{3}{4}[/tex] of it and then increasing the result by [tex]\frac{3}{5}[/tex] of it gives us the fraction of [tex]\frac{45}{32}[/tex].

To increase [tex]\frac{15}{16}[/tex] by [tex]\frac{3}{4}[/tex] of it, we can multiply [tex]\frac{15}{16}[/tex] by [tex]\frac{3}{4}[/tex], which gives us:

[tex]\frac{15}{16}[/tex] × [tex]\frac{3}{4}[/tex] = [tex]\frac{45}{64}[/tex]

Adding this result to [tex]\frac{15}{16}[/tex], we get:

[tex]\frac{15}{16}[/tex] + [tex]\frac{45}{64}[/tex] = [tex]\frac{225}{256}[/tex]

Now, to increase this result by [tex]\frac{3}{5}[/tex] of it, we can multiply [tex]\frac{225}{256}[/tex] by 3/5, which gives us:

[tex]\frac{225}{256}[/tex] × [tex]\frac{3}{5}[/tex] = [tex]\frac{135}{256}[/tex]

Adding this result to [tex]\frac{225}{256}[/tex], we get the final answer:

[tex]\frac{225}{256}[/tex] + [tex]\frac{135}{256}[/tex] = [tex]\frac{360}{256}[/tex]

Simplifying this fraction, we get:

[tex]\frac{360}{256}[/tex] = [tex]\frac{45}{32}[/tex]

The problem involves increasing a fraction by a certain percentage twice. To solve the problem, we first find the increase in the fraction by multiplying it with the given percentage. We then add the result to the original fraction to get the new fraction. This process is repeated for the second increase. Finally, we simplify the resulting fraction if possible. In this specific problem, we are increasing [tex]\frac{15}{16}[/tex] by [tex]\frac{3}{4}[/tex] of it and then increasing the result by [tex]\frac{3}{5}[/tex] of it to find the resulting fraction [tex]\frac{45}{32}[/tex].

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The probability that the proportion of persons more than 6 feet tall will differ from the population proportion by more than 5%  is approximately 0.0456.

The standard error of the sample proportion is:

SE = √[(p × (1 - p)) / n]

where p is the population proportion, and n is the sample size.

Substituting the given values, we get:

SE = √[(0.56 × 0.44) / 643] ≈ 0.025

To find the probability that the sample proportion differs from the population proportion by more than 5%, we need to find the z-scores for the upper and lower bounds of the interval:

Lower bound: 0.56 - 0.05 = 0.51

Upper bound: 0.56 + 0.05 = 0.61

z_lower = (0.51 - 0.56) / 0.025 ≈ -2.00

z_upper = (0.61 - 0.56) / 0.025 ≈ 2.00

Using a standard normal distribution table or calculator, we can find the probabilities for these z-scores:

P(Z < -2.00) ≈ 0.0228

P(Z > 2.00) ≈ 0.0228

The probability that the sample proportion differs from the population proportion by more than 5% is the sum of these two probabilities:

P(|p - 0.56| > 0.05) = P(Z < -2.00) + P(Z > 2.00) ≈ 0.0456

Therefore, the probability that the proportion of persons more than 6 feet tall in a random sample of size 643 will differ from the population proportion by more than 5% is approximately 0.0456, rounded to four decimal places.

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The proportion of Year 9 pupils in the music club is approximately 46.7%.

A ratio or value that may be stated as a fraction of 100 is called a percentage.

To find the proportion of Year 9 pupils in the music club as a percentage, follow these steps:

To get proportion as a percentage divied number of Year 9 pupils by total pupils multiplied by 100.

Proportion as a percentage = [tex]\frac{Year \:9 \:pupils}{total \:pupils} \times 100[/tex]
Divide the number of Year 9 pupils by the total number of pupils.

78 (Year 9 pupils) ÷ 167 (total pupils)

= 0.4671
Multiply the result by 100 to convert the proportion to a percentage.
0.4671 × 100

= 46.71%.

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Step-by-step explanation:

42/100 = 21/50 about 42%

Step-by-step explanation:

The area of a right triangle like this is   area = 1/2 * base * height

   base and height are the LEGS of the right triangle

  this one pictured piece area is:        1/2 * 14 in  * 11 in = 77 in^2

    He needs 12 of them ....so total is then   12 * 77 in^2 = 924 in^2 needed

The value of x is 29.5 units. Since the segments inside the circle have the same length, we can set  52.5  - x = 23 and get the value of x.

It is half of the diameter of the circle. The radius is used to calculate the area of a circle and the length of an arc or a circular sector.

In order to find the value of x, we need to first determine the radius of the circle.

In this problem, the first shorter side is 45 units, and the second shorter side is 27 units. Thus, we can find the radius of the circle by using the following method,

Radius of the circle = √(45² + 27²)

= √(2754) = 52.5 units

Now that we know the radius of the circle, we can use this information to find the value of x. We know that the total length of the first segment is  52.5 units. This means that the length of the segment outside the circle is x units and the length of the segment inside the circle is 52.5  - x units.

Similarly, the total length of the second segment is 50 units, so the length of the segment outside the circle is 27 units and the length of the segment inside the circle is

50 - 27 = 23 units.

Since the segments inside the circle have the same length, we can set  52.5  - x = 23 and solve for x.

52.5  - x = 23

x =  52.5  - 23

x = 29.5 units

Therefore, the value of x is 29.5 units.

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Hence, point P's coordinates are (6, 3) as the midpoint of the line segment from R to Q, which is the precise halfway point between R and Q.

A point's location on a line or in space can be determined using a set of numbers called coordinates. An x-coordinate and a como, which denote the horizontal as well as vertical ranges from a bench mark known as the origin, are the two numbers that make up coordinates in two-dimensional space. Three numbers, the x, y, and z coordinates, which describe the distances from origin in the x, y, and g directions, respectively, might make up coordinates in three-dimensional space. Among other disciplines, coordinates are frequently employed in physics, arithmetic, and geometry.

given

The midpoint of the line segment from R to Q, which is the precise halfway point between R and Q, must be located in order to determine the coordinates of point P.

We can separately aver the x- and y-coordinates to get the middle.

The midpoint's x-coordinate is (4 + 8)/2, which equals 6.

(0 + 6)/2 = 3 is the midpoint's y-coordinate.

Hence, point P's coordinates are (6, 3) as the midpoint of the line segment from R to Q, which is the precise halfway point between R and Q.

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Answer:

(-3.5 , 2.3)

Step-by-step explanation:

I know

Part A:The volume of cat food in the can is approximately 9.62 cubic inches.

Part B:The ratio of cubic inches to ounces is approximately 1.66:1.

Volume is a measure of the amount of space occupied by an object or a substance. It is the quantity of three-dimensional space enclosed by a closed surface or bounded by a given set of points. Volume is typically measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³).

PART A:

The volume of a cylinder can be calculated using the formula V = πr²h, where V is the volume, r is the radius, and h is the height. Since the diameter of the can is 3.5 inches, the radius is half of that, or 1.75 inches. The height of the can is 1 inch.

Plugging these values into the formula, we get:

V = π(1.75)²(1)

V ≈ 9.62 cubic inches

Therefore, the volume of cat food in the can is approximately 9.62 cubic inches.

PART B:

To write a ratio of cubic inches to ounces, we need to divide the volume of the can (in cubic inches) by the weight of the cat food (in ounces):

Ratio = Volume of cat food in can (cubic inches) / Weight of cat food (ounces)

Ratio = 9.62 cubic inches / 5.8 ounces

Ratio ≈ 1.66 cubic inches per ounce

Therefore, the ratio of cubic inches to ounces is approximately 1.66:1.

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Answer:

[tex]\large\boxed{(2, -3)}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked for the Center Coordinates given a circle.}[/tex]

[tex]\large\underline{\textsf{What is a Circle?}}[/tex]

[tex]\textsf{A Circle is a curved shape that is commonly used to present a equidistant (same}[/tex]

[tex]\textsf{distance apart) from a Center point.}[/tex]

[tex]\textsf{When we create an equation for a circle, we should keep in mind of what the}[/tex]

[tex]\textsf{coordinates of the center point are, and the Radius. For this problem an equation}[/tex]

[tex]\textsf{has been given to us.}[/tex]

[tex]\boxed{\begin{minipage}{20 em} \\ \underline{\textsf{\large Equation of a Circle (Standard Form);}} \\ \\ \tt \tt (x-h)^{2} + (\tt y-k)^{2} = r^{2} \\ \\ \underline{\textsf{\large Where;}} \\ \textsf{h represents the x-coordinate of the center.} \\ \textsf{k represents the y-coordinate of the center.} \\ \tt r^{2} \ \textsf{represents the radius of a circle squared.} \end{minipage}}[/tex]

[tex]\textsf{*Note that if we are given the formula, the radius is already squared, unless}[/tex]

[tex]\textsf{specified in the directions.}[/tex]

[tex]\tt (x-2)^{2} + (y+3)^{2} = 9[/tex]

[tex]\textsf{Our main focus should be h and k. Notice how both point values are negative.}[/tex]

[tex]\textsf{The Center Point is represented as the opposite given to us in the formula.}[/tex]

[tex]\underline{\textsf{Find the Opposite of -2 and 3;}}[/tex]

[tex]\tt -2 \rightarrow \boxed{2}[/tex]

[tex]3 \rightarrow \boxed{-3}[/tex]

[tex]\underline{\textsf{Center Coordinates;}}[/tex]

[tex]\large\boxed{(2, -3)}[/tex]

Answer:

Option D is the correct answer

D. f(n) = 95 + 60(n - 1)

Step-by-step explanation:

Solution:

The coordinates of the triangle's image in the question serve as an example of transformation and are A(-2,4), B (-3,7), and C (0,6).

The triangle's coordinates are as follows:

(-6,-1), (-5,2) and (-3,0) (-3,0)

The new points are created when the triangle is mirrored over the line y = 2.

(-6,5), (-5,2) and (-3,4) (-3,4)

Then, we use the translation to translate the triangle's picture.

(x,y) -> (x + 3, y +2)

We thus have:

(-6,5) => (-6 + 3, 5 + 2) = (-3,7) (-3,7)

(-5,2) => (-5 + 3, 2 + 2) = (-2,4) (-2,4)

(-3,4) => (-3 + 3, 4 + 2) = (0,6) (0,6)

Hence, the triangle's image's coordinates are A(-2,4), B (-3,7), and C (0,6) respectively.

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3. The measure of angle S in the given pentagon is 155.33 degrees. 4. The value of x is 9. 5. The value of x is 40 degrees. 6. The value of angle C is 33 degrees. 7. The polygon has 30 sides.

A polygon having 5 sides and 5 angles is called a pentagon. Two terms, Penta and Gonia, both of which denote five angles, combine to form the word "pentagon." End to end, the sides of a pentagon come together to form a shape. Every side of a regular pentagon has the same length, and its five angles are all the same size. A pentagon is said to as irregular if its side length and angle measurement are not equal.

The sum of angles of a pentagon is equal to 540 degrees.

Thus,

5x + 2 + 10x - 3 + 8x - 19 + 13x - 31 + 7x - 11 = 540

42x - 62 = 540

42x = 602

x = 14.33

The angle of s is:

13(x) - 31 = 13(14.33) - 31 = 155.33

Hence, the measure of angle S in the given pentagon is 155.33 degrees.

4. In a regular hexagon, each angle is equal, and the sum of all the angles is equal to 720 degrees.

6A = 720

A = 120

11x + 21 = 120

x = 9

5. The angle of a nonagon is 140 degrees.

Now, 140 + x = 180

x = 80 degrees.

6. For the given triangle we have:

exterior angle of C = D + E

Substituting the value of D and E as:

7x - 2 = 180 - 9x + 31 + 180 - 4x + 33

7x - 2 = 360 - 13x + 64

20x = 426

x = 21.3

Angle C = 180- (7(21.3) - 2) =  33 degrees.

7. single angle = (n-2) x 180 / n

168n = (n - 2) 180

168n = 180n - 360

360 = 12n

n = 30

The polygon has 30 sides.

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Answer:

a

Step-by-step explanation:

A tree should therefore have 38,900 leaves on average by the eighth week of spring.

An equation that depicts a linear model on a graph is referred to as a linear equation. This polynomial equation has a factor whose greatest power is one. The formula for a linear equation is y = mx + b, were x and y are factors, m is the line's gradient or slope, and b is the y-intercept, or the place where the line crosses the y-axis. The line's steepness is determined by its slope, and its point of intersection with the y-axis is indicated by its y-intercept. Science and mathematics both frequently model and examine relationships between variables using linear equations.

given

B is the right response for the linear equation y = 4700x + 1500, which can be used to approximate the data distribution.

We may enter x = 8 into the calculation to get the predicted average number of leaves on a tree 8 weeks after spring has begun:

y = 4700(8) + 1500

y = 38,900

A tree should therefore have 38,900 leaves on average by the eighth week of spring.

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Answer:

A

Step-by-step explanation:

Given:

r (radius) = 5 in

h (height) = 5 in

Find: A (surface area) - ?

.

[tex]a(surface) = a(lateral) + a(2 \: bases)[/tex]

First, we have to find the lateral surface:

[tex]a(lateral) = 2\pi \times r \times h = 2 \times 3.14 \times 5 \times 5 = 157 \: {in}^{2} [/tex]

Then, we have to find the area of the base and multiply it by 2, since the shown figure is a cylinder, which has 2 identical bases:

[tex]a(2 \: bases) = 2 \times \pi {r}^{2} = 2 \times 3.14 \times {5}^{2} = 157 \: {in}^{2} [/tex]

Now, let's add everything together and we'll get the answer:

[tex]a(surface) = 157 + 157 = 314 \: {in}^{2} [/tex]

Answer:

36.4

Step-by-step explanation:

In morning, builder worked for = 25 in a hour.

Let hour be ? hr.

then 25? = Time he worked in morning.

In afternoon,he worked for= 910 of ? hour = 910? hr

Times he worked more = 910?/25? = 36.4 times

25*6 =

Answer:

11/3

Step-by-step explanation:

2[tex]\frac{1}{5}[/tex] = 11/5

2[tex]\frac{1}{5}[/tex] ÷ [tex]\frac{3}{5}[/tex] = 11/5 · 5/3 = 55/15 = 11/3

Therefore, the correct option is C). graph with the x axis labeled number of days and the y axis labeled total amount of

sunglasses and a line going from the point 0 comma 52 through the point (1,49).

mathematics, a graph is a data structure that represents a collection of vertices (also known as nodes) and edges between them.

A graph can be used to represent a wide range of real-world systems, such as social networks, transportation networks, and electrical circuits.

In a graph, vertices are usually represented as points or circles, and edges are represented as lines or arrows that connect pairs of vertices. Each edge can be directed (pointing from one vertex to another) or undirected (connecting two vertices without any specific direction).

Graphs can be classified in many ways, such as by their density (the ratio of edges to vertices), their connectivity (how many separate components the graph has), and their degree distribution (the distribution of the number of edges connected to each vertex). Graph theory, which is the study of graphs, has many practical applications in computer science, mathematics, and other fields.

Which graph shows the relationship given in the table?

A) graph with the x axis labeled number of days and the y axis labeled total amount of

sunglasses and a line going from the point 0 comma 52 through the point 1 comma 50.

B) graph with the x axis labeled number of days and the y axis labeled total amount of

sunglasses and a line going from the point 0 comma 56 through the point (1,54)

C) graph with the x axis labeled number of days and the y axis labeled total amount of

sunglasses and a line going from the point 0 comma 52 through the point (1,49)

D) graph with the x axis labeled number of days and the y axis labeled total amount

of sunglasses and a line going from the point 0 comma 56 through the point (1,53)

Based on the given data in the table, the inventory of sunglasses decreases as the number of days since the opening of the eyeglasses store increases. This suggests a negative correlation between the two variables.

To visualize this relationship, we can plot the data points on a scatter plot and draw a line of best fit. Based on the options provided, the closest graph to the relationship given in the table is option C) with the x-axis labeled as number of days, the y-axis labeled as the total amount of sunglasses, and a line going from the point 0,52 through the point 1,49.

Option A) has a decreasing trend, but the line does not pass through all the given data points.

Option B) has a similar decreasing trend, but the values on the y-axis are higher than those in the table.

Option D) has a decreasing trend, but the values on the y-axis are higher than those in the table, and the line does not pass through all the given data points.

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A: 75% of items are classified as C items, 18.75% as B items, and 6.25% as A items.

A-B-C examination is an instrument utilized for stock administration, which orders things into three classifications: A, B, and C, in light of their worth and significance. Classification A things have a high worth however a low volume, and their administration requires close consideration and control. Class B things have moderate worth and volume and require moderate control. Classification C things have a low worth yet a high volume, and their administration can be loose. The reason for the examination is to recognize which things need the most consideration and control, and which things can be dealt with less consideration and cost-actually. The examination assists in streamlining with reviewing levels, decreasing expenses, and expanding benefits.

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So, the hose can complete the job alone in approximately 2.62 hours, and the inlet pipe can complete the job alone in approximately 1.62 hours.

Let the time it takes for the hose alone to fill the pond be H hours, and the time it takes for the inlet pipe alone be P hours. According to the given information:

1) P = H - 1 (The inlet pipe alone can complete the job in one hour less time than the hose alone)

2) In one hour, the hose fills 1/H of the pond, and the inlet pipe fills 1/P of the pond. Together, they can fill the pond in one hour, so: (1/H) + (1/P) = 1

Now, substitute the value of P from equation 1 into equation 2:

(1/H) + (1/(H-1)) = 1

To solve for H, first find a common denominator (H*(H-1)):

(H-1) + H = H*(H-1)

Combine the terms on the left:

2H - 1 = H^2 - H

Rearrange to form a quadratic equation:

H^2 - 3H + 1 = 0

Now, solve the quadratic equation using the quadratic formula:

[tex]H = (3 + sqrt(5))/2 or H = (3 - sqrt(5))/2[/tex]

However, since H > 0, the only valid solution is H = (3 + sqrt(5))/2 ≈ 2.62 hours.

Now, find the time it takes for the inlet pipe alone to complete the job:

P = H - 1 = 2.62 - 1 = 1.62 hours

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The common ratio of the second geometric progression is 1/5.

A geometric progression or a geometric sequence is the sequence, in which each term is varied by another by a common ratio. The next term of the sequence is produced when we multiply a constant (which is non-zero) to the preceding term. It is represented by:

a, ar, ar2, ar3, ar4, and so on.

Let the common ratio of the second geometric progression be r. Then the sum to infinity of the first progression is:

S1 = a1/(1 - r1), where a1 = 25 and r1 = 1/2

And the sum to infinity of the second progression is:

S2 = a2/(1 - r), where a2 = 40 and r is the common ratio of the second progression

We know that S1 = S2, so we can set the two expressions equal to each other:

S1 = S2

a1/(1 - r1) = a2/(1 - r)

Substituting the given values:

25/(1 - 1/2) = 40/(1 - r)

Simplifying:

50 = 40/(1 - r)

Multiplying both sides by (1 - r):

50 - 50r = 40

Subtracting 50 from both sides:

-50r = -10

Dividing both sides by -50:

r = 1/5

Therefore, the common ratio of the second geometric progression is 1/5.

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Answer:

f(-3/2) = -411/16.

Answer:

(2,1)          (2,1)

1=5(2)-9   1=-2(2)+5

1=10-9      1=-4+5

Step-by-step explanation:

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a) The probability that the battery lasts more than 4 hours is 0.758 (rounded to 3 decimal places).

b) The 25% value is 240 minutes, and the 75% value is 310 minutes.

c) The value of life in minutes that is exceeded with 95% probability is 357 minutes.

a) To find the probability that the battery lasts more than 4 hours (240 minutes), we first need to convert 240 minutes into a z-score.
z = (X - μ) / σ
z = (240 - 275) / 50
z = -0.7
Now, we'll use a z-table to find the probability that the battery lasts more than 4 hours:
P(Z > -0.7) = 1 - P(Z ≤ -0.7) = 1 - 0.2420 = 0.758
The probability that the battery lasts more than 4 hours is 0.758 (rounded to 3 decimal places).
b) To find the quartiles, we'll use the z-table to find the z-scores corresponding to 25% and 75%:
25%: z = -0.674
75%: z = 0.674
Now, we'll convert the z-scores back into minutes:
Q1 = μ + z * σ = 275 + (-0.674) * 50 = 240 (rounded to the nearest integer)
Q3 = μ + z * σ = 275 + (0.674) * 50 = 310 (rounded to the nearest integer)
The 25% value is 240 minutes, and the 75% value is 310 minutes.
c) To find the value of life in minutes that is exceeded with 95% probability, we first find the z-score corresponding to 95%:
95%: z = 1.645
Now, we'll convert the z-score back into minutes:
X = μ + z * σ = 275 + (1.645) * 50 = 357 (rounded to the nearest integer).

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Answer:

Step-by-step explanation:

Search up the area of both. rectangle is LxW therefore the area is 18.  the other is trapezium therefore, ((a+b)xh)/2 therefore the area is 20. trapezium has larger area

Answer trapezoid has  greater area

Step-by-step explanation: rec: 6*3= 8,  trapezoid [ (6+2) * 5 ]1/2  = 20

The corresponding inequality for this graph is

0 <= x <= 5

An inequality is a statement that two values are not necessarily equal. In other words, it expresses a relation between two quantities that can be either less than, greater than, less than or equal to, or greater than or equal to each other. Inequalities are typically written using symbols such as "<" (less than), ">" (greater than), "≤" (less than or equal to), and "≥" (greater than or equal to).

The graph represents a shaded rectangle with sides on the x and y axes, and with one corner at the origin (0,0). The top-right corner of the rectangle is at the point (5,5), and the sides of the rectangle are parallel to the axes.

The corresponding inequality for this graph is 0 <= x <= 5, which can be read as "x is greater than or equal to 0 and less than or equal to 5".

Therefore, the correct answer is:

0 <= x <= 5

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The complete question is:

Which of the following inequalities matches the graph?

Ox≤5

0<=x<=5

Answer:

Step-by-step explanation:

14.516129%

Answer:

The equation of the given circle is (x-2)^2 + (y+3)^2 = 9, which is in the standard form of a circle: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.

Comparing the given equation with the standard form, we can see that the center of the circle is (2, -3) and the radius is 3.

Therefore, the radius of the circle is 3 units.

1. The cannonball is at 70 meters before it is launched.

2. The cannonball reaches its maximum height at about 3 seconds.

3. The maximum height of the cannonball is about 115 meters.

4. It takes about 8 seconds for the cannonball to reach the ground.

I don't know the answer to number 5 - sorry :(

I hope the rest are correct