MATHEMATICS COLLEGE

Find an equation of the circle that satisfies the given conditions. (Give your answer in terms of x and y.)Center

(4, −5)

and passes through

(7, 4)

Answers

Answer 1

Answer:

Answer:

$(x-4)^2+(y+5)^2=90$

Step-by-step explanation:

The equation of a circle of radius r, centered at the point (a,b) is

$(x-a)^2+(y-b)^2=r^2$

We already know the center is at $(4,-5)$ , we are just missing the radius. To find the radius, we can use the fact that the circle passes through the point (7,4), and so the radius is just the distance from the center to this point (see attached image). So we find the distance by using distance formula between the points (7,4) and (4,-5):

radius $=√((7-4)^2+(4-(-5))^2)=√(3^2+9^2)=√(90)$

And now that we know the radius, we can write the equation of the circle:

$(x-4)^2+(y-(-5))^2=√(90)^2$

$(x-4)^2+(y+5)^2=90$

Related Questions

A bacterial culture starts with 500 bacteria and doubles in size every half-hour.(a) How many bacteria are there after 3 hours?Answer: Since 3 hours equals 6 half-hours, the culture will have doubled 6 times.Therefore, there will be500 · 26 = 32,000bacteria.(b) How many bacteria are there after t hours?Answer: Since t hours is the same as 2t half-hours, the culture will have doubled 2ttimes. Therefore, there will be500 · 22tbacteria.(c) How many bacteria are there after 40 minutes?Answer: There are two possible answers depending on how you interpret the set-upto the problem. If each bacterium in the culture doubles once every half-hour on thehalf-hour, then each one will double after exactly 30 minutes, and then not again until60 minutes have passed. In that case, there will be500 · 2 = 10004bacteria after 40 minutes.On the other hand, if each bacterium doubles exactly once per half-hour, but at somerandom time within that half-hour, then it makes sense to think of the populationfunction P(t) = 500 · 22t as continuous. In that case, since 40 minutes is4060=23of an hour, the population will be500 · 2223 = 500 · 243 ≈ 1259after 40 minutes.
An isocost line will be shifted further away from the origin:_______. a. if the prices of both inputs increase. b. if total cost increases. c. if there is an advance in technology.d. All of the above are correct.
Someone help me please
16+10/5-3*2=12 true or false.
The magnitude of an earthquake depending on the energy it produces can be modeled using the equationM = 0.6666 log x - 3.2. Complete the sentences about the model.The curve representing the relationship includes the pointThe growth factor isAn earthquake with an energy level of has a magnitude of

Suppose that a digitized TV picture is to be transmitted from a source that uses a matrix of 480 * 500 picture elements (pixels), where each pixel can take on one of 32 intensity values. Assume that 30 pictures are sent per second. (This digital source is roughly equivalent to broadcast TV standards that have been adopted.) Find the source rate R (bps).

Answers

Answer:

36,000,000 bps

Step-by-step explanation:

Matrix of 480 by 500 = 480 X 500 = 240,000 pixels

Intensity values per pixel = 32. This simply means the color variations in this TV.

The bit per pixel for an intensity value of 32 is 5 (That's 2 raised to the power of 5)

Pictures sent per second = 30

Source rate R (bps) = Total number of pixels in the matrix X bit per pixel X Number of pictures sent per second.

Source rate R (bps) = 240,000 X 5 X 30 = 36,000,000 bps

Final answer:

The source rate for the digitized TV picture is 230,400,000 bps.

Explanation:

The source rate can be calculated by multiplying the number of pixels per picture element by the number of intensity values per pixel and by the number of pictures sent per second.

So, the source rate R (bps) is given by:

R = (480 * 500) * 32 * 30

Calculating this, we find that the source rate is 230,400,000 bps.

Learn more about Calculating the source rate for a digitized TV picture transmission here:

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+ AlpQLScihp oans IbEmC-HAVOXMXB3Betzzi9sI8550WzDcwaron have a spinner divided into 8 equal sections. Each section is bered with a number 1 through 8. Salma is going to spin the spinner 1600 times. Theoretically, how many times should she land on a 1, 2, 3

Answers

Answer:

Salma should land her spinner on a 1, 2 or 3 about 600 times.

Step-by-step explanation:

Since Salma has a spinner divided into 8 equal sections, and each section is bered with a number 1 through 8, and Salma is going to spin the spinner 1600 times, to determine, theoretically, how many times should she land on a 1, 2, 3 the following calculations must be performed:

8 = 100

3 = X

3 x 100/8 = X

300/8 = X

37.5 = X

100 = 1600

37.5 = X

37.5 x 1600/100 = X

60000/100 = X

600 = X

Therefore, Salma should land her spinner on a 1, 2 or 3 about 600 times.

For each of the following four statements, indicate whether it is possible or not according to probability theory. Explain your answer. (1) The probability that a customer will buy 5 items in a single purchase is 30% ___________________________ (2) The probability that a customer will buy 3 items in a single purchase is 101% ___________________________ (3) The probability that a customer will buy 3 items in a single purchase is 99% ___________________________ (4) The probability that a customer will buy 8 item

Answers

Answer:

a) According to probability theory, the following are possible:

(1) The probability that a customer will buy 5 items in a single purchase is 30%. This represents a 0.30 chance of the customer buying 5 items.

(3) The probability that a customer will buy 3 items in a single purchase is 99% This means that there a 0.99 chance that the customer will buy 3 items.

b) According to probability theory, the following are not possible:

2) The probability that a customer will buy 3 items in a single purchase is 101%. Probability is always equal to 1 or 100%. It cannot exceed 100%.

(4) The probability that a customer will buy 8 item. This part lacks the necessary information to solve the problem.

Step-by-step explanation:

Probability describes the likelihood or chance of an event happening out of the many possible events that can take place. The sum of all probabilities for a particular event is always equal to 1. This shows that probability does not exceed 100%.

What does it mean to evaluate?

Answers

Answer:

Means to simply solve, sometimes you may need to show your thinking, depending on the question.

Step-by-step explanation:

Answer:

Evaluate means to assess or determine something.

Step-by-step explanation:

Compare to the graph f(x)=x^2 the graph of g(x)=(x-2)+3 is the result of translating f(x) 1.2 units up 3 units to the right
2. 2 units down and 3 units up
3. 2 units right and 3 units up
4 2 units left and 3 units right

Answers

Answer:

i believe it is 4 but i'm not so sure

Step-by-step explanation:

Final answer:

The graph of g(x)=(x-2)^2+3 compared to the graph of f(x)=x^2 is translated 2 units to the right and 3 units upwards.

Explanation:

To understand the transformation of graphs in mathematical terms, consider the initial function f(x) = x^2. The transition to the new function g(x)=(x-2)^2+3 is a result of a shift or translation of the graph. This transformation behaves as per the following rule: g(x) = f(x-h)+k where 'h' units is the horizontal displacement and 'k' units is the vertical displacement.

In the function g(x), x shifts two units to the right (as indicated by (x-2)) and three units upward (as indicated by +3).

So, the correct answer is 2 units right and 3 units up.