Part A: Use the Pythagorean Theorem to derive the standard equation of the circle, with center at (a, b) and a point on the circle at (x, y). Show all necessary math work.

Part B: If (a, b) = (5, –2) and c = 10, determine the domain and range of the circle.

Part C: Is the point (10, 2) inside the border of the circle if (a, b) = (5, –2) and c = 10? Explain using mathematical evidence.

Answers

Answer 1

The distance to the point is less than c=10, so the point is inside the circle.

Given that, (a, b) = (5, –2) and c = 10.

What is domain and range of the function?

The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively. For example, if the relation is, R = {(1, 2), (2, 2), (3, 3), (4, 3)}, then:

Domain = the set of all x-coordinates = {1, 2, 3, 4}

Range = the set of all y-coordinates = {2, 3}

Part A:

Use of the Pythagorean theorem gets you to the equation for a circle in essentially one step:

Sum of squares of sides = square of hypotenuse

(x -a)²+(y -b)² = c² circle centered on (a, b) with radius c.

Part B:

The circle will be defined for values of x in the domain f ± c, and for values of y in the range b ± c.

domain: 5 ± 10 = [5, -5]

Range: -2 ±10 = [8, -11]

Part C:

The distance from point (10, 2) to (a, b)=(5, -2) is

c² = (10-5)² +(-2-2)²

c² = 25+16

c² = 41

c=√41

c=6.4

The distance to the point is less than c=10, so the point is inside the circle.

Therefore, the distance to the point is less than c=10, so the point is inside the circle.

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Related Questions

A mathematical phrase represented by numbers, variables, and operations is a(n)
pls help:)

Answers

Answer:

Expression

Step-by-step explanation:

Answer: Expression

Got this right!!!

Hope this helps!!!

When Alana was born, her grandma put $1000 into a money market account that earns 9% interest each year. How much will be in the account when Alana is 21?

Answers

The amount that would be in the account when Alana is 21 is $2890

How to determine the value

We have to know the formula for simple interest.

This is expressed as;

S.I = PRT/100

Given that the parameters of the formula are enumerated as;

SI is the simple interestP is the principal amountR is the interest rateT is the time taken

From the information given, substitute the values, we have;

SI = 1000 × 9 × 21/100

Multiply the values,

Then, divide by the denominator, we have;

SI = $1890

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Keller Construction is considering two new investments. Project E calls for the purchase of earthmoving equipment. Project H represents an investment in a hydraulic lift. Keller wishes to use a net present value profile in comparing the projects. The investment and cash flow patterns are as follows: Use Appendix B for an approximate answer but calculate your final answer using the formula and financial calculator methods.

Answers

Based on the net present value profile, Project H has a higher NPV than Project E.

To compare the net present value (NPV) of Project E and Project H, we need to calculate the present value of cash flows for each project and determine which one has a higher NPV. The cash flow patterns for the two projects are as follows:

Project E:

Initial investment: -$100,000

Cash flows for Year 1: $40,000

Cash flows for Year 2: $50,000

Cash flows for Year 3: $60,000

Project H:

Initial investment: -$120,000

Cash flows for Year 1: $60,000

Cash flows for Year 2: $50,000

Cash flows for Year 3: $40,000

To calculate the present value of cash flows, we need to discount them using an appropriate discount rate. The discount rate represents the required rate of return or the cost of capital for the company. Let's assume a discount rate of 10%.

Using the formula method, we can calculate the present value (PV) of each cash flow and sum them up to obtain the NPV for each project:

For Project E:

PV = $40,000/(1 + 0.10)^1 + $50,000/(1 + 0.10)^2 + $60,000/(1 + 0.10)^3

PV = $36,363.64 + $41,322.31 + $45,454.55

PV = $123,140.50

For Project H:

PV = $60,000/(1 + 0.10)^1 + $50,000/(1 + 0.10)^2 + $40,000/(1 + 0.10)^3

PV = $54,545.45 + $41,322.31 + $30,251.14

PV = $126,118.90

Using the financial calculator method, we can input the cash flows and the discount rate to calculate the NPV directly. By entering the cash flows for each project and the discount rate of 10%, we find that the NPV for Project E is approximately $123,140.50 and the NPV for Project H is approximately $126,118.90.

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What is the number of solutions in this system?
one solution
no solution
infinitely many solutions
First answer is Brainlyist

Answers

I could answer but u have no picture of the question

Brainliest ?

When Michael was 10 years old, Sam was 14. Sam is now 28 and Michael is 24.

Answers

Answer:

4 years difference

Step-by-step explanation:

Write the explicit formula for the given sequence.
1.5, 2.25, 3, 3.75, ...
need done asap

Answers

Answer: $a_{n}=1.5+0.75(n-1)$

Step-by-step explanation:

The common difference is 2.25-1.5=0.75$a_{n}=1.5+0.75(n-1)$. So, the explicit formula is

Write the explicit formula for the given sequence.1.5, 2.25, 3, 3.75, ...need done asap

Solve this problem using the proper formula. A lot is in the shape of a trapezoid. The sum of the bases is 280 feet. If the area of the lot is 8,400 square feet, what is the distance across the lot, i.e., the altitude of the figure? The altitude of the trapezoid is feet.

Answers

9514 1404 393

Answer:

60 ft

Step-by-step explanation:

The formula for the area of a trapezoid is ...

A = 1/2(b1 +b2)h

Fill in the given information and solve for h.

8400 ft² = (1/2)(280 ft)h

h = 8400 ft²/(140 ft) = 60 ft

The altitude of the trapezoid is 60 feet.

Question 51 ptsThe point (-4,-2) lies on a circle. What is the length of the radius of this circle if thecenter is located at (-8, -10)?O 4√5O 2√54080PreviousNext ▸

Answers

Given,

The coordinates of the point on the circle is (-4, -2).

The coordinates of the center of the circle is (-8, -10).

Reuired

The length of the center of the circle.

By using the distance formula, the radius of the circle can be calculated.

The distance formula is,

$Distance=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

Substituting the value of the coordinates of the points,

$\begin{gathered} Distance=\sqrt{(-10-(-2))^2+(-8-(-4))^2} \\ =\sqrt{(-10+2)^2+(-8+4)^2} \\ =\sqrt{(-8)^2+(-4)^2} \\ =\sqrt{64+16} \\ =\sqrt{80} \\ =\sqrt{4\times4\times5} \\ =4\sqrt[]{5} \end{gathered}$

Hence,

12=-4(-6x-3) solve for x

Answers

12 = -4(-6x-3)
12 = 24x + 12
0 = 24x
0 = x

I think the answer is x=O

please help me i need the answers help me please

Answers

Answer:

scientists

Step-by-step explanation:

What is the factored form. Help doing test rn!!!

Answers

Answer:

(y^3-2)(x^2-2)

Step-by-step explanation:

x^2y^3-2y^3 can be factored. This will be equal to y^3(x^2-2). Then for the other half it will be equal to -2(x^2-2). Because the insides are the same, the equation is the outside two number y^3 and -2 added together time the inside number x^2-2. This will make the expression (y^3-2)(x^2-2).

If this helps please mark as brainliest

Given the original statement "If a number is negative, the additive inverse is positive,” which are true? Select three options.

Answers

A. If p = a number is negative and q = the additive inverse is positive, the original statement is p → q.
B. If p = a number is negative and q = the additive inverse is positive, the inverse of the original statement is ~p → ~q.
D. If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q.

Twenty standard cartons of octal boxes weigh a total of 1,100 pounds. Find the weight per carton.

Answers

Twenty standard cartons of octal boxes weigh a total of 1,100 pounds. The weight per carton is 55 pounds.

Given that twenty standard cartons of octal boxes weigh a total of 1,100 pounds. We need to find the weight per carton.

How to find the weight per carton? To find the weight per carton, we need to divide the total weight of twenty standard cartons of octal boxes by 20.Let's assume the weight of each carton be x.

Therefore, the equation can be formed asx * 20 = 1,100 Solving the above equation for x, x = 1,100/20 Therefore, the weight per carton is 55 pounds. So, twenty standard cartons of octal boxes weigh a total of 1,100 pounds.

The weight per carton is 55 pounds.

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I am not sure how to do this. Please help.

Answers

Answer:

Step-by-step explanation:

If ∆MNP is equilateral, then each of the arcs MN, NP and PM will be 120°. An inscribed angle from anywhere that intercepts one of these arcs will have measure 60°. That is, angle MQP is 60°. We already know angle MOQ is 60° (half of arc MN), so ∆MOQ is equilateral, and MO=MQ=PO.

Points M and N were drawn using Q as a center, and PO as a radius.

The following are the annual incomes (in thousands of dollars) for 8 randomly chosen, U.S. adults employed full-time.
44, 44, 54, 54, 65, 39, 54, 44
Send data to calculator
(a) What is the mean of this data set? If your answer is not an
integer, round your answer to one decimal place.
(b) What is the median of this data set? If your answer is not
an integer, round your answer to one decimal place.
(c) How many modes does the data set have, and what are
their values? Indicate the number of modes by clicking in the
appropriate dircle, and then indicate the value(s) of the
mode(s), if applicable.
0
Zero modes
one mode:
Two modes:

Answers

Answer:

(a) To find the mean of the data set, sum up all the values and divide by the total number of values.

44 + 44 + 54 + 54 + 65 + 39 + 54 + 44 = 398

Mean = 398 / 8 = 49.75

Rounded to one decimal place, the mean of this data set is 49.8.

(b) To find the median of the data set, i need to arrange the values in ascending order first:

39, 44, 44, 44, 54, 54, 54, 65

The median is the middle value in the sorted data set. In this case, we have 8 values, so the median is the average of the two middle values:

(44 + 54) / 2 = 98 / 2 = 49

Rounded to one decimal place, the median of this data set is 49.0.

In this case, the mode refers to the value(s) that occur(s) with the highest frequency.

From the data set, i see that the value 44 appears three times, while the value 54 also appears three times. Therefore, there are two modes: 44 and 54.

The width of a rectangular slab of concrete is 14 m less than the length. The area is 32 m². What are dimensions of rectangle? The length of the slab?

Answers

The dimensions of the rectangular slab are 16 meters in length and 2 meters in width.

Let's assume the length of the rectangular slab of concrete is L meters. According to the given information, the width is 14 meters less than the length, so the width would be L - 14 meters.

The formula for the area of a rectangle is A = length × width. In this case, the area is given as 32 m², so we can set up the equation:

32 = L × (L - 14)

Expanding the equation, we get:

32 = L² - 14L

Rearranging the equation, we have:

L² - 14L - 32 = 0

To solve this quadratic equation, we can either factorize it or use the quadratic formula. In this case, it's easier to use the quadratic formula:

L = (-b ± √(b² - 4ac)) / (2a)

Here, a = 1, b = -14, and c = -32. Substituting these values into the formula, we get:

L = (14 ± √((-14)² - 4 × 1 × (-32))) / (2 × 1)

Simplifying further:

L = (14 ± √(196 + 128)) / 2

L = (14 ± √324) / 2

L = (14 ± 18) / 2

Therefore, we have two possible values for L:

L₁ = (14 + 18) / 2 = 16

L₂ = (14 - 18) / 2 = -2

Since the length of the slab cannot be negative, we discard the negative value.

Thus, the length of the rectangular slab is 16 meters. To find the width, we subtract 14 meters from the length:

Width = 16 - 14 = 2 meters

Therefore, the dimensions of the rectangle are 16 meters by 2 meters.

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The Chang family and the Robinson family each used their sprinklers last summer. The Chang family's sprinkler was used for 25 hours. The Robinson family's
sprinkler was used for 15 hours. There was a combined total output of 1275 L of water. What was the water output rate for each
rates was 65 L per hour?

Answers

Water output rate of Chang family was 30 L per hour and the water output rate of Robinson family was 35 L per hour.

What are Linear Equations?

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Let x be the water output rate of Chang family and y be the water output rate of Robinson family.

x + y = 65

25x + 15y = 1275

Multiplying the first equation throughout with 15,

15x + 15y = 975

Subtracting 15x + 15y = 975 from 25x + 15y = 1275,

10x = 300

x = 30

y = 65 - 30 = 35

Hence the water output rate of Chang family and the Robinson family is 30 L per hour and 35 L per hour respectively.

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Match the base to the corresponding height,

Answers

You have the right answers already

Step-by-step explanation:

hint base x height

or length x width

s² + 2t,
when s=5
and t = -9.

Answers

25+2(-9) would be it with the s and t replaced then simplified and the answer would be
25+(-18)=7

Which of the following is a true polynomial identity?
a) a^6+b^6 = (a^2 + b^2)(a^4 + a^2b^2 + b^4)
b) a^6 - b^6 = (a^2+b^2)(a²-ab+b²)(a²+ab + b²)
c) a^6 - b^6 = (a³-b³)(a-ab+b)(a²+ab+b²)
d) a^6 - b^6 = (a²-b²)(a²-ab+b^2)(a^2+ab+b^2)

Answers

c or d i think is the correct answer

ITS THE FOURTH QUESTION

Answers

The surface areas of the figures are 336, 82 and 836

How to calculate the surface areas

From the question, we have the following parameters that can be used in our computation:

The figures

For the triangular prism, we have

Surface area = 2 * 1/2 * 6 * 8 + 12 * 10 + 8 * 12 + 6 * 12

Surface area = 336

For the rectangular prism, we have

Surface area = 2 * (7 * 3 + 3 * 2 + 2 * 7)

Surface area = 82

For the cylinder, we have

Surface area = 2π * 7 * (7 + 12)

Surface area = 836

Answers

Step-by-step explanation:

Cross multiply

M= x( k -6)

If the measure of angle ABC is 68°, what is the measure of arc AB?

Answers

Answer:

136

Step-by-step explanation:

While there is no picture for this question, I was able to find this question online, so that should be the correct answer.

what is circumference?

Answers

The distance/measurement around a circle.

Measurement around the circle

A bag contains 120 marbles some are red and the rest are black there are 19 red marbles for every black marble how many red marbles are in the bag

Answers

Answer:

6 black marbles

Step-by-step explanation:

19+1=20

120/20=6

6×19=114

120-114=6

Can anyone help me with this i need help quick

Answers

Answer:

Step-by-step explanation:

y=mx+n m is slope if slopes are perpendicular m1.m2=-1

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

m1=2/3

m2=-3/2

y=(2/3)x-3 m=2/3 n= -3

y=(-3/2)x+2 m = -3/2 n = 2

y = - 3x² - 2x - 3
Is the function quadratic

Answers

Answer:

Yes

Step-by-step explanation:

Any equation that is to the second degree is quadratic.

Are the following events independent or dependent? Randomly selecting a ball from a BINGO tumbler without replacement. Then randomly selecting another ball from the BINGO tumbler.

Answers

The event of selecting the first ball from the BINGO tumbler without replacement is an independent event whereas then, randomly selecting another ball from the BINGO tumbler will be a dependent event.

The event of selecting the first ball from the BINGO tumbler without replacement is an independent event as it is not influenced or changed by any factor. The outcome totally depends on itself.

Then randomly selecting another ball from the BINGO tumbler will be a dependent event as it will be influenced by the ball that is being already withdrawn from the tumbler.

Therefore, the event of selecting the first ball from the BINGO tumbler without replacement is an independent event whereas then, randomly selecting another ball from the BINGO tumbler will be a dependent event.

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find the area of a rectangle with a length of 10 inches and a width of 4 inches

Answers

Answer:

40 in²

---------------------

Formula for area of a rectangle with dimensions l and w is:

A = lw

Substitute 10 for l and 4 for w:

A = 10*4A = 40 in²

−2 2/21 +(−0.25÷(− 1/4 )−1.5÷(− 3/16 ))÷(−4 1/11 )
pls answer this is a hundred point question

Answers

The answer is -4.29523809524 . (The second period is NOT another point. It’s just marking the end of a sentence. Yes, I’m a grammar & math freak)

Answer:

-4.29523809524

Step-by-step explanation:

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