P= (x,y) is an arbitrary point on the circle x^2+y^2=36

1. Express the distance d from P to the point A= (8,0) as a function of the x-coordinate of P

2. What are the domain and range of this function d(x)?

Answers

Answer 1

Let (x,y) be an arbitrary point on the circle.

Then d = √[x-3)2 + (y-0)2] = √[x2 - 6x + 9 + y2]

Since x2 + y2 = 1, y2 = 1-x2.

So, d = √[x2 - 6x + 9 + 1 - x2]

     d = √(-6x+10)

Domain:  x is the x-coordinate of a point on the circle centered at (0,0) with radius 1.  So, -1≤x≤1.

             But, for d to be defined, we need -6x+10 ≥ 0.  So, x ≤ 5/3  (True for all x in [-1,1]).

             Domain = [-1,1]

Range:    -1 ≤ x ≤ 1   So, 6 ≥ -6x ≥ -6

                                    16 ≥ -6x+10 ≥ 4

                                     4 ≥ √(-6x+10) ≥ 2   That is, 2 ≤ d ≤4

              Range:  [2,4]

Step-by-step explanation:


Related Questions

pls help
-21 ÷ b = 3, b = ? and uhm this one too
3c + 1 = 10, c = ?

Answers

Answer:

-21 ÷ b = 3, b =        b=-7

3c + 1 = 10, c =        c=1/7

Hope this helps!

What is the equation of the line that passes through the point (3, -3) and has a
slope of o?

Answers

Answer:

y = -3

Step-by-step explanation:

point = (3, -3)

slope (aka m) = 0

y = mx + b

-3 = (0)(3) + b

b = -3

y = (0)x - 3

y = -3

what is the slope perpindicular to line 5x+3

Answers

Answer:

[tex]-\frac{1}{5} x+b[/tex] (b can equal any number- you can use 3)

Step-by-step explanation:

To find the slope, you take mx (in this case 5x), get the number by itself, flip the sign, then get the reciprocal.

5 -> -5 -> [tex]-\frac{1}{5}[/tex]

What is the domain and range please?

Answers

Answer:

Domain: -2 < x < 2

Range: 1 < y < 5

Step-by-step explanation:

Domain is the set of numbers that are on the x axis

Range is the set of numbers that are on the y axis

¿Cuantas dimensiones tiene una cebolla?

Answers

Answer:

Una cebolla es un objeto tridimensional, en tanto tiene una profundidad, una altura y una anchura específicas.

Se entiende por tres dimensiones a la posibilidad de percibir un objeto a través de tres expresiones geométricamente diferentes: a través de su altura, es decir, su longitud; a través de su anchura, es decir, su extensión hacia los lados; y a través de su profundidad, entendida como la extensión que tiene el objeto desde sus bordes hacia adentro.



200x - 400 > 40x - 80

Answers

Answer:

x>2

That is the answer do you want the work?

In 2010 the Network Club membership was 2,500. With an annual growth rate of approximately 8%, compounded continuously, what will the membership be in 2020?

Answers

Answer:

5563.85 But round the nearest whole number is 5564

Step-by-step explanation:

Formule is P=Ie^(r)(t)

If, In 2010 the Network Club membership was 2,500. With an annual growth rate of approximately 8%, compounded continuously,  then 5563.85 is the population in 2022.

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

Given,

In 2010 the Network Club membership was 2,500.

Annual growth rate of approximately 8%

8% is converted to decimal value by dividing 8 with 100

8/100=0.08

[tex]P=Ie^{rt}[/tex]

p is the final population

I is the initial population

[tex]p=Ie^{0.08(10)}[/tex]

[tex]p=2500e^{0.8}[/tex]

p=5563.85

Hence, 5563.85 is the population in 2020.

To learn more on Percentage click:

https://brainly.com/question/28269290

#SPJ5

Find the slope of a line that includes the points (4, -2) and (5,0).​

Answers

Answer:

The slope is 2

Step-by-step explanation:

Find the slope and the y-intercept of the graph of y
-4/5x - 2

Answers

Answer:

slope - (-4/5)

y- intercept - (0,-2)

Step-by-step explanation:

Answer:

the slope is -4/5 and the y intercept is -2

Step-by-step explanation:

Help me please. I’m trying very hard.

Answers

Answer:

27/3

Step-by-step explanation:

50-(18+5)= 27

27/3

y+3=2(x+5), write the equation of the line in slope intercept form.

Answers

Answer:

slope intercept form: y=mx+b

y+3=2(x+5)

step 1: use distributive property

y+3=2(x)+2(5)

y+3=2x+10

step 2: subtract 3 on both sides to make y by itself

y+3=2x+10

-3 -3

final answer: y=2x+7

The ratio of boys to girls in a camp is 6 to 8. How many girls are there in the camp if there are 96 boys in the camp?

Answers

Answer:

128 girls

Step-by-step explanation:

The ratio of boys to girls is 6 to 8. We need to find how many girls there are if there are 96 boys in the camp. One way to solve this is by using cross multiplication:

[tex]\frac{6}{8}[/tex] = [tex]\frac{96}{x}[/tex]

multiply the 6 by the x: 6x

multiply 8 by 96: 768

6x = 768

divide both sides of the equation by 6 to isolate the x:

6x/6 = 768/6

x = 128

When there are 96 boys in camp, there will be 128 girls.

Answer:

6/8=96/x

Step-by-step explanation:

7(1 - x) = -3(x - 2) What is x please help me

Answers

7(1-x)=-3(x-2) distribute(multiply)
7-7x=-3x+6 add 7 to both sides.
+7 +7
7=4x+6 Subtract 6 to both sides.
-6 -6
1=4x divide by 4.
4 4
1/4=X this is the answer
I hope this helps you :D

which fraction is larger 3/4 or 7/9 and find the common denominator

Answers

Answer:

the answer is 7/9

Step-by-step explanation:

09) The ratio of the number of jackfruit in baskets P, Q
and R is 6:2:5. The total number of jackfruit
in basket Pis 48 more than the number of
jackfruit in basket Q. Calculate the total number
of jackfruits in the three baskets.
A 121 B 144 C 156 D 169​

Answers

Answer:

156 jackfruits

Step-by-step explanation:

Let there are 6x jackfruit in baseket P, 2x in basket Q and 5x in basket R.

The total number of jackfruit  in basket P is 48 more than the number of  jackfruit in basket Q. ATQ,

6x = 48 + 2x

Solving for x.

6x - 2x = 48

4x = 48

x = 12

Jackfruits in basket P = 6x = 6(12) = 72

Jackfruits in basket Q = 2x = 2(12) = 24

Jackfruits in basket R = 5x = 5(12) = 60

Total no of jackfruits = 72 + 24 + 60

= 156

So, there are 156 jackfruits in the three baskets.

heeeeeeeellllllpppppp quickly​

Answers

Answer:

A

Step-by-step explanation:

Hey hope someone can figure this out hopefully it's not that hard.

A chocolate box has the shape of a prism with a base that is a
rhombus. Each side length of the rhombus is 3.6 cm.
The angles between adjacent sides of the base are 60° and 120°.
The prism is 10.8 cm long.

a) Draw a net for this box.
b) How is your net different from the cardboard net from
which the box is made? Explain.

Answers

Part (a)

See the diagram below for the net for this box. We have two rhombuses that are the two bases of the rhombic prism. The six rectangles form the lateral sides.

In geometry, a net is effectively the outer surface of a 3D object, but it has been laid flat on a plane. Think of unwrapping a present without throwing any pieces away. The net would be the wrapping laid out flat. As another example, a net of a cardboard box would be laying the box flat. So you're unfolding the box. This is mentioned in part (b).

====================================================

Part (b)

The main difference from this net compared to a net for a cardboard box is that everything is a rectangle for a cardboard box. This is because a cardboard box folds up into a rectangular prism.

So in the diagram below, you'll replace each rhombus with a rectangle. You'll make all four angles 90 degrees.

A teacher wrote the following part of a chemical equation
involving water (H20) and carbon dioxide (CO2):
H2O + CO2?
What is the most likely result of the chemical reaction represented by this
equation?
A. H2Ca3
B. HNO3
C. Nacl
D. H2CO3
Brown is

Answers

Answer:

D

Step-by-step explanation:

H2CO3

ithink it is the answer maybe

Answer:

D. H2CO3

Step-by-step explanation:

D is the correct answer

BRAINLIEST TO WHO ANSWERS FIRST
(4x^2 −2x−6)- (7x−9)

Answers

Answer:

4x^2-9x+3

Step-by-step explanation:

(4x^2 −2x−6)- (7x−9)

=(4x^2-2x-6-7x+9)

=(4x^2-9x+3)

4x^2-9x+3is the answer

Answer:

4x² - 9x + 3

Step-by-step explanation:

(4x² - 2x - 6) - (7x - 9)

4x² - 2x - 6 - 7x + 9

4x² - 2x - 7x - 6 + 9

4x² - 9x + 3

-TheUnknownScientist

WORTH A BRAINLIEST I NEED HELP ON BOTH PLEASE EXPLAIN AND SJOW YOUR WORK!!

Answers

Answer:

- 4

Step-by-step explanation:

B .

-7 -(-3) = -7 + 3

start at -7 and move 3 to the right

difference is -4

WILL MARK BRAINLYIST IF YOU ANSWER CORRECTLY!!!!!! As water evaporates from a potted plant, its weight changes at a rate of -1 5/8ounces per day. Part A Estimate the change in the potted plant’s weight after one week. Explain your thinking. Part B Write and solve an equation using exact values to show the change in the plant’s weight after one week. Part C Explain how your estimate shows your answer is reasonable.

Answers

For part A it would be 11 3/8 ( I did the math fam ) for part b it would be y = 1 5/8x, you just substitute the x for 7 and you’d get the answer from part a, For part C you would just say that you multiplied the 1 5/8 rate by 7 to get the total amount of weight lost within that week

Now I’ll take that brainliest fam, lmk if it was right

Read the excerpt from The Strange Case of Dr. Jekyll and Mr. Hyde.

This hall, in which he was now left alone, was a pet fancy of his friend the doctor’s; and Utterson himself was wont to speak of it as the pleasantest room in London. But tonight there was a shudder in his blood; the face of Hyde sat heavy on his memory; he felt (what was rare with him) a nausea and distaste of life; and in the gloom of his spirits, he seemed to read a menace in the flickering of the firelight on the polished cabinets and the uneasy starting of the shadow on the roof. He was ashamed of his relief, when Poole presently returned to announce that Dr. Jekyll was gone out.

Which statement best describes how the author establishes mood in the excerpt?

a.The author’s description of the grand room creates an admiring mood.
b.The author’s description of physical symptoms creates an anxious mood.
c.The author’s mention of Utterson’s thoughts creates a sentimental mood.
d.The author’s mention of Utterson’s spirits creates a spiritual mood.

Answers

Answer:

b.The author’s description of physical symptoms creates an anxious mood.

Y’all I need help with this! Someone help me please and thank you! Can y’all like tell me the steps if possible! (Y=Mx+b)

Question:Y+2x=16

Answers

Answer:

y = -2x + 16

Step-by-step explanation:

y = mx + b

__________

y + 2x = 16

y + 2x - 2x = 16 - 2x

y = -2x + 16

Answer:

Y=-2x+16

Step-by-step explanation:

PLS GIVE BRAINLIEST

help I will mark brainlist

Answers

Answer:

D.) j

Step-by-step explanation:

J because if in one month there is $32 and then in 2 months there are $64 its multiplying 32 times 2 and that gets 64 then 64 plus 32 is 96 then plus 32 again and that gives you 128. Its multiplying 32 times 2 then 32 times 3 then 32 times 4 and that gives you your answer.

Hope this helped!

Fifth-grade students plant a class garden. They plant 7 1/6 rows of tomatoes and 3 1/2 rows of carrots. How many fewer rows of carrots than rows of tomatoes do the students plant?

Answers

Answer:

3 2/3

Step-by-step explanation:

7 1/6 - 3 1/2= 3 2/3

this is easy just answer

4x-2+8=
(x=5)

Answers

Answer:

........................................26

What is the solution of the proportion 3/5=13/x ? Round to the nearest tenth if necessary.

Answers

Answer:x=21 2/3

Step-by-step explanation:

Answer:

x = 3/65

Step-by-step explanation:

3/5=13/x

3/5*1/13 = x

3/65 = x

Please help with the problem below.

Answers

Step-by-step

measure angle 1 is corresponding to measure angle 5

measure angle 5= measure angle 1= 71*

measure angle 5 + measure angle 8 = 180*

71*+ measure angle 8=180*

measure angle 8=109

Answer:

[tex]m\angle5 = 71\degree^{\circ}[/tex],

[tex]m\angle8=109^{\circ}[/tex]

Step-by-step explanation:

Given that [tex]a[/tex] and [tex]b[/tex] are parallel and [tex]m\angle1=71^{\circ}[/tex]:

[tex]m\angle5 = 71^{\circ}[/tex] (Corresponding angles are equal when [tex]a\parallel b[/tex] )

[tex]m\angle8+m\angle5=180^{\circ}[/tex] (The two angles make up the angle of a straight line: [tex]180^{\circ}[/tex]

[tex]m\angle8 + 71^{\circ} = 180^{\circ}[/tex]

[tex]m\angle8 = 109^{\circ}[/tex]

[tex]\therefore m\angle5=71^{\circ};m\angle8=109^{\circ}[/tex]

Hope this helps :)

slope from two points

Answers

Answer:

[tex]\frac{12}{7}[/tex]

Step-by-step explanation:

use the formula [tex]\frac{y - y'}{x - x'}[/tex]

so you would get

[tex]\frac{4 - (-8)}{0 - (-7)}[/tex]

Those negatives becomes a positive and you get 4+8 = 12 and 0+7 = 7

you final answer would be [tex]\frac{12}{7}[/tex]

Answer: I am pretty sure the answer is D.

Step-by-step explanation:

so this is how u find the slope from two points... You have (-7,-8) and (0,4) you then take -7 and subtract that by 0 so -7-0 and then -8-4. and -7-0/-8-4 = 7/12. plz tell me if I am wrong.

The expression -7y is a

Term

Constant

Variable​

Answers

Answer:

in -7y y is variable and -7 is Constant

Step-by-step explanation:

Constant: A number that cannot change its value. In the expression 2x+4y−9 , the term 9 is a constant. Like Terms: Terms that contain the same variables such as 2m , 6m or 3xy and 7xy

variable is a symbol which functions as a placeholder for varying expression or quantities, and is often used to represent an arbitrary element of a set.

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