Find the equation of the tangent to the circle x2 + y2 = 109 at point (-10,3)

Answers

Answer 1

Answer:

10x - 3y = -109 .

Step-by-step explanation:

x^2 + y^2 = 109

Implicit Differentiation:

2x + 2y.y' = 0

y' = -2x/2y = -x/y

So at the point (-10,3) the gradient of the tangent is -(-10)/3 = 10/3.

Equation of the tangent:

y - y1 = m(x - x1)

y - 3 = 10/3(x + 10)

y - 3 = 10/3 x + 100/3

3y - 9 = 10x + 100

-109 + 3y = 10x

10x - 3y = -109  


Related Questions

PLEASE HELP ME WITH THIS !!

Answers

Answer: C

Step-by-step explanation:

When Flipped Down A is on the same point as D

Answer:

c

Step-by-step explanation:

because they are mirrored the only one that is equivilent is c

b doesnt corrospond to f it corrosponds to e

bc corrosponds to ef

ab corrosponds to ed.

Pablo had $319 in his savings account. He got $28 for helping a neighbor, and he saved all but $11 of it.

How much is in Pablo's savings account now?

A.
$330

B.
$336

C.
$347

D.
$358

Answers

Answer:

the correct answer is B. $336

Step-by-step explanation:

you first add 319 and 28. Then, you subtract the product with 11.

To be honest I think the answer is B

Regis leans a 10-foot ladder against a wall. The base of the ladder makes a 65 angle with the ground.
(a)
What is the distance, In feet, from the base of the ladder to the base of the wall? Round to the nearest tenth of a foot.
(b) Regis needs to move the ladder so that it reaches a window 9.6 feet above the ground.
How many feet closer to the building does he need to move the base of the ladder?

Answers

The distance, In feet, from the base of the ladder to the base of the wall is 4.2 ft.

He needs to move the ladder 0.1 ft closer to the base of the building.

The situation forms a right angle triangle.

Right angle triangle

Right angle triangle has one of its angles as 90 degrees. The sides and angle can be found using trigonometric ratios.

The length of the ladder is the hypotenuse of the triangle formed. Therefore, the distance, In feet, from the base of the ladder to the base of the wall can be calculated as follows;

cos 65° = adjacent / hypotenuse

cos 65° = d / 10

d = 10 × 0.42261826174

d = 4.22618261741

d = 4.2 ft

She needs to move the ladder so it reached a window 9.6 feet above the ground. Therefore, the distance from the base of the ladder and the wall is as follows;

cos 65 = d / 9.6

d = 9.6 × 0.42261826174

d = 4.05696

d = 4.1

Therefore, he needs to move the ladder 0.1 ft closer to the building.

learn more on right angle triangle here: https://brainly.com/question/14988069

Landon is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if he spins a spinner with four equal-sized sections labeled Red, Green, Blue, Orange and spins a spinner with three equal-sized sections labeled Walk, Run, Stop?

Answers

The total number of ways this can be done is 144 ways

How to determine the number of outcomes

Generally, the total outcomes that are there when n objects are spinned is expressed as n!

n! = n(n-1)(n-2)!

If he spins a spinner with four equal-sized sections labeled Red, Green, Blue, Orange and three equal-sized sections labeled Walk, Run, Stop, the total outcome is expressed as:

Total outcome = 4! * 3!
Total outcome = 24*6
Total outcome = 144 ways

Hence the total number of ways this can be done is 144 ways

Learn more on combination here: https://brainly.com/question/11732255

List the following fractions from least to greatest 1/6 2/3 1/2 1/3

Answers

Answer:

1/6 < 1/3 < 1/2 < 2/3

Step-by-step explanation:

We can turn the following to decimal;

1/6 = 0.16666666666        

2/3 = 0.66666666666

1/2 = 0.5

1/3 = 0.33333333333

0.16666666666   < 0.33333333333 < 0.5 < 0.66666666666

Thus, from least to greatest is 1/6 < 1/3 < 1/2 < 2/3

~Learn with Lenvy~

PLEASE HELP!!! I"LL MARK AS BRAINLIEST!!!A local water park has two types of season passes. Plan A costs a one-time fee of $139 for admission plus $8 for parking every trip. Plan B costs a one-time fee of $43 for parking plus $24 for admission every trip. How many visits must a person make for plan A and plan B to be equal in value?

Answers

Answer:

6 visits

Step-by-step explanation:

Plan A: 139+8x

Plan B: 43+24x

Set the equations equal to each other.

[tex]139 + 8x = 43 + 24x[/tex]

Subtract 43 from both sides.

[tex]96 + 8x = 24x[/tex]

Subtract 8x from both sides.

[tex]96 = 16x[/tex]

Divide both sides by 16.

[tex]x = 6[/tex]

The answer would be 6 visits! I hope this helps!

8) Evaluate this expression.

7.4 - (-3.7)

A) -3.7

B) 8.4

C) 11.1

D) 13.21

Answers

Answer:

C) 11.1

Step-by-step explanation:

7.4 -(-3.7)

- and - make +

7.4 + 3.7 = 11.1

Looking at the statement below, what is the current balance in the account if the beginning balance was $894.83?

Please help a bro out

Answers

Answer: $355.39

Step-by-step explanation: subtract 174.25,180.96,184.24 from 8194.84 =

Which of the following best describes the graph below

Answers

Answer:

i believe its A

Step-by-step explanation:

Answer:

B. The graph is not a function.

Step-by-step explanation:

We are given the graph of a relation. It is required to determine whether the graph represents a function or not. 'If a vertical line passing through the graph of the relation cuts the graph at at-most one point, then the given graph represents a function else not'. So, if we plot the vertical line 'x = 3' in the figure, we see that, The vertical line drawn crosses the graph at two points A and B as shown below. Thus it would be B

A bedroom door in the house has the same dimension as the front door but the length is 30 inches rather than 36 inches how much greater is the volume of the front door than than the bedroom door

Answers

Answer:

6/5

Step-by-step explanation:

Calculate the volume by multiplying the measured length and width of the space together, then multiply the result by the height of the room. From the example, 10 * 25 feet = 250 square feet, and 5 * 10 feet = 50 square feet.

i need help finding x and y​

Answers

Answer:

x is 5 and y is 6

Step-by-step explanation

we find 2/3 factors that equal 10. 2 and 3. the only other number that can be added that equals 10 is 5. i apply the same logic to y

Answer:

Y -- 6

X -- 5

Step-by-step explanation:

we first find y by finding the side that is the longest that is parallel to y (16) we also find that two sets of fives are also parallel to y and 16 as seen in the first screenshot. Then to find the missing value we will subtract the 5 two times from 16 to find y. 16 - 5  = 11 - 5 = 6.

we do the same thing to find x, (10 - 2 = 8) (8 - 3 = 5) X = 5

proof for the extreme value theorem

Answers

In calculus, the extreme value theorem states that if a real-valued function f is continuous on the closed interval [a, b], then f must attain a maximum and a minimum, each at least once

can someone plssss help me with this. I WILL MARK BRAINLIEST

Answers

Answer:

5 payments

Step-by-step explanation:

First we add up the prices for the lunches and the movies :)

3 x 5 = 15

15 + 9.5 = 24.5

Second we subtract the 24.5 from the 35 :)

35 - 24.50 = 10.5

Now we divide the price of the cd player by the 10.50 to get the total number of payments :)

50/10.5 = 5

Finally to check it one more time, we multiply the 10.5 by 5 and if it equals 50 or over, it is correct!! :D

10.5 x 5 = 52.5!!!

You did it!

Your correct answer is 5 payments!!

Have a great day!!!

Please rate and mark brainliest!!

Answer: he will have enough in 5 allowance payments

Explanation:
35+5=40 (starting cash)
40-24.5=15.5 (week 1)
15.5+35-24.5=26 (week 2)
26+35-24.5=36.5 (week 3)
36.5+35-24.5= 47 (week 4)
47+35-24.5=57.5 (week 5)

The longer leg of a right triangle is 1 cm longer than the shorter leg. The hypotenuse is 9 cm longer than the shorter leg. Find the side lengths of the
triangle.
cm
Length of the shorter leg: 0
Length of the longer leg: 0
Length of the hypotenuse: 0
cm
cm

Answers

Answer:

Shorter leg = 20 cm.

Longer leg = 21cm.

Hypotenuse = 29 cm

Step-by-step explanation:

Let the shorter leg be x cm long

Then longer leg = x + 1 and hypotenuse = x + 9 cm long

So by Pythagoras:

x^2 + (x + 1)^2 = (x + 9)^2

0 = x^2 + 18x + 81 - x^2 - (x^2 + 2x + 1)

x^2 + 18x + 81 - x^2 - x^2 - 2x - 1 = 0

-x^2 + 16x + 80 = 0

x^2 - 16x - 80 = 0

(x - 20)(x + 4) = 0

So x = 20   (we ignore the negative root).

So longer leg = 20 + 1 and hypotenuse = 20 + 9.

You have four $20 bills, ten $5 bills, and twelve $1 bills in your wallet. If you reach into your wallet twice, what is the probability that you will pull out a $1 bill the first time and a $5 bill the second time?

Answers

Answer:

2/28 ?

Step-by-step explanation:

if I'm wrong so sorry

choco chip cookies cost $3.20 for the 15oz size . The 18oz size $3.75 Which is the better buy

Answers

Answer:

18 oz

Step-by-step explanation:

Choco Chip Cookies (15 oz): [tex]\frac{\$3.20}{15oz}=\frac{\$0.213}{oz}[/tex]

Choco Chip Cookies (18 oz): [tex]\frac{\$3.75}{18oz}=\frac{\$0.208}{oz}[/tex]

So, the 18oz package is the better buy by about [tex]\$0.005[/tex]

Solve for c
Can you pls help me??

Answers

Answer:

5(c+3)=85

divide both sides by 5

c+3=17

taking 3 to the other side gives us -3

c=17-3

c=14

There should be 2 answers

Answers

[tex]|6m-2|=0\\\\\implies 6m-2 =0~~~~~~~~~~~~~;[\text{If}~ |x| = 0 ~\text{then}~ x = 0]\\\\\implies m = \dfrac 26 = \dfrac 13[/tex]

Katie ate dinner at a restaurant. The bill came to $77. If she left an 18% tip, how much was the tip?


Can someone pls help me?​

Answers

Answer:

$13.86

Step-by-step explanation:

Just multiply 77 by 18 percent as a decimal (.18) to get the answer, which is $13.86

Hopefully this helps- let me know if you have any questions!

Need help on number 10
If tan C is 3/4, find the sin C.

Answers

Answer:

sin C = 3/5

Step-by-step explanation:

see image.

It helps to draw a picture. Tan C is the ratio of the OPP/ADJ.

Pythagorean theorem or if you know Pythagorean triples are a shortcut to find the hypotenuse.

Once you know the hypotenuse, use the ratio for sine to solve the question. Sine is OPP/HYP.

see image.

please help! What is 75 % of 62-(98/4)

Answers

Answer:

28.13

Step-by-step explanation:

62 - (98/4)

62 - 24.5 = 37.5

75% of 37.5 is 28.125, or 28.13.

Answer:

22

Step-by-step explanation:

98/4 = 24.5

62-24.5 = 37.5

75% of 37.5

= about 22

express in the form 1 : n give n as a simplifeid fraction 8 : 6​

Answers

Answer:

So, Simplified fraction of 8:6 is 4:3.

What is the sum of the interior angles of a regular polygon with 7 sides

Answers

Answer:

the answer is 900 degrees

Step-by-step explanation:

brainliest?

Answer:

900°

Step-by-step explanation:

sum of interior angles of n sides polygon=(n-2)×180

n=7

Hence sum of interior angles of 7 sided polygon=(7-2)×180

=5×180

=900°

Can the sides of a triangle have lengths 2, 6, and 7?

Answers

Answer:

Yes

Step-by-step explanation:

The third largest side is 7 and the other two sides added are bigger than seven.

2 + 6 = 8

Is this answer accurate?

What is the value of y in the equation 4x +3 y= 23 when x=2 , x=6

Answers

Answer:

5, -⅓

Step-by-step explanation:

x = 2:

4x + 3y = 23

3y = 23 - 4(2)

3y = 15

y = 5

x = 6:

4x + 3y = 23

3y = 23 - 4(6)

3y = -1

y = -⅓

Solve by completing the square

Answers

Answer:

The answer is (-6 + √41), (-6 – √41)

Step-by-step explanation:

We are given an equation

x² + 12x = 5

Subtract 5 from both side we get,

x² + 12x – 5 = 5 – 5

x² + 12x – 5 = 0

we get the equation in the form of

ax² + bx + c = 0

Here, a = 1, b = 12, c = (-5)

Now, Add and subtract (b/2a)² we get,

x² + 12x + (12/2)² – (12/2)² – 5 = 0

x² + 12x + (6)² – (6)² – 5 = 0

(x + 6)² – 36 – 5 = 0

(x + 6)² – 41 = 0

Now, add 41 both side we get,

(x + 6)² – 41 + 41 = 0 + 41

(x + 6)² = 41

√(x + 6)² = √41

x + 6 = ±√41

x = -6 + √41, -6 – √41

Thus, The roots of the equation is

(-6 + √41) and (-6 – √41).

-TheUnknownScientist 72

The length of a rectangular garden is 4 more than three times the width. If the perimeter of the garden 104 feet, what are the dimensions of the garden.

Write your system of equations:
Answer the question being asked:

Answers

Answer:

12 ft by 40 ft

Step-by-step explanation:

Let L represent the length and W the width.  Then L = 3W + 4.

The perimeter formula is P = 2L + 2W or P = 2(L + W).

Substituting 104 ft for P, we get 104 ft = 2(L + W), which reduces to

52 ft = L + W, or 52 ft = 3W + 4 + W.

Therefore, 52 ft = 4W + 4.  

Solving this for W, we get 48 ft = 4W, or W = 12 ft.

Then, because L = 3W + 4, L = 3(12 ft) + 4 = 40 ft = L

The dimensions of the garden are 12 ft by 40 ft.

Jodi has a collection of 153 shells. She gives 39 shells to her sister Sherri. Then their mother gives each sister 28 shells.

Part A
How many shells does Sherri have now?

A.
28

B.
67

C.
142

D.
181

Part B
How many shells does Jodi have now?

A.
28

B.
67

C.
142

D.
181

Answers

Answer:

Part-A= C

Part-B= B

Step-by-step explanation:

153-39=114

114+28=142

39+28=67

Answer:

Part A is b and Part B is c good luck

What is the balance point for the following data set? 19 80 15 20​

Answers

The balance point of the dataset is the mean of the dataset

The balance point of the dataset is 20

How to determine the balance point?

From the dataset, we have the following frequency table

Data (x)     Frequency (f)

15                    2

24                   1

26                  1

The balance point of the dataset is the mean value of the dataset, and the mean is calculated as:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

This gives

[tex]\bar x = \frac{15 * 2 + 24 * 1 + 26 *1}{2 +1+1}[/tex]

Evaluate the sum

[tex]\bar x = \frac{80}{4}[/tex]

Evaluate the quotient

[tex]\bar x = 20[/tex]

Hence, the balance point of the dataset is 20

Read more about mean at:

https://brainly.com/question/14532771

At the movie theatre , child admission is $ 6.40 and adult admission is $ 9.60 . On Monday , 153 tickets were sold for a total sales of $ 1270.40 . How many adult tickets were sold that day ?

Answers

Answer:

91 adult tickets

Step-by-step explanation:

Algebra is really useful here:

Let a = number of adult tickets sold and c = number of child tickets sold.

Thus, we can say that

a + c = 153 (number of tickets)

6.40c + 9.60a = 1270.4. (cost of all of the tickets)

Solving,

c = 153 - a

6.40(153 - a) + 9.60a = 1270.4

979.2 - 6.40a + 9.60a = 1270.4

3.20a = 291.2

a = 91

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