The line l is tangent to the circle with equation x^2 + y^2=10 at the point P.
Determine the equation of line l.
Answers
Given:
The equation of a circle is
[tex]x^2+y^2=10[/tex]
A tangent line l to the circle touches the circle at point P(1,3).
To find:
The equation of the line l.
Solution:
Slope formula: If a line passes through two points, then the slope of the line is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Endpoints of the radius are O(0,0) and P(1,3). So, the slope of radius is
[tex]m_1=\dfrac{3-0}{1-0}[/tex]
[tex]m_1=\dfrac{3}{1}[/tex]
[tex]m=3[/tex]
We know that the radius of a circle is always perpendicular to the tangent at the point of tangency.
Product of slopes of two perpendicular lines is always -1.
Let the slope of tangent line l is m. Then, the product of slopes of line l and radius is -1.
[tex]m\times m_1=-1[/tex]
[tex]m\times 3=-1[/tex]
[tex]m=-\dfrac{1}{3}[/tex]
The slope of line l is [tex]-\dfrac{1}{3}[/tex] and it passs through the point P(1,3). So, the equation of line l is
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-3=-\dfrac{1}{3}(x-1)[/tex]
[tex]y-3=-\dfrac{1}{3}(x)+\dfrac{1}{3}[/tex]
Adding 3 on both sides, we get
[tex]y=-\dfrac{1}{3}x+\dfrac{1}{3}+3[/tex]
[tex]y=-\dfrac{1}{3}x+\dfrac{1+9}{3}[/tex]
[tex]y=-\dfrac{1}{3}x+\dfrac{10}{3}[/tex]
Therefore, the equation of line l is [tex]y=-\dfrac{1}{3}x+\dfrac{10}{3}[/tex].
Related Questions
At a school social, parents attended with their children. Everyone had a choice between a sweet snack and a salty snack. Here is a two-way table showing the number of adults and children who made each choice of snack.
sweet snack salty snack total
adult 57 88 145
child 77 31 108
total 134 119 253
Answers
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
what us the answe
re
Which mixed number is equal to 27/6?
Answers
Answer:
4 [tex]\frac{3}{6}[/tex]
Step-by-step explanation:
help please i will give brainlist
Answers
Answer:
Angle 1 is 67 and Angle 2 is 46
Step-by-step explanation:
what is 2 1/2 times 1 2/8
Answers
Answer:25/8 or if mixed number 3 1/25
Step-by-step explanation:
Can you solve this quadratic by taking the square root?: x^2-6x=-8
Answers
Answer:
Step-by-step explanation:
To solve this you could complete the square, use the quadratic formula, or factor it. This equation is easily factorable.
x^2-6x+8=0
(x-2)(x-4)=0
So x=(2,4)
Can you please help me with this problem.
Answers
Answer:
C
Step-by-step explanation:
Calculator did it lol
Tony's town had an election last month. 180 people voted in the election and 720 did not vote. What percentage of the people voted?
Answers
Hope this helps!
Answer:
20%
Step-by-step explanation:
180 + 720 = 900 total people in town
180/900 or 180 ÷ 900 = 0.2 or 20%
Hope this helps!
how many faces does the following shape have
Answers
Answer:
6.
Step-by-step explanation:
Faces in other words is the number of individual shapes on one shape. In this case, how many rectangles is on this shape. Hope this helps have a good day!
Answer:
rectangle is
Edges=12
Faces=6
Vertices=8
I am the Real Da Baby
LESS GOOO!
Answers
Answer:
yuuhhhhh
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
I am da real baby :) lol
What is the equation of the following line? Be sure to scroll down first to see
all answer options.
Answers
Answer:
i did this before the answer is c
Answer: 1/5 x
Step-by-step explanation:
find the area of the figure.
Answers
Answer:
6000
Step-by-step explanation:
multiply all the sides
Answer:
102
Step-by-step explanation:
Write the formula. A = [tex]\frac{1}{2}[/tex] x B x H
Cut the figure
6 + 6 + 5=16
16 + 10=26
26 x 6=156
156 ÷ 2=78
6 x 4=24
78 + 24=102
Solve the system:
x+4y=1
3x+5y=10
Answers
Answer:
[tex]x=6.25\\y=-1.25[/tex]
Step-by-step explanation:
[tex]3x+5y=10\\x+3y=1\\\\[/tex]
Second equation times 3:
[tex]3x+9y=3[/tex]
1st equation minus equation above:
[tex]-4y=7\\y=-7/4[/tex]
Insert to equation:
[tex]3x+\frac{-35}{4}=10\\12x-35=40\\12x=75\\x=75/12=6.25[/tex]
What is the nth term rule of the linear sequence below?
5,8,11,14,17
(btw it says the nth term not the 9th.)
Answers
9514 1404 393
Answer:
an = 5 +3(n -1)
Step-by-step explanation:
The n-th term of an arithmetic sequence is ...
an = a1 +d(n -1)
Here, you have first term a1=5 and common difference d=8-5=3, so the n-th term is ...
an = 5 +3(n -1)
_____
If you like, you can simplify this to ...
an = 5 +3n -3
an = 3n +2
Answer:
it's 3n-3
Step-by-step explanation:
Given that R=7x+5Y find Y when X=9 and R=35 give your answer as an improper fraction in its simplest form
Please help
Answers
Answer:
y = -28/5
Step-by-step explanation:
R = 7x +5y
35 = 7(9) + 5y
35 = 63 +5y
-5y= 63- 35
-5y/-5 = 28/-5
Y = -28/5
Answer:
Y = - [tex]\frac{28}{5}[/tex]
Step-by-step explanation:
Given
R = 7X + 5Y ← substitute X = 9, R = 35
35 = 7(9) + 5Y
35 = 63 + 5Y ( subtract 63 from both sides )
- 28 = 5Y ( divide both sides by 5 )
- [tex]\frac{28}{5}[/tex] = Y
Harper invested $930 in an account paying an interest rate of [tex]\frac{19}{2}[/tex]% compounded monthly. Zoey invested $930 in an account paying an interest rate of [tex]\frac{37}{4}[/tex] % compounded continuously. To the nearest dollar, how much money would Harper have in her account when Zoey's money has tripled in value?
Answers
Answer:2861
Step-by-step explanation:
P < 4.75 represents the prices p in dollars that Paige is willing to pay for popcorn. The inequality p < 8.00 represents the prices p in dollars that Paige is willing to pay for a movie ticket. At how many theaters would Paige be willing to buy a ticket and popcorn?
Answers
Answer:
1 theater
Step-by-step explanation:
Given
[tex]P<4.75[/tex] --- Popcorn
[tex]P < 8.00[/tex] --- Movie
See attachment for the table that shows ticket and popcorn prices at five movie theater chains
Required
The number of theaters that supports the given inequality
The given inequality can be combined to give:
[tex]P < 4.75\ and\ P<8.00[/tex]
From the table entries, only one theater supports this inequality.
Where
[tex]P = 4.25[/tex] --- Movie
[tex]P = 7.25[/tex] --- Popcorn
Which gives:
[tex]4.25 < 4.75\ and\ 7.25<8.00[/tex]
What is the resulting equation when the expression for y in the second equation is substituted into the first equation-3x+2y=-3
Y=4x+1
Answers
Answer:
x=-5/11, y=-9/11. (-5/11, -9/11).
Step-by-step explanation:
3x+2y=-3
y=4x+1
---------------
3x+2(4x+1)=-3
3x+8x+2=-3
11x=-3-2
11x=-5
x=-5/11
y=4(-5/11)+1
y=-20/11+11/11
y=-9/11
laura counted 14 red cars in the sales lots of car dealerships. what is the prime factorization of 14
A 2x7
B 1x14
C 2x2x5
D 2x2x2
help, please
Answers
Answer:
a is correct
hope this helps
I need help I don’t understand this at all please
Answers
Step-by-step explanation:
[tex] \tan( \alpha ) = \frac{15}{9} = \frac{7}{h } \\ h = \frac{7 \times 9}{15} = 4.2[/tex]
simplify as far as possible:3x+4y+7y
Answers
Answer:
3x+4y+7y = 3x + 11 y
Step-by-step explanation:
We need to simplify the given expression i.e.
3x+4y+7y
We know that, the like terms gets add up i.e. the sum of 4y and 7y equals 11 y
So,
3x+4y+7y = 3x + 11 y
Hence, the final simplification should be 3x + 11 y.
3(2x-4)-8=5+x
MUST SHOW WORK
Answers
Answer:
5
Step-by-step explanation:
3(2x-4)-8=5+x
6x-12-8=5+x
6x-x-20=5
5x-20=5
5x=5+20
5x=25
x=25/5
x=5
URGENT!!! For quiz now!
Solve the pair of simultaneous equations using matrix methods.
1) x + y =2 , x + y =3
2) 3x + 2y = 14 , x + 4y =12
3) -3x + 2y = -16 , -x - 5y = -10
4) y = 2x - 5 , 7x - 2y =16
Answers
Answer:3?
Step-by-step explanation:
Please help what's the answer
Answers
Answer:
I think the answer the second one
Answer:
No, (4, -2) is only a solution for the red equation.
I hope this helps!
A cuboid has sides of length 10cm 6cm and 7cm
Find the total surface area of the cuboid
Answers
i do not know guy i just want those points...thanx for those lol
well but i do know this i had the exam of maths so i am explaining it to u but u needa mark this as the brainliest answer
Answer:
Total surface area of a cuboid is 376 square centimeter.
Step-by-step explanation:
Given : A cuboid of length 10 cm breadth 8 cm and height 6 cm.
To find : The total surface area of a cuboid?
Solution :
The total surface area of a cuboid is
Where, l is the length l=10 cm
b is the breadth b=8 cm
h is the height h=6 cm
Substitute the value in the formula,
Therefore, Total surface area of a cuboid is 376 square centimeter.
Please help me
In a city all the houses are either three or four storeyed the ratio of the number of three storyed building to four storeyed building is 5:3 if the total number of buildings is 488 find the number of four storeyed buildings.
Answers
Get the answer using calculator please
Solve the following values for x and y :
Answers
Answer and Step-by-step explanation:
2(5x - 5) = 6x + 50
Distribute the 2 to the 5x and -5.
10x - 10 = 6x + 50
Add 10 to both sides, and subtract 6x from both sides.
4x = 60
Divide both sides by 4.
x = 15
5y + 5 = 7y - 9
Subtract 5 from both sides, and 7y from both sides.
-2y = -14
Divide both sides by -2.
y = 7
#teamtrees #PAW (Plant And Water)
Please help me out, im in algebra and struggling with a problem, I will award 30 points but I need an answer fast. 1/3^-2 = 1/9. or -1/9. or 9
Answers
Answer:
it is 9
Step-by-step explanation:
when u multiply u will flip and it will not affect
Grade 10 math help please. Please show work
Answers
Answer:
43.94?
Step-by-step explanation:
I think if you use inverse cos you should get the correct number. So, to find cos, you need to know the adjacent side and the hypotenuse. Here, the reference angle would be the person holding the kite. The distance from the person to the barn is the adjacent side, which is 18. The string of the kite, I assume, would be 25.
cos(∅) = [tex]\frac{18}{25}[/tex]
cos(∅) = 0.72
cos⁻¹(0.72) = 43.94
I don't know if that's what you're looking for, but... If it's not correct, lmk so I can rewrite it. :)
Whats the answer to this question lol
Answers
Answer:
1/12
Step-by-step explanation:
Multiply 1/2 x 1/6 = 1/12
Scott earns $16.85 per hour at his job. He works 7 hours per day, 4 days per week. What is Scott's gross monthly income for 4 weeks? a. $471.80 b. $943.60 c. $1,415.40 d. $1,887.20 Please select the best answer from the choices provided A B C D
Answers
Answer:
the gross monthly income for 4 weeks is $1,887.20
Step-by-step explanation:
The computation of the gross monthly income for 4 weeks is shown below:
= Earning per hour × number of hours works per day × number of days works per week × number of weeks
= $16.85 × 7 × 4 × 4
= $1,887.20
Hence, the gross monthly income for 4 weeks is $1,887.20
Answer:
d
Step-by-step explanation: