The line l is tangent to the circle with equation x² + y2 = 169 at the point P.
By thinking about the radius or otherwise, determine the gradient of the line l.
Answers
Given:
The equation of a circle is
[tex]x^2+y^2=169[/tex]
A tangent line l to the circle touches the circle at point P(12,5).
To find:
The gradient 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(12,5). So, the slope of radius is
[tex]m_1=\dfrac{5-0}{12-0}[/tex]
[tex]m_1=\dfrac{5}{12}[/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 \dfrac{5}{12}=-1[/tex]
[tex]m=-\dfrac{12}{5}[/tex]
Therefore, the gradient or slope of the tangent line l is [tex]-\dfrac{12}{5}[/tex] .
Related Questions
Wiki
Help I’ll give Brainly est
Answers
Solve:
V5x+1+6=4
V=square root
Answers
Answer:
the answer is c hope it help
Answer: D
Step-by-step explanation:
1. movethe constanat to the right
2. Calculate
3.The statement is false
PLS help ASAP I DONT have time to answer this, it also detects if it’s right or wrong.
Answers
Answer:
C. 43.98
Step-by-step explanation:
6 of 7
£25 = 700 rubles, how many £ are in 1,260 rubles?
£
Answers
Answer:
45
Step-by-step explanation:
25 = 700
Y = 1260
Now you need to do cross multiplication .
25 X 1260=700Y
Since it's in a multiplying form you can simplify by dividing 700 by 25
1260=700Y/25
1260=28Y
Y=45
pls help on my homework. due tonight
i need help asap
Match the given graphs with the corresponding functions in the table below. Use the letter in the
bottom left corner of the graph.
b) Given the function ff(xx) = llllll3(xx + 2) − 1, state the following characteristics:
Asymptote:__________________ End Behavior: _______________________________________
_______________________________________
c) Describe what an asymptote is, and write the end behavior in your words.
Answers
Answer:
A line that a curve approaches as it heads towards infinity
The asymptote is -2 there is no end behavior
Step-by-step explanation:
The vertices of GHJ are shown below. If this triangle is translated 2 units right and 1 unit down, what is the coordinate for vertex G'?
G (10, 10)
H (12, 12)
I (14, 14)
A
(12, 10)
B
(10, 9)
C
(12, 9)
D
(12, 14)
Answers
what is 30% of $240?
Answers
Answer:
72
Step-by-step explanation:
.30×240
72
Answer:
$72
Step-by-step explanation
You need to turn a percent into a decimal. To do that, you move the decimal twice to the left so, 30%=.3.Multiply: 240*.3=72$72Hope this helped!! :)
Stay safe and have a wonderful day/night!!!!!
Brainliest?!?!
Calculate the length of the unknown side of each triangle.
a)
3 cm
5 cm
Give your answers to the nearest mm.
Answers
Answer:
5.8cm or 58mm
Step-by-step explanation:
HELP ASAP!!! Please give a step-by-step explanation, or you will be reported!
The table gives the probabilities that orphaned pets in animal shelters in six cities are one of the types listed. The probability that a randomly selected orphan pet in an animal shelter in Austin is a dog is _____ %. The probability that a randomly selected orphaned dog in the same animal shelter in Austin is a Chihuahua is _____ %. (Round to the nearest hundredth.)
Answers
For all the dogs: you have 2.65+2.46+3.67+2.91 = 11.69%
Now, the probability of getting a chihuahua would be 3.44/11.69=0.2942= 24.92
Step-by-step explanation:
there ya go!!
Answer:
The probability that a randomly selected orphan pet in an animal shelter in Austin is a dog is 11.71% .
The probability that a randomly selected orphaned dog in the same animal shelter in Austin is a Chihuahua is 29.37% .
Step-by-step explanation:
2.76% + 2.86% + 3.44% + 2.65% = 11.71%
11.71 / 3.44 = .2937
.2937 = 29.37%
this it's just where someone who comes across this and wants points
Answers
Answer:
hows your day going? :)
please answer asap 17 brainy points is all I had left
Answers
Answer:
A) 69.08 m
Step-by-step explanation:
C=2πr
C=2π(11)
C=22π
C≈69.12
Answer:
drraaaaaa wild'n out boiii
Step-by-step explanation:
Taking my points back.
Write a sentence to answer each question:
How much warmer is 82 than 40?
Answers
Answer:
82 is 42 degrees warmer than 40
Step-by-step explanation:
if you subtract 40 from 82, you get 42 meaning that the answer will be 42 degrees more than 40
Poppy has one bag of beads. She is going to make three difference necklaces.
For the first necklace, she needs 3/8 of a bag of beads. For the second, she
needs 1/8 of a bag of beads. For the third, she needs 5/8 of a bag. What
fraction of a bag of beads does she need? Does she have enough? Explain.
Answers
Answer:
9/8 of a bag
she doesn't have enough beads.
Step-by-step explanation:
Bag of bead poppy has = 1
Bag of bead needed for necklace 1 = 3/8 of a bag
Bag of bead needed for necklace 2 = 1/8 of a bag
Bag of bead needed for necklace 3 = 5/8 of a bag
Total bag of beads needed = 3/8 + 1/8 + 5/8
= (3+1+5)/8
= 9/8
She needs 9/8 of a bag of bead
9/8 = 1 1/8
Therefore, she doesn't have enough beads.
Im struggling a bit can someone help me :)
Answers
Answer:
1
Step-by-step explanation:
Please help!!!
Factor the following
[tex]3x^3-x^2y+6x^2y-2xy^2+3xy^2-y^3[/tex]
Show work to receive full credit
Answers
Answer:
(3x - y)(x + y)²Step-by-step explanation:
3x³ - x²y + 6x²y - 2xy² + 3xy² - y³ =x²(3x - y) + 2xy(3x - y) + y²(3x - y) =(3x - y)(x² + 2xy + y²) = (3x - y)(x + y)²Answer:
[tex](3x-y)(x+y)^2[/tex]
Step-by-step explanation:
[tex]3x^3-x^2y+6x^2y-2xy^2+3xy^2-y^3[/tex]
Multiply and combine like terms.
[tex]3x^3+xy^2-y^3+5xy^3[/tex]
Consider [tex]3x^3+xy^2-y^3+5xy^3[/tex] as a polynomial over variable x.
[tex]3x^3+5xy^2+y^2x-y^3[/tex]
Find one factor of the form kx^m +n, where kx^m divides the monomial with the highest power 3x^3 and n divides the constant factor −y^3 . One such factor is 3x−y. Factor the polynomial by dividing it by this factor.
[tex](3x-y)(x^2+2xy+y^2)[/tex]
Consider [tex]x^2+2xy+y^2[/tex]. Use the perfect square formula, [tex]a^2+2ab+b^2[/tex] = [tex](a+b)^2[/tex], where a=x and b=y.
[tex](x+y)^2[/tex]
Rewrite the complete factored expression.
[tex](3x-y)(x+y)^2[/tex]
Simplify: 10x+2x-3= 9
A. x=-1
B. x=-2
C. x=1
D. x=2
Answers
Answer:
C. x = 1
Step-by-step explanation:
Combine like terms
10 + 2 − 3 = 9
12 − 3 = 9
Add 3 to both sides of the equation
12 − 3 + 3 = 9 + 3
Add the numbers
12 = 9 + 3
12 = 12
[tex]\frac{12x}{12} = \frac{12}{12}[/tex]
Cancel terms that are in both the numerator and denominator
[tex]x = \frac{12}{12}[/tex]
Divide the numbers
x = 1
Therefore the correct answer is C. x = 1
Answer:
C. x = 1
Step-by-step explanation:
Have a great day
Round to nearest degree.
8
х
11
Answers
Answer:
36
Step-by-step explanation:
tan^-1(8/11)=36.027
The first term in a sequence is 13. The term to term rule is "take away 5" write an expression in terms of n , for the nth term of the sequence
Answers
9514 1404 393
Answer:
an = 13 -5(n -1)
Step-by-step explanation:
The "take away 5" rule means the common difference between terms is d=-5. For first term a1=13, the n-th term is ...
an = a1 +d(n -1)
an = 13 -5(n -1)
Can you help me with my work don’t send no link
Answers
Answer:
A and C!
Step-by-step explanation:
a: for a just move all the terms not containing x to the right side of the equation!
c: divide each term by 4 and simplify!
-
hope this helped <3
On a map,1 inch represents 5 miles.joel measure 2 1/2 inches between two cities on the map. how many miles apart are the two cities?
Answers
Answer:
12.5 miles
Step-by-step explanation:
5/2 inch*5 miles/ i inch= 25/2 miles or 12.5 miles
if my anwer helps please mark as brainliest.
find the value of given expression
[tex] \sqrt{29 - 4} [/tex]
Answers
Answer= +/- 5
Answer:
5
Step-by-step explanation:
[tex] \sqrt{29 - 4} \\ = \sqrt{25} \\ = 5[/tex]
Geometry Angle of elevation/depression
Answers
Answer:
m∠ACB = 49.88°
Step-by-step explanation:
From the figure attached,
Measure of wire AC attached to the top 'C' of the building BC = 340 m
Horizontal distance between the base 'B' of the building and point A = 260 m
Angle of depression = ∠ACB
By applying sine rule in the given triangle,
sin(∠ACB) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{AB}{BC}[/tex]
= [tex]\frac{260}{340}[/tex]
m∠ACB = [tex]\text{sin}^{-1}(764706)[/tex]
= 49.88°
help!!!!? pleaseeeeee
Answers
Answer:
19.47
Step-by-step explanation:
I plugged it into a right triangle trig calculator
Answer:
HERE ARE SOME NOTES ON HOW TO DO these types of geo- problems and some more ! SORRY .
See attachment below!
Step-by-step explanation:
If your in High school Geometry, I could help with that and more!
If your someone who likes to have Notes.. I could send you some PDF's and more for Geometry!! I took Geometry and have good notes!
Please contact me for any concerns or questions!x + 6 = -6
please help me pls
Answers
explanation...
−
6
=
6
−
6
+
6
=
6
+
6
add both sides to the equation
and then simplify
One equation in a system is 4x – 2y = 8. Which equation gives the system no solution?
Answers
Answer:
-8
Step-by-step explanation:
Correct me if i'm wrong
A car traveled 3600 miles in 3 hours. Find the speed of the car.
Answers
Answer:
speed=distance/time
speed=3600/3
speed=1200m/s
Answer:
The car is going 1200 miles per hour.
Step-by-step explanation:
Whats the y-int?
Whats the domain and range?
Answers
Answer:
Y intercept is (0,50) or b=50
At his new job, Jeremiah can choose an hourly rate of $9 plus a $50 weekly bonus for opening the store, or an hourly rate of $10 per hour with no opening bonus. The equations model his salary options.
y = 9x + 50
y = 10x
What does x represent?
the number of times he opened the store
the number of hours worked per week
the total amount he earns each week
the amount of money earned per day
Answers
Answer:
The correct option is B
Step-by-step explanation:
just did the test on Ed.
203/4108 as a percent
a. 4.94%
b. 20.24%
c. 0.049%
d. 49.42%
Answers
I’m timed plsss answer correctly I’ll mark u brainliest
Answers
Answer:
[tex]\sqrt{125}[/tex]
Step-by-step explanation:
Use Pythagorean theorem since you have a right triangle [tex]15^{2}[/tex] = [tex]10^{2} + x^{2}[/tex]
225 = 100 + [tex]x^{2}[/tex] so x = [tex]\sqrt{125}[/tex]
Answer:
x = 5[tex]\sqrt{5}[/tex]
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
x² + 10² = 15²
x² + 100 = 225 ( subtract 100 from both sides )
x² = 125 ( take the square root of both sides )
x = [tex]\sqrt{125}[/tex] = [tex]\sqrt{25(5)}[/tex] = 5[tex]\sqrt{5}[/tex] ← in simplest radical form