Here is a circle, centre O, and the tangent to the circle at the point (8,15)

Answer:

y = -8/15x + 289/15

Explanation:

Given a circle with a radius of 17, and a centre at the origin (0,0), to find a line tangent to the point (8,15), there are a list of methods we could use to solve this problem. Instead of using derivatives (used to find the slope or gradient of a function at a given point), we can use the inverse tangent (goes from output to input, instead of input to output, but the inputs will still act as a function, which means you can only get one input for each output, this will get you from the side proportion to the angle, instead of angle to side proportion) as we know that a line connecting the origin to the point is always perpendicular to that line which is tangent to it. We can just take the opposite reciprocal (because when two lines are perpendicular, they always have opposite reciprocal slopes) of that, and then trace that slope back to the y-axis to find the it's y-intercept.

An opposite reciprocal just means to take that number, flip it's numerator, and denominator, and then make it negative.

So let's just use basic algebra to find the line going through points (0,0), and (8,15).

Because the line goes through the origin, we already know the y intercept is 0, so all we need to do is find the slope.

So slope [m] = (y2-y1)/(x2-x1).

Where (x1,y1) is the first point, and (x2, y2) is the second point. so m = 15-0/8-0 = 15/8.

Know that we have the slope of the first line, the perpendicular line will go through the same point, and have an opposite reciprocal -n^-1.

So 15/8 → 8/15 → -8/15 [this is the slope of the tangent].

Now since we know a point, and a slope, we can backtrack to find its y-intercept.

We can use point slope form:

y – y1 = m(x – x1)

(x1,y1) is the point we know [(8,15)], m is the slope we know [-8/15], and (x,y) is the point we are looking for. Also don't forget, since we are looking for a y-intercept, set x to zero because a y-intercept of anything is when x = 0.

Since we are only looking for y

y – y1 = m(x – x1) will become y = m(-x1) + y1.

This is because -y1 will cancel out when you add both sides by y1, and when x is 0, x1 will remain by itself in the form -x1.

So y = m(-x1) + y1 → y = (-8/15)(-8) + (15) →

64/15 + 15 = 64/15 + 15×15/15 = (64 + 225) / 15 = 289/15 [this is the y-intercept of the tangent line]

Now that we know the slope, and y- intercept of the tangent line, we can write the following equation in slope intercept:

m = -8/15, b = 289/15 → y = mx + b →

y = -8/15x + 289/15.

Answer:

y = -8/15x + 289/15

HELP PLS I NEED TO SOLVE THAT EQUATION NEED HELP ASAP

I need help on this please ​

3. Rectangle ABCD is shown on the coordinate grid below.
у
10
8 units
12 units
- 10 -8
X
9 units
D
o
7 units

Which is closest to the length of diagonal
AC?

Compare heterogeneous and homogeneous?

Ten baseballs weigh 1,417.4 grams. About how much does 1 baseball weigh? Round your answer to the nearest tenth of a gram. Round your answer to the nearest gram.. Which answer would you give if someone asked, "About how much does a baseball weigh?" Explain your choice.

Which equation represents a line that passes through the two points in the table?

Which statement is true? The equation –3|2x + 1.2| = –1 has no solution. The equation 3.5|6x – 2| = 3.5 has one solution. The equation 5|–3.1x + 6.9| = –3.5 has two solutions. The equation –0.3|3 + 8x| = 0.9 has no solution.

Find V. 10 points plz.

Graph the line.
y=-5x+4
15 points

help
me
do
this
im
about
to
fail

what is the slope and y intercept of y=3?

If you ride your bike 30 kilometers in 2 hours, what is your average speed?

Give the equation of the line, perpendicular to the line with equation y=2x+1, that passes
through the point (8,-2)

Circle Q has a circumference of approximately 50 centimeters. Circle Q with diameter d is shown. What is the approximate length of the diameter, d? Use 3.14 for . Round to the nearest tenth of a centimeter. 4.0 centimeters 8.0 centimeters 15.9 centimeters 31.8 centimeters

How do I solve for the missing angle?!
And please include explanations​ on how you got the answer

As of July 1, 2014, the population of India was about 1,267,000,000.
How can you write this number in scientific notation?
1. Move the decimal point to the right of the first digit. What is the first factor?
2. Count the number of digits after the decimal point. How many places did you move the decimal point?
3. Did you move the decimal point to the right or to the left? What does this tell you about the power of 10 in the second factor?
4. What is the second factor written as a power of 10?
5. Write the population of India in scientific notation

What is the slope of the graph of 5x-2y=20 ?

A:
-10

B:-2 over 5

C:5 over 2

D:
5

A 9 pound bag of brown rice cost 40. 32 what is the price per ounce

how do you add or subtract [-4]+6

How do you add integers with different signs?

The volume of a box (v) varies directly with its length (l) if one of the boxes has a volume of 325 cubic inches and a length of 13 inches what is the costant of proportionality for the group of boxes

please help I only have about a few minutes!
Which equation best models the relationship shown in the table?

# 4-15 Convert the given amount to the given unit

4. 63 yd; feet

5. 168h; days

6. 2.5lb; ounces

7. 200 cm; meters

8. 4 min; seconds

9. 5kg; pounds

a biker can ride a bicycle 18 miles in 3 hours. the messenger estimates that it will take 7 hours to bike 22 miles. here is the messengers work:


step 1: 22-18=4


step 2: 3+4=7


what mistake did the messenger make?


• the messenger did not make a mistake. the estimate is correct


• the 3 and 4 should have been multiplied instead of added.


• the messenger used addition and Subtraction instead of multiplication and division


• the 22 and 18 should have been divided instead of subtracted


• the 22 and 18 should have been averaged instead of subtracted

What is the slope of the line that passes through the points (8,2) and (9,3)? Write
your answer in simplest form.

The system of inequalities in the graph represents the change in an account, y, depending on the days delinquent, x. On a coordinate plane, 2 dashed straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 2) and (0, 0). Everything to the right of the line is shaded. The second line has a negative slope and goes through (negative 2, 2) and (0, 0). Everything to the left of the line is shaded. Which symbol could be written in both circles in order to represent this system algebraically? y Circle x y Circle –x ≤ ≥

What is a rule for

h
 
′
(
x
)

h
′
(x) space, h, prime, left parenthesis, x, right parenthesis, space if

h
(
x
)
=
−
1
x
 
h(x)=
sin
−1
x

The function y = 3x + 42 models the average number of dogs at an animal shelter, where x is the number of days after July 1. The
function y = 4x + 7 models the average number of cats at the animal shelter, where x is the number of days after July 1. After how many
days is the average number of cats and dogs at the shelter the same?
A. 35 days
B. 49 days
C. 7 days
D. 5 days

Please help asap!
i will give brainliest :)

Karen bought 11/12 pound of fruit salad. How many 1/3 ​ pound servings of fruit salad are in 11/12 ​pound?