1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Mashcka [7]
3 years ago
13

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

Mathematics
2 answers:
harina [27]3 years ago
4 0

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 →

<u>y = -8/15x + 289/15</u><u>.</u>

frosja888 [35]3 years ago
4 0

Answer:

y = -8/15x + 289/15

You might be interested in
Show 2 + 5 in number line.
Butoxors [25]

Explanation:

To mark 2/5; move two parts on the right-side of zero. To mark 11/5; move eleven parts on the right-side of zero. To mark -8/5; move eight parts on the left-side of zero. To mark -3/5; move three parts on the left-side of zero.

6 0
2 years ago
Read 2 more answers
3) Expresa mediante una fórmula la función que a un número entero x le hace corresponder el doble del número siguiente a x. Haz
jonny [76]

Answer: The function is: f(x) = 2*(x +1)

Step-by-step explanation:

This can be translated to:

"write an equation of a function where a whole number x corresponds to the next number to x"

the next whole number to x is x+1., and we want the double of that.

Then we have that our function is:

f(x) = 2*(x +1)

Now we can do a little table of it:

f(0) = 2*(0 + 1) = 2

f(1) = 2*(1 + 1) = 4

f(2) = 2*(2+ 1) = 6

8 0
3 years ago
Read 2 more answers
Please help, the questions just have to be simplified
dimaraw [331]
6c^2d^{-3}\ \times\ 3c^3d^{-4}=6\cdot3\cdot c^{2+3}d^{-3+(-4)}=18c^5d^{-7}=\frac{18c^5}{d^7}


\frac{-16p^6q^5}{20q^7}=-\frac{16}{20}p^6q^{5-7}=-\frac{4}{5}p^6q^{-2}=-\frac{4p^5}{5q^2}
8 0
3 years ago
Read 2 more answers
In math what is imaginary I stand for
ahrayia [7]
Imaginary number is one that when squared gives a negative result. ... With imaginary numbers, when you square them, the answer is negative. They are written like a real number, but with the letter i after them, like this: 23iThe letter i means it is an imaginary number.
4 0
3 years ago
Draw a circle and then draw the following parts on the diagram.
poizon [28]

Here's a photo of the diagram

3 0
3 years ago
Other questions:
  • How to divide u by v, subtract t from the result, then add w to what you have. I don't understand
    6·2 answers
  • Two 1.60cm×1.60cm plates that form a parallel-plate capacitor are charged to ± 0.711nC . What is the potential difference across
    8·2 answers
  • Andrea has just created a scale drawing of her bedroom room which is 18 feet long by 12 feet wide. The scale drawing shows the l
    9·1 answer
  • What is the area in square meters of 6 triangles
    5·1 answer
  • 2x+5-x=3 (2×-3) solve each equation
    6·1 answer
  • a desert recipe calls for 3 cups of flour and 1 cup of sugar.It serves 4 people if the recipe must be altered to serve 12 people
    6·1 answer
  • Select all the correct answers. Which statements are correct interpretations of the logarithmic function f(x) = 7 log2 x, with r
    8·1 answer
  • Is (3,-3) a solution of y≤ -5x+3
    14·1 answer
  • In the equation y=3x+2 , the expression f(x) would replace which part of the function ?
    10·1 answer
  • 9 divided by 8 is equal to 9 multiplied by _
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!