Anybody know w]t[f this is.

Let L be a tangent line to the hyperbola x y = 2 at x = 9 . Find the area of the triangle bounded by L and the coordinate axes.

mafiozo [28]

Answer:

$A = 4$

Step-by-step explanation:

The equation of the slope of the tangent line L is obtained by deriving the equation of the hyperbola:

$y = \frac{2}{x}$

$y'=-2\cdot x^{-2}$

The numerical value of the slope is:

$y' = -2 \cdot (9)^{-2}\\y' = -\frac{2}{81}$

The component of the y-axis is:

$y = \frac{2}{9}$

Now, the tangent line has the following mathematical model:

$y = m \cdot x + b$

The value of the intercept is found by isolating it within the equation and replacing all known variables:

$b = y - m \cdot x$

$b = \frac{2}{9}-(-\frac{2}{81} )\cdot (9)\\b = \frac{4}{9}$

Thus, the tangent line is:

$y = -\frac{2}{81}\cdot x + \frac{4}{9}$

The vertical distance between a point of the tangent line and the origin is given by the intercept.

$d_{y} = \frac{4}{9}$

In order to find horizontal distance between a point of the tangent line and the origin, let equalize y to zero and clear x:

$-\frac{2}{81}\cdot x + \frac{4}{9}=0$

$-\frac{2}{9}\cdot x + 4 = 0$

$x = 18$

$d_{x} = 18$

The area of the triangle is computed by this formula:

$A = \frac{1}{2}\cdot d_{x}\cdot d_{y}$

$A = \frac{1}{2}\cdot (18)\cdot (\frac{4}{9} )$

$A = 4$

4 0

4 years ago

At the city museum, child admission is $ 5.30 and adult admission is $ 8.50 . On Tuesday, 162 tickets were sold for a total sale

zaharov [31]

Ekrnjhbgv,jhdx,jfhbgv,jhgsdt

7 0

3 years ago

Which description best compares the graphs given by the equations:

nexus9112 [7]

x - 5y = -5, -5x - 25y = 25

First, you'll need to get the x variable by itself.

x - 5y = -5
 +5 +5
 x = 0
So x is plotted on the 0.

For the second part of the first equation, you'll be looking for what the y variable represents.

x - 5y = -5
-x -x
 -5y = -5
 5 5
 y = 1
So y is plotted on the 1 on the vertical line above the 0.

For the first part of the second equation, you'll do the same thing as in the first equation.

-5x - 25y = 25
 +25 +25
 -5x = 50
 5 5
x = 10
So the x for this equation is plotted on 10 on the horizontal line.

For the second part of the second equation, you will do the same thing as in the first equation.

-5x - 25y = 25
+5 +5
 -25y = 30
 25 25
y = 1.2
So the y for the second half of the second question is plotted on 1.2 on the vertical line.

<h2>Answer: B) Perpendicular</h2>

Perpendicular means the lines may or may not be of equal length and they will not be perfectly in line with each other.

Parallel means the lines may or may not be of equal length but will be perfectly in line with each other.

Intersecting means the lines may or may not be of equal length but will touch each other.

6 0

2 years ago

Help please 2+2-1-1+6=x

natita [175]

Answer:

$2+2-1-1+6=x : x = 8$

Step-by-step explanation:

$2+2-1-1+6=x\\$

Switch sides:

$x=2+2-1-1+6$

Add/Subtract the numbers: $2+2-1-1+6=8$

$x = 8$

Hope I helped, if so may I get brainliest and a thanks?

Thank you, have a good day! =)

8 0

3 years ago

Read 2 more answers

PLZ help thnx

Pepsi [2]

Answer:

A) $40

B) 40M = P

C) $3,120

Step-by-step explanation:

Given that at her salon, last week Tammy did 25 manicures and collected $ 1000, to calculate the slope to represent the manicures, write an equation to represent this relation and determine how much would Tammy make if she did 78 manicures in a month the following calculations should be performed:

A)

1000/25 = X

40 = X

Thus, each manicure costs $ 40.

B)

40M = P

C)

78 x 40 = X

3.120 = X

So if she did 78 manicures in a month, Tammy would earn $ 3,120.

8 0

3 years ago