Mathematics, 15.07.2019 15:30 daydallas01

Find an equation of the tangent line to the hyperbola y = 3/x at the point (3, 1).

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Answer from: juanmias

The equation of the line tangent to the hyperbola at the point (3,1) is $y = -\frac{1}{3}\cdot x + 2$ .

Procedure - Determination of a line tangent to a hyperbola

By analytical geometry we know that tangent lines are described by the line equation:

$y = m\cdot x + b$ (1)

Where:

- Independent variable.

- Slope.

- Intercept.

- Dependent variable.

By calculus we know that the slope of the tangent line is defined by the first derivative of the hyperbola evaluated at point of tangence:

$m = -\frac{3}{x^{2}}$ (2)

If we know that x = 3 and y = 1 , then the equation of the tangent line is:

Slope

$m = -\frac{1}{3}$

Intercept

$b = 1-\left(-\frac{1}{3} \right)\cdot (3)$

b = 2

The equation of the line tangent to the hyperbola at the point (3,1) is $y = -\frac{1}{3}\cdot x + 2$ . $\blacksquare$

To learn more on tangent lines, we kindly invite to check this verified question: link

Answer from: lillyd2873

Let's find the derivative of that hyperbola in order to find a slope formula to help us with this equation. We already have an x and y value. The derivative is found this way: $y'= \frac{x(0)-3(1)}{x^2}$ so $y'=- \frac{3}{x^2}$ . The derivative supplies us with the slope formula we need to write the equation. Sub in the x value of 3 to find what the slope is: $y'=- \frac{3}{3^2}=- \frac{3}{9}=- \frac{1}{3}$ . So in our slope-intercept equation, x = 3, y = 1, and m = -1/3. Use these values to solve for b. $1=- \frac{1}{3}(3)+b$ so b = 2. The equation, then, for the line tangent to that hyperbola at that given point is $y=- \frac{1}{3}x+2$

Answer from: Quest

6,250

step-by-step explanation:

to get the area, multiply 360 by 160.(57,600)

to find out how many bags of fertilizer it will take, first figure out how many square feet one bag can hold. divide 1000 by 8(125) to get the unit rate(how many square feet one pound of fertilizer can hold)and multiply it by 50(6250). if i haven't made a mistake, that is the answer.

Answer from: Quest

in if you ask questions, the points are taken from your total and given to the one who answered it..

so if i have 30 points and i ask a question for 5 points, then when someone asks a question i will lose 5 points and the answerer earns 5

happy to

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Find an equation of the tangent line to the hyperbola y = 3/x at the point (3, 1)....