What intervals would you use to determine where

What is the answer to the question

Llana [10]

The answer would be B

7 0

3 years ago

Find an equation of the tangent line to the hyperbola x2 a2 − y2 b2 = 1 at the point (x0, y0).

nalin [4]

The equation of the tangent line is $y = \frac{b^{2} x_{0}x }{a^{2} y_{0} } - \frac{b^{2} x_{0}^{2} }{a^{2} y_{0} } + y_{0}$

To find the tangent to the hyperbola $\frac{x^{2} }{a^{2} } - \frac{y^{2} }{b^{2} }$ at (x₀, y₀), we differentiate the equation implicitly to find the equation of the tangent at (x₀, y₀).

So, $\frac{d}{dx} (\frac{x^{2} }{a^{2} } - \frac{y^{2} }{b^{2} }) = \frac{d0}{dx}\\\frac{d}{dx} \frac{x^{2} }{a^{2} } - \frac{d}{dx}\frac{y^{2} }{b^{2} }= 0\\\frac{2x }{a^{2} } - \frac{dy}{dx}\frac{2y }{b^{2} } = 0\\\frac{2x }{a^{2} } = \frac{dy}{dx}\frac{2y }{b^{2} } \\\frac{dy}{dx} = \frac{b^{2}x }{a^{2}y }$

So, at (x₀, y₀)

$\frac{dy}{dx} = \frac{b^{2} x_{0} }{a^{2} y_{0} }$

So, the equation of the tangent line is gotten from the standard equation of a line in point-slope form

So, $\frac{y - y_{0} }{x - x_{0} } = \frac{b^{2} x_{0} }{a^{2} y_{0} } \\y - y_{0} = \frac{b^{2} x_{0} }{a^{2} y_{0} }(x - x_{0}) \\y = \frac{b^{2} x_{0} }{a^{2} y_{0} }(x - x_{0}) + y_{0} \\y = \frac{b^{2} x_{0}x }{a^{2} y_{0} } - \frac{b^{2} x_{0}^{2} }{a^{2} y_{0} } + y_{0}$

So, the equation of the tangent line is $y = \frac{b^{2} x_{0}x }{a^{2} y_{0} } - \frac{b^{2} x_{0}^{2} }{a^{2} y_{0} } + y_{0}$

Learn more about equation of tangent line here:

brainly.com/question/12561220

3 0

3 years ago

Which model represents the product 3×25? (Giving brainliest.)

Anarel [89]

I think that is the answer because it says 2/5 where two rows are shaded and three more rows remain unshaded so, when you add that three and two it's altogether 5, so I think that is the answer, please check out the document I have uploaded.

7 0

2 years ago

Read 2 more answers

A store has a 10% off sale on pants. With this discount, the price of one pair of pants before tax is $17.10 What was the origin

Leno4ka [110]

Answer:

$171

Step-by-step explanation:

A store has a 10% off sale on pants. With this discount, the price of one pair of pants before tax is $17.10 What was the original price of the pants?

Let x represent the original price of the pair of pants

From the question, we know that:

10% of x = $17.10

10/100 × x = $17.10

10x/100 = $17.10

Cross Multiply

10x = 100 × $17.10

10x = 1710

x = 1710/10

x = $171

Hence, the original price of the pants = $171

6 0

3 years ago

A train travels from station A to station B. If the train leaves station A and makes 75 km/hr, it arrives at station B 48 minute

SSSSS [86.1K]

Answer:

A) 290 km
B) 4 hours
C) 72.5 km/h

Step-by-step explanation:

Let distance be d and time t

At 75 km/h speed the distance is

d = 75(t - 48 min) = 75(t - 48/60 hours)

At 50 km/h speed the distance is

d = 50t + 40

Since the distance is same, we get the equation:

75(t - 48/60) = 50t + 40
75t - 75*4/5 = 50t + 40
75t - 60 = 50t + 40
75t - 50t = 40 + 60
25t = 100
t = 4 hours

A) The distance between A and B

d = 50*5 + 40 = 290 km

B) Time is

4 hours as found above

C) The speed = d/t

Speed = 290/4 = 72.5 km/h

6 0

3 years ago