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4 years ago

A crate full of oranges weighed 15 lb.

Mathematics

1 answer:

Vlad [161]4 years ago

5 0

What's the question ? You're just stating something..

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56. How many tangent lines to the curve <img src="https://tex.z-dn.net/?f=y%3Dx%20%2F%28x%2B1%29" id="TexFormula1" title="y=x /(

PIT_PIT [208]

There are 2 tangent lines that pass through the point

$y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2$

and

$y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2$

Explanation:

Given:

$y=\frac{x}{x+1}$

The point-slope form of the equation of a line tells us that the form of the tangent lines must be:

$y=m(x-1)+2$ $[1]$

For the lines to be tangent to the curve, we must substitute the first derivative of the curve for $m$ :

$\frac{dy}{dx} =\frac{d(x)}{dx}(x+1)-x^\frac{d(x+1)}{dx} \\ \\$

$\frac{dy}{dx} =\frac{x+1-x}{(x+1)^2}$

$\frac{dy}{dx}= \frac{1}{(x+1)^2}$

$m=\frac{1}{(x+1)^2}$ $[2]$

Substitute equation [2] into equation [1]:

$y=\frac{x-1}{(x+1)^2}+2$ $[1.1]$

Because the line must touch the curve, we may substitute $y=\frac{x}{x+1}:$

$\frac{x}{x+1}=\frac{x-1}{(x+1)^2}+2$

Solve for x:

$x(x+1)=(x-1)+2(x+1)^2$

$x^2+x=x-1+2x^2+4x+2$

$x^2+4x+1$

$x\frac{-4±\sqrt{4^2-4(1)(1)} }{2(1)}$

$x=-2$ ± $\sqrt{3}$

$x=-2$ ± $\sqrt{3}$ <em> </em> $and$ $x=-2-\sqrt{3}$

There are 2 tangent lines.

$y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2$

and

$y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2$

8 0

3 years ago

X2 – 12x + 37 = 0 in simplest a + bi form

Andreas93 [3]

Answer:

x=6+1

Step-by-step explanation:

4 0

3 years ago

Pls help me with this problom asap!!!!

Nataly [62]

Answer:

4 1/2. Root 18 simplifies to 4.242640687, which is less than 4.50

8 0

3 years ago

Read 2 more answers

A certain television is advertised as a 55-inch TV (the diagonal length). If the width of the TV is 42 inches, how many inches t

Mumz [18]

Answer:

69.20in

Step-by-step explanation:

Given data

diagonal of the TV d= 55in

Widht of the TV w= 42 in

Hight h= ???

Applying the Pythagoras theorem

d^2= w^2+ h^2

substitute

55^2= 42^2+ h^2

3025= 1764+ h^2

3025+1764= h^2

4789= h^2

h=√4789

h= 69.20

Hence the Heigth is 69.20in

7 0

3 years ago

Kareem made $273 for 13 hours of work. at the same rate, how many hours would he have to make to work to make $147?

klio [65]

Answer:

105

Step-by-step explanation:

273/13 × 5= 105

That's the correct answer

5 0

2 years ago