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2 years ago

12

Find the unit rate for 344 miles in 11 hours.

2 answers:

SVEN [57.7K]2 years ago

6 0

Answer is D hope this helps

pickupchik [31]2 years ago

4 0

the answer is D.) 31.27

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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

2 years ago

Indicate true or false as to whether the following equation is quadratic 2x-4x+1=0

saul85 [17]

The answer to the problem would be false

3 0

2 years ago

Read 2 more answers

At The Last Book Store, 4 books cost $28. How many books could you buy for $49?

Mila [183]

7

You divide 28 by 4 and get 7. Then you divide 49 by whatever you get.

3 0

2 years ago

What is m∠LQK ?<br><br> Enter your answer in the box.

Lady_Fox [76]

∠LQK+∠GQL=90º
Therefore:
(4n-15)+(3n)=90
7n=90+15
7n=105
n=105/7
n=15

∠LQK=4n-15=4(15)-15=60-15=45

Answer: ∠LQK=45º

5 0

2 years ago

Read 2 more answers

Ahmose drank 35% of a 400mL container of orange juice. Tutankhamun drank 45% of a 350mL container of orange juice. Who drank mor

OlgaM077 [116]

Answer:

Tutankhamun

Step-by-step explanation:

7 0

2 years ago