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3 years ago

9

Ian has 22 ounce iced tea. He drinks 10 ounces. Enter the percentage of ounces Ian has left of his iced tea. Round your answer t

o the nearest hundredth

1 answer:

lisabon 2012 [21]3 years ago

8 0

Answer:

54.55%

Step-by-step explanation:

If he drank 10 ounces, that means he has 12 ounces of the tea left.

Find the percent that he has left by dividing 12 by 22, and multiplying it by 100

(12/22) x 100

= 54.55

So, Ian has approximately 54.55% left of his iced tea

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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

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

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2 years ago

A train stops at Atlanta, then at Bayville, and then at Colleyville. The

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Answer:

See Explanation

Step-by-step explanation:

<em>The question is incomplete as what is required of the question is not stated.</em>

<em>However, since the question is only limited to distance, a likely question could be to calculate the distance from Bayville to Colleyville.</em>

Represent the distance from Atlanta to Colleyville with AC

Represent the distance from Atlanta to Bayville with AB

Represent the distance from Bayville to Colleyville with BC

So, we have that:

$AC = 25.5\ miles$

$AB = 10\frac{2}{3}\ miles$

The relationship between AB, AC and BC is:

$AC = AB + BC$

Make BC the subject of formula:

$BC = AC - AB$

$BC = 25.5 - 10\frac{2}{3}$

Convert fraction to decimal

$BC = 25.5 - 10.7$

$BC = 14.8$

<em>Hence, the distance from Bayville to Colleyville is 14.8 miles</em>

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Area is base x height
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Step-by-step explanation:

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