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lisabon 2012 [21]
3 years ago
5

Find the equation of the tangent line. y=(9-x^2)^1/3 at (1,2)​

Mathematics
1 answer:
Schach [20]3 years ago
7 0

Get the derivative:

<em>y</em> = (9 - <em>x</em>²)¹ʹ³

d<em>y</em>/d<em>x</em> = 1/3 (9 - <em>x</em>²)⁻²ʹ³ d/d<em>x</em> [9 - <em>x</em>²]

d<em>y</em>/d<em>x</em> = 1/3 (9 - <em>x</em>²)⁻²ʹ³ (-2<em>x</em>)

d<em>y</em>/d<em>x</em> = -2/3 <em>x</em> (9 - <em>x</em>²)⁻²ʹ³

Evaluate it at <em>x</em> = 1 :

d<em>y</em>/d<em>x</em> (1) = -2/3 • 8⁻²ʹ³

Since 8 = 2³, we have

8⁻²ʹ³ = 1 / 8²ʹ³ = 1 / (2³)²ʹ³ = 1 / 2² = 1/4

Then the tangent line has equation

<em>y</em> - 2 = 1/4 (<em>x</em> - 1)   →   <em>y</em> = 1/4 <em>x</em> + 7/4

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telo118 [61]
It's 4/3 because of the distance formula
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3 years ago
A recipe used 2/3 cup of sugar for every 2 teaspoons of butter. How much sugar was used per teaspoon of butter
myrzilka [38]

Answer:

2/3cups 2 teaspoons

(2/3 )cups/2teaspoons =1/3 cups per teaspoon

Answer= 1/3 cups per teaspoon

8 0
3 years ago
Read 2 more answers
So can anyone help me with #1 and 2 and show work I have no idea what I’m doing
Neporo4naja [7]

Answer:

1.

x = 44*2

<h2>x = 88</h2>

2.

x = 62*2

<h2>x = 124</h2>

3.

x = 108/2

<h2>x = 54</h2>

4.

x = 160/2

<h2>x = 80</h2>

5.

12x = 60*2

12x = 120

x = 120/12

<h2>x = 10</h2>

6.

5x = 50/2

5x = 25

x = 25/5

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3 0
3 years ago
100 POINTS 10 QUESTIONS PLEASE HELP PICTURES BELOW PLEASE SPECIFY WHICH QUESTION YOU ARE ANSWERING
Semenov [28]

Answer:

The answers are \frac{2}{5}, \frac{1}{4}, \frac{1}{10}, \frac{5}{2}, \frac{5}{8}, \frac{4}{1}, \frac{8}{5}, and \frac{10}{1}.

Step-by-step explanation:

Proportions are fractions that can be made by using the given numbers, which in this case are 2, 5, 8, and 20. Let's pair each one with the other three and then simplify if possible.

First, let's begin with 2:

\frac{2}{5} = \frac{2}{5}

\frac{2}{8} = \frac{1}{4}

\frac{2}{20} = \frac{1}{10}

Then, let's do 5:

\frac{5}{2} = \frac{5}{2}

\frac{5}{8} = \frac{5}{8}

\frac{5}{20} = \frac{1}{4}

Note that we already have \frac{1}{4}, so we do not need to include an additional one.

Now, let us do 8:

\frac{8}{2} = \frac{4}{1}

\frac{8}{5} = \frac{8}{5}

\frac{8}{20} = \frac{2}{5}

See how we already have \frac{2}{5}, so we won't have to include that as well.

Finally, let's do 20:

\frac{20}{2} = \frac{10}{1}

\frac{20}{5} = \frac{4}{1}

\frac{20}{8} = \frac{5}{2}

Now see that we already have both \frac{4}{1} and \frac{5}{2}, so we won't have to include both of them, as they are both extras.

Hence, the answers are \frac{2}{5}, \frac{1}{4}, \frac{1}{10}, \frac{5}{2}, \frac{5}{8}, \frac{4}{1}, \frac{8}{5}, and \frac{10}{1}.

<h2><u><em>PLEASE MARK AS BRAINLIEST!!!!!</em></u></h2>
8 0
3 years ago
Read 2 more answers
Let p= x^2-7.
Advocard [28]

Since p = x² - 7, you can substitute/plug in p for x² - 7

So:

(x² - 7)² - 4x² + 28 = 5

(p)² - 4x² + 28 = 5      You can factor out -4 from (-4x² + 28)

p² - 4(x² - 7) = 5        Plug in p

p² - 4p = 5        Subtract 5

p² - 4p - 5 = 0        Your answer is C

8 0
3 years ago
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