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aalyn [17]
2 years ago
8

Find the slope of the graph of the equation at the given point. (If an answer is undefined, enter UNDEFINED.)

Mathematics
1 answer:
juin [17]2 years ago
7 0

Answer:

Undefined.

Step-by-step explanation:

We want to find the slope of the graph of the equation:

\displaystyle x^2 - y^2 = 81

At the point (9, 0).

In other words, we want to evaluate dy/dx when <em>x</em> = 9 and <em>y</em> = 0.

Find dy/dx. We can take the derivative of both sides with respect to <em>x: </em>

\displaystyle \begin{aligned} \frac{d}{dx}\left[ x^2 - y^2\right] = \frac{d}{dx}\left [ 81\right] \\ \\ 2x - 2y \frac{dy}{dx} &= 0 \\ \\ \frac{dy}{dx} = \frac{x}{y}\end{aligned}

Then the slope of the graph at the point (9, 0) will be:

\displaystyle \begin{aligned} \frac{dy}{dx}\Big|_{(9, 0)} &= \frac{(9)}{(0)} \\ \\ &= \text{Und.}\end{aligned}

In conclusion, the slope of the graph at the point (9, 0) is undefined.

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Write an expression to represent the pattern 19, 27, 35, 43
Mama L [17]

Answer

1) The expression to represent the pattern is 11 + 8n

2) The expression to represent the pattern is 80 - 9n

Step-by-step explanation:

1) Lets study the pattern;

- 19 , 27 , 35 , 43 , ..................

27 - 19 = 8

35 - 27 = 8

43 - 35 = 8

The difference is constant between each two consecutive terms

It is an arithmetic sequence

Lets take about the arithmetic sequence

If the first term is a and the constant difference is d

a1 = a , a2 = a + d , a3 = a + 2d , a4 = a+ 3d , ........

an = a + (n - 1)d, where n the position of the term in the sequence

Now we will use this rule to find the expression of our pattern

a = 19 , d = 8

an = 19 + (n - 1)(8) ⇒ an = 19 + 8n - 8 ⇒ an = 11 + 8n

Lets check it;

a3 = 11 + 8(3) = 11 + 24 = 35 ⇒ true

The expression to represent the pattern is 11 + 8n

Step 2) Lets study the pattern;

- 71 , 62 , 53 , 44 , ...

62 - 71 = -9

53 - 62 = -9

44 - 53 = -9

The difference is constant between each two consecutive terms

It is an arithmetic sequence

We will use the same rule above to find the expression of the pattern

a = 71 , d = -9

an = 71 + (n - 1)(-9) ⇒ an = 71 + -9n + 9 ⇒ an = 80 - 9n

Lets check it;

a4 = 80 - 9(4) = 80 - 36 = 44 ⇒ true

The expression to represent the pattern is 80 - 9n

7 0
3 years ago
What is step two in the problem solving process
miskamm [114]
Hey there,
It would be devising a plan

Hope this helps :))

<em>~Top♥</em>
6 0
3 years ago
Whats the hcf of 108 and 308​
inna [77]

Answer:

i think this should help

5 0
3 years ago
Read 2 more answers
What is 12 divided by 3/4
Tpy6a [65]
12 divided by 3/4 =
16

<span>It is 16 because the reciprocal of 3/4 is 4/3 and 12 as a fraction is 12/1. So 12/1 x 4/3 is 48/3. And if you divide 48 by 3 you will get 16. If you don't get 16 then you did the wrong calculation.</span>

Hope I Helped You!!! :-)

Have A Good Day!!!
8 0
3 years ago
Read 2 more answers
What 5x23p9x2 and what is the common number?
loris [4]
Hi There! :)

<span>What 5x23p9x2 and what is the common number?

5</span>×23=115
<span>115</span>×9=1035
<span>1035</span>×2=2070
<span>
Therefore 2070 is the answer
</span>

5 0
3 years ago
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