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Vikki [24]
2 years ago
8

Find an equation for the tangent to the curve at the given point y=x^3 , (2,8)

Mathematics
1 answer:
Yuliya22 [10]2 years ago
5 0

\bf y=x^3\implies \left. \cfrac{dy}{dx}=3x^2 \right|_{x=2}\implies \stackrel{\stackrel{m}{\downarrow }}{12} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{8})~\hspace{10em} slope = m\implies 12 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-8=12(x-2) \\\\\\ y-8=12x-24\implies y=12x-16

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What scale factor was used when going from the grey triangle to the yellow triangle
sertanlavr [38]

Answer:

Scale factor of 1/3

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
2x + 7 = 27 or 3 + 3x = 30
Leokris [45]

Step-by-step explanation:

2x + 7 = 27 OR 3 + 3x = 30.

2x = 27 - 7 OR 3x = 30 - 3

2x = 20 OR 3x = 27

x = 20/2 OR x = 27/3

x = 10 OR x = 9

5 0
2 years ago
(a) The probability that an automobile being filled with gasoline will also need an oil change is 0.35; the probability that it
cricket20 [7]

Answer:

0.714 ; 0.556 ; (A1 n A2 n A3) = 0

Step-by-step explanation:

Given that :

P(oil) = 0.35

P(filter) = 0.45

P(oil n filter) = 0.25

1)

P(filter | Oil) = P(oil n filter) / P(oil)

P(filter | Oil) = 0.25 / 0.35 = 0.714

11)

P(Oil | filter) = P(oil n filter) / P(filter)

P(Oil | filter ) = 0.25 / 0.45 = 0.556

Number of red aces = 2

Queen or king = 4 + 4 = 8

Number on card greater than 3 and less than 8 = {4,5,6,7} = 4 card ; for 4 suits = 4 * 4 = 16

Total number of cards in deck = 52

Choosing without replacement :

Hence,

A1 = 2 / 52

A2 = 8 / 51

A3 = 16 / 50

(A1 n A2 n A3) ;this means card common to all three events.

However, (A1 n A2 n A3) = 0 because ;

1.) No red ace card is greater than 3 and less than 8.

11.) An ace card can neither be a king nor a queen

3 0
2 years ago
Which equation are equivalent to 1/5+2/3|2-x|=4/15?
disa [49]

Answer:

• 2/3|2 -x| = 1/15

• |2 -x| = 1/10

• 1/5 +|4/3 -2/3x| = 4/15

Step-by-step explanation:

Starting with the given equation, subtract 1/5 = 3/15.

(2/3)|2 -x| = 4/15 - 3/15

(2/3)|2 -x| = 1/15 . . . . . . . . matches the first choice

Now, multiply by 3/2.

|2 -x| = 3/30

|2 -x| = 1/10 . . . . . . . . . . . . matches the third choice

___

If you decide to distribute the coefficient 2/3 instead, you have

1/5 + |2·2/3 -x·2/3| = 4/15

1/5 + |4/3 -2/3x| = 4/15 . . . . matches the selected choice

5 0
2 years ago
Read 2 more answers
Mr. Stanton bought 2.6 yards of fabric for $8.94. About how much was the cost per yard?
lapo4ka [179]

In order to find CPU (Cost per unit) we must take the cost, and divide it by the number of units.

So,

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Since we are talking about money, it is implied to round to the nearest cent, so the final answer is

$3.44

4 0
3 years ago
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