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tatuchka [14]
3 years ago
13

How to use implicit differentiation to find an equation of the tangent line?

Mathematics
1 answer:
Arada [10]3 years ago
5 0
The slope of the line is the dy/dx value every time it appears in the differential equation. By substituting values for x and y in the DE, the slope can be found for the tangent at a point. This is the value of m in y=mx+a. To find a, plug in the tangent point.
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What is 04.151515... into a fraction
Sergio039 [100]

Answer:

\displaystyle 4.\overline{15} = \frac{137}{33}.

Step-by-step explanation:

Start by separating this decimal number into its integer part and its fraction part:

4.151515\cdots = 4 + 0.151515\cdots

The most challenging task here is to express 0.151515\cdots as a proper fraction. Once that fraction is found, expressing the original number 4.151515\cdots will be as simple as rewriting a mixed number as an improper fraction.

Let x = 0.151515\cdots. (x + 4) would then represent the original number.

Note that the repeating digits appear in groups of two. Therefore, if the digits in x are shifted to the left by two places, the repeating part will continue to match:

\begin{aligned}x = 0.&151515\cdots && \\ 100\, x = 15.& 151515\cdots \end{aligned}.

Note, that this "shifting" is as simple as multiplying the initial number by 100 (same as 10 raised to the power of the number of digits that needs to be shifted.)

Subtract the original number from the shifted number to eliminate the fraction part completely:

\begin{aligned}&(100\, x) - x \\ &= 15.151515\cdots\\  & \phantom{=}- 0.151515\cdots\\&=15 \end{aligned}.

In other words:

99\, x = 15.

\displaystyle x = \frac{15}{99} = \frac{5}{33}.

Therefore, the original number would be:

\displaystyle x + 4 = \frac{5}{33} = \frac{132 + 5}{33} = \frac{137}{33}.

4 0
3 years ago
Which worker is paid less than the minimum hourly wage
abruzzese [7]

Answer:

?

Step-by-step explanation:

we need the options here?

3 0
3 years ago
What is the measure of angle x?<br><br> Enter your answer in the box.
Cloud [144]

Answer:

the measure of angle x is 48

7 0
3 years ago
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Determine the slope for the line below
kow [346]

Answer:

C : 20

good luck, hope this helped!

7 0
3 years ago
What is the value of these coins?
Alborosie

Answer:

$2.39

Step-by-step explanation:

4 pennies=4

2 nickels=10

10 dimes=100

5 quarters=125

$2.39

3 0
3 years ago
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