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Solnce55 [7]
2 years ago
13

Use the differential to approximate the expression. Then use a calculator to approximate the quantity, and give the absolute val

ue of the difference in the two results to four decimal places.
√
53
Mathematics
1 answer:
scoray [572]2 years ago
7 0

9514 1404 393

Answer:

   0.0056

Step-by-step explanation:

  f(x) = √(49 +x)

  f'(x) = 1/(2√(49 +x))

A linear approximation of f(x) expanded about x=0 is ...

  f(x) ≈ f(0) + f'(0)x = 7 +x/(2·7)

Then for √53, we have x=4

  f(4) ≈ 7 +4/14 = 7 2/7 . . . . . approximate √53 using differentials

__

The calculator value of √53 is about 7.280110, so the difference in results is ...

  approx - actual ≈ 7.285714 -7.280110 = 0.005604 ≈ 0.0056

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Klio2033 [76]

9514 1404 393

Explanation:

We can find the slope by solving for y.

  3x +2y +7 = 5x +3y +10

  -2x -3 = y . . . . . . . . . . . . . add -5x-10-2y to both sides of the equation

In this form, the slope (m) is the coefficient of x, -2. Hence m = -2.

__

<em>Alternate solution</em>

A graph of the equation shows it has an x-intercept of -1.5 and a y-intercept of -3. The slope (m) is then "rise" divided by "run", or ...

  m = rise/run = -3/1.5

  m = -2

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34566+986994689999999
Jlenok [28]

Answer:

9.8699469e+14 and/or 986994690000000

Step-by-step explanation:


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The sum of the square of the number and a second number is 42
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Step-by-step explanation:

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