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Oksana_A [137]
1 year ago
12

Approximate pi plus the square root of 70 to the nearest hundredth.

Mathematics
1 answer:
stich3 [128]1 year ago
5 0

Answer:

  11.51

Step-by-step explanation:

In general, a calculator is required to evaluate the irrational sum ...

  π + √70

<h3>Calculator result</h3>

The result from a readily-available online calculator is shown in the attachment.

  π + √70 ≈ 11.51

__

<em>Additional comment</em>

You have probably memorized pi to several digits: 3.1416. To obtain the required estimate means you need to approximate √70 to about the same level of precision.

For a number n = a² +b, the square root can be approximated by the continued fraction ...

  √n ≈ a +b/(2a +b/(2a +...))

Effectively, the root (r) can be iterated from the recursive formula ...

  r' = a +b/(a +r)

For √70, we have 70 = 8² +6   ⇒   a=8, b=6

If the initial approximation of the root is r0≈a=8, then a couple of iterations gives ...

  r1 = 8 + 6/(8 +r0) = 8 + 6/(8 +8) = 8 3/8

  r2 = 8 + 6/(8 +r1) = 8 +6/(8 +8 3/8) = 8 48/131

This has sufficient accuracy for the purpose. The decimal equivalent of the sum then becomes ...

  3.1416 +8.3664 = 11.5080 ≈ 11.51

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Delvig [45]

Answer:The equation that models the solution will be

33 = 22k / 6

Step-by-step explanation:

The two types of variation involved in this problem are direct variation and inverse variation.

In direct variation, when one item changes in the positive or negative direction, the other item also changes in the positive or negative direction.

In inverse variation, when one item changes in the positive or negative direction, the other item also changes in the negative or positive direction.

From the information given,

c varies directly with b

If we introduce a direct proportionality constant, k, then,

c = kb

c also varies inversely with a

If we introduce an inverse proportionality constant, k, then,

c = k/b

Therefore, c = kb / a

When a=6 , b=22 and c=33.

The equation that models the solution will be

33 = 22k / 6

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3 years ago
When solving a linear system by substitution, how do you decide which variable to solve first?
rosijanka [135]

Answer: whichever one is easiest to get by itself.

Step-by-step explanation:

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Write the slope-intercept form of the equation of each line 13x-2y=14
HACTEHA [7]

Answer:

Step-by-step explanation:

First, lets put this into y=mx+b form.

You can bring the 13x over to the 14, by subtracting and you get -2y=14-13x, or also -2y = -13x + 14

Then you can divide both sides by -2 to get y, and you get

-2y/-2 = -13x/-2 + 14/-2 which is simplified to y=13/2x + (-7) which is

y=13/2x-7

                                {[( IMPORTANT )]}

 THIS HAS THE SLOPE IN A IMPROPER FRACTION... CHECK IF YOU USE MIXED NUMBERS OR IMPROPER FRACTIONS

the mixed number form is y = 7     1/2 x -7

Hope this helps!

       

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3 years ago
I need a helping hand
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Step-by-step explanation:

5 0
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Solve the system of equations: <br> X+y+z=5<br> -3x-4y+4z=15<br> 2x-y-4z=-8
atroni [7]

Answer:

  (x, y, z) = (3, -2, 4)

Step-by-step explanation:

The attachment shows a solution using a graphing calculator where the first equation is solved for z, and that expression is substituted into each of the other two equations. The solution to that system is (x, y) = (3, -2). Using these values in the expression for z, we find ...

  z = 5 -(3 +(-2)) = 4

The solution is (x, y, z) = (3, -2, 4).

__

Your graphing calculator and/or online tools can give you the reduced row echelon form of the augmented matrix representing the system:

  \left[\begin{array}{ccc|c}1&1&1&5\\-3&-4&4&15\\2&-1&-4&-8\end{array}\right]

__

If you're solving by hand, you can do the substitution described above to eliminate z from one equation. You can eliminate z from another equation by adding the last two:

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  (-3x -4y +4z) +(2x -y -4z) = (15) +(-8)   ⇒   -x -5y = 7

This pair of equations can be solved for x and y in any of the usual ways. Using the second equation to substitute for x, for example, gives you ...

  -7(-5y -7) -8y = -5   ⇒   27y = -54   ⇒   y = -2

  x = -5(-2) -7 = 3

  z = 5 -(3) -(-2) = 4

_____

<em>Additional comment</em>

If all that is needed is a solution, we prefer a graphical or matrix approach. These take about the same amount of time. Both require a little additional effort to determine exact values when the solutions are not integers.

6 0
2 years ago
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