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frutty [35]
2 years ago
11

15 / √31 - 4

Mathematics
1 answer:
NeX [460]2 years ago
6 0

Answer:

\frac{15}{ \sqrt{31} - 4}} = \sqrt{31} + 4

Step-by-step explanation:

\frac{15}{\sqrt{31} - 4}\\\\=\frac{15}{\sqrt{31} - 4} \times \frac{\sqrt{31} + 4}{\sqrt{31}+ 4} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \   [  \ rationalizing \ the \ denominator \ ]\\\\=\frac{15( \sqrt{31} + 4 )}{(\sqrt{31})^2 - (4)^2}  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  \ \ \ [ \ (a-b)(a+b) = a^2 - b^2 \ ]\\\\=\frac{15 ( \sqrt{31} + 4)}{31 - 16}\\\\=\frac{15 (\sqrt{31} + 4)}{15}\\\\= \sqrt{31} + 4

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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage r
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Answer:

Step-by-step explanation:

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Value of y will be decreased by (1.00 - 0.59)100 =  41% for each unit increase in x.

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Anne runs 6 laps on a track. She runs a total of 1 mile, or 5,280 feet. Write and solve an equation to find the distance, in fee
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HELP 50 POINTS NOW HELP HELP HELP HLEP
koban [17]

Answer:

a=42°

b=138°

Step-by-step explanation:

the sum of angles on a triangle is 180°

so

18+120+a=180

138+a=180

a=180-138

a=42

a+b=180 because a ans b are linear pair of angles.

Definiton:A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

a=42 from before

it means that b=180-42=138

3 0
3 years ago
Find n for which the nth iteration by the Bisection Method guarantees to approximate the root of f(x) = 2x^2 − 3x − 2 on [−2, 1]
Lady_Fox [76]

Answer:

n = 29 iterations would be enough to obtain a root of f(x)=2x^2-3x-2 that is at most 10^{-8} away from the correct solution.

Step-by-step explanation:

You can use this formula which relates the number of iterations, n, required by the bisection method to converge to within an absolute error tolerance of ε starting from the initial interval (a, b).

n\geq \frac{log(\frac{b-a}{\epsilon} )}{log(2)}

We know

a = -2, b = 1 and ε = 10^{-8} so

n\geq \frac{log(\frac{1+2}{10^{-8}} )}{log(2)}\\n \geq 29

Thus, n = 29 iterations would be enough to obtain a root of f(x)=2x^2-3x-2 that is at most 10^{-8} away from the correct solution.

<u>You can prove this result by doing the computation as follows:</u>

From the information given we know:

  • f(x)=2x^2-3x-2
  • \epsilon = 10^{-8}

This is the algorithm for the Bisection method:

  1. Find two numbers <em>a</em> and <em>b</em> at which <em>f</em> has different signs.
  2. Define c=\frac{a+b}{2}
  3. If b-c\leq \epsilon then accept c as the root and stop
  4. If f(a)f(c)\leq 0 then set <em>c </em>as the new<em> b</em>. Otherwise, set <em>c </em>as the new <em>a</em>. Return to step 1.

We know that f(-2)=2(-2)^2-3(-2)-2=12 and f(1)=2(1)^2-3(1)-2=-3 so we take a=-2 and b=1 then c=\frac{-2+1}{2} =-0.5

Because 1-(-0.5)\geq 10^{-8} we set c=-0.5 as the new <em>b.</em>

The bisection algorithm is detailed in the following table.

After the 29 steps we have that 6\cdot 10^{-9}\leq 10^{-8} hence the required root approximation is c = -0.50

8 0
3 years ago
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