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Step2247 [10]
3 years ago
10

Please help, due in 1 day; which is tomorrow

Mathematics
2 answers:
MrRa [10]3 years ago
6 0
Already answered in the other one.
GrogVix [38]3 years ago
5 0
1) 360°-18°-18°-3x°-3x°=0
     6x=324°
      x=54°
2) 180°-49°-(x+3)°=0
      (x+3)°=131°
      x=128°
3) 90°-42°-4x°=0
   4x°=48°
    x=12°
4) 180°-86°-2x°=0
   2x°=94°
   x=47°
5) 360°-117°-117°-3x°-3x°=0
   6x=126°
  x=21°
6) 90°-66°-8x°=0
    8x=24°
    x=3°
7) 180°-22°-(x-5)°=0
     (x-5)°=158°
     x=163°
8)  90°-2x°-2x°=0
     4x°=90°
     x=22.5° (i don't know if you can leave it like this or you have to write it in                      another way)
9) 90°-57°-3x°=0
   3x°=33°
   x=11°
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A. Evaluate the polynomial
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a) y = x³− 5x² + 6x + 0.55 at x = 1.37.

Use 3-digit arithmetic with chopping. Evaluate the percent relative round-off error.

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b. Express y as y = ((x − 5)x + 6)x + 0.55 (this is the same equation). Use again 3-digit arithmetic with chopping. Evaluate the percent relative round-off error and compare with part (a). Make the conclusion about which form of the polynomial is superior.

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Step-by-step explanation:

a) y = x³− 5x² + 6x + 0.55 at x = 1.37.

Use 3-digit arithmetic with chopping. Evaluate the percent relative round-off error.

Let's evaluate before applying the 3 digit arithmetic chopping rule

y = 1.37³ - 5 × 1.37² + 6 × 1.37 + 0.55

y = 1.956853

Let evaluate each components of the polynomial one by one

Note that: 3-digit arithmetic chopping means to approximate chop off or remove number after the 3 significant figures.

y = x³− 5x² + 6x + 0.55 at x = 1.37.

x³ = 1.37³ = 2.571353

≈ 2.57

x² = 1.37² = 1.8769

≈ 1.88

5x² = 1.87 × 5

= 9.35

x = 1.37

6x = 1.37 × 6

6x = 8.22

Evaluating the polynomial

y = 2.57 - 9.38 + 8.22 + 0.55

y = 1.98

The percent relative round-off error =

1.956853 - 1.98/1.956853 × 100

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b. Express y as y = ((x − 5)x + 6)x + 0.55 (this is the same equation). Use again 3-digit arithmetic with chopping. Evaluate the percent relative round-off error and compare with part (a). Make the conclusion about which form of the polynomial is superior.

y = ((x − 5)x + 6)x + 0.55

Evaluating with the 3 digit chop off rule is applied

= ((1.37 - 5)1.37 + 6)1.37 + 0.55

=( 1.8769 - 6.85) + 6) 1.37 + 0.55

= (- 4.9731 + 6 )1.37 + 0.55

= 1.0269 × 1.37 + 0.55

= 1.406853

= 1.956853.

≈ 1.96

Note in: evaluating before applying the 3 digit arithmetic chopping rule

y = 1.37³ - 5 × 1.37² + 6 × 1.37 + 0.55

y = 1.956853

The percent relative round-off error

1.956853 - 1.96/1.956853 × 100

= -0.161%

Comparing part a and b together, part b is more superior because the percent(%) error is smaller when compared to part a

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