Lingz
12.08.2020 •
Mathematics
Plz Help! Will mark brainliest! Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and sin ∠X = 5 over 5 and 59 hundredths. Part A: Use complete sentences to explain the special relationship between the trigonometric ratios of triangles XYZ and ABC. You must show all work and calculations to receive full credit. (5 points) Part B: Explain how to find the measures of segments CB and AB. You must show all work and calculations to receive full credit. (5 points)
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Ответ:
Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and sin ∠X = 5 over 5 and 59 hundredths. Part A: Use complete sentences to explain the special relationship between the trigonometric ratios of triangles XYZ and ABC. You must show all work and calculations to receive full credit. (5 points) Part B: Explain how to find the measures of segments CB and AB. You must show all work and calculations to receive full credit.
Ответ:
Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and sin ∠X = 5 over 5 and 59 hundredths. Part A: Use complete sentences to explain the special relationship between the trigonometric ratios of triangles XYZ and ABC. You must show all work and calculations to receive full credit. (5 points) Part B: Explain how to find the measures of segments CB and AB. You must show all work and calculations to receive full credit.
Ответ:
Consider this example: say we want to convert x = 11 0101 1001₂ to base 3.
The binary expansion of x is
x = 1×2⁹ + 1×2⁸ + 1×2⁶ + 1×2⁴ + 1×2³ + 1×2⁰
which in base 10 reduces to
x = 512 + 256 + 64 + 16 + 8 + 1 = 857
Recall the first several powers of 3:
3⁰ = 1; 3¹ = 3; 3² = 9; 3³ = 27; 3⁴ = 81; 3⁵ = 243; 3⁶ = 729
Now it's a matter of computing quotients and remainders. Pick the largest power of 3 that fits into the target number, then check the remainder and repeat.
• How many times does the 729 go into 857? 1 time, and it leaves a remainder of 128, or
857 = 1×729 + 128 = 1×3⁶ + 128
• How many times does 81 go into 128? Also 1 time, so
128 = 1×81 + 47 = 1×3⁴ + 47
• How many times does 27 go into 47? Also 1 time,
47 = 1×27 + 20 = 1×3³ + 20
• How many times does 9 go into 20? 2 times,
20 = 18 + 2 = 2×9 + 2 = 2×3² + 2
• How many times does 1 go into 2? Also 2 times,
2 = 2 + 1 = 2×1 + 0 = 2×3⁰
So we found
857 = 1×3⁶ + 1×3⁴ + 1×3³ + 2×3² + 2×3⁰
which is the ternary expansion of x,
x = 1 011 202₃