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Semenov [28]
2 years ago
12

Claire had 4 1/6 feet of string. She used some string to hang out decorations. Now she has 1 5/6 feet of string left. How much s

tring did claire use? Draw a model and solve.
Mathematics
1 answer:
vodka [1.7K]2 years ago
8 0

Answer:

Length of string used by Claire = 7 / 3 feet

Step-by-step explanation:

Given:

Length of string Claire in starts = 4\frac{1}{6} feet

Length of string Claire in end = 1\frac{5}{6} feet

Find:

Length of string used by Claire

Computation:

Length of string Claire in starts = 4\frac{1}{6} feet = 25 / 6 feet

Length of string Claire in end = 1\frac{5}{6} feet = 11 / 6 feet

Length of string used by Claire = Length of string Claire in starts - Length of string Claire in end

Length of string used by Claire = [25 / 6] - [11 / 6]

BY taking LCM

Length of string used by Claire = [25 - 11] / 6

Length of string used by Claire = 14 / 6

Length of string used by Claire = 7 / 3 feet

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Find the complex fourth roots of 81(cos(3π/8)+isin(3π/8)). a) Find the fourth root of 81. b) Divide the angle in the problem by
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Answer:

The answer is below

Step-by-step explanation:

Let a complex z = r(cos θ + isinθ), the nth root of the complex number is given as:

z_1=r^{\frac{1}{n} }(cos(\frac{\theta +2k\pi}{n} )+isin(\frac{\theta +2k\pi}{n} )),\\k=0,1,2,.\ .\ .,n-1

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z_{k=0}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8}  +2(0)\pi}{4} )+isin(\frac{\frac{3\pi}{8}  +2(0)\pi}{4} ))=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})] \\z_{k=0}=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})]\\\\z_{k=1}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8}  +2(1)\pi}{4} )+isin(\frac{\frac{3\pi}{8}  +2(1)\pi}{4} ))=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})] \\z_{k=1}=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})]\\\\

z_{k=2}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8}  +2(2)\pi}{4} )+isin(\frac{\frac{3\pi}{8}  +2(2)\pi}{4} ))=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})] \\z_{k=2}=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})]\\\\z_{k=3}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8}  +2(3)\pi}{4} )+isin(\frac{\frac{3\pi}{8}  +2(3)\pi}{4} ))=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})] \\z_{k=3}=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})]

3 0
3 years ago
What is the answer to this too?
inn [45]

Answer:

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Step-by-step explanation:

to find the amount of days in 6 weeks, you multiply 6 and 7 which will get you 42. Then 42/4 is 10.5. This means it will go through 10 full half-lifes. you divide 500 by 2 10 times and 0.3453 g is the closest answer.

7 0
3 years ago
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