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qwelly [4]
3 years ago
5

26. Law of sines, please give a step by step explanation

Mathematics
1 answer:
Stels [109]3 years ago
5 0

Answer:

  174.6 ft

Step-by-step explanation:

It can be helpful to draw a diagram of the triangle we're concerned with. (See attached.)

We know the angle at the end of the shadow inside the triangle is 52°-22° = 30°. We assume the tree is growing straight up out of the hillside, so its angle with the hill inside the triangle is 90°+22° = 112°. Then the remaining angle between the shadow and the tree at the top of the tree is ...

  180° -30° -112° = 38°

Now, we have the angle opposite the tree, and the angle opposite the known side length of the triangle (215 feet along the hill, AC in the diagram). This is enough information to usefully use the Law of Sines.

  c/sin(C) = a/sin(A)

  c = a(sin(C)/sin(A)) = (215 ft)(sin(30°)/sin(38°)) ≈ 174.6 ft

The height of the tree is about 174.6 feet.

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A random sample of adults were asked whether they prefer reading an e-book over a printed book. The survey resulted in a sample
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Answer: (0.10\ ,\ 0.18)

Step-by-step explanation:

According to the empirical rule, the 95% confidence interval for the true population proportion is given by :-

(p'-2\sigma_{p'}\ ,\ p'+2\sigma_{p'})

Given : . The survey resulted in a sample proportion of p′=0.14, with a sampling standard deviation of σp′=0.02, who preferred reading an e-book.

Then, the 95% confidence interval for the true proportion of adults who prefer e-books will be :-

(0.14-2(0.02)\ ,\ 0.14+2(0.02))\\\\=(0.14-0.04\ ,\ 0.14+0.04)\\\\=(0.10\ ,\ 0.18)

Hence, the 95% confidence interval for the true proportion of adults who prefer e-books= (0.10\ ,\ 0.18)

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3 years ago
Determine the intervals on which the function is increasing, decreasing and constant
viva [34]

Answer:

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  • decreasing: (0, ∞)

Step-by-step explanation:

The function goes up to the right until it gets to the vertex at x=0. Then it goes down to the right. That is, it is ...

  increasing from -∞ to 0 (not including 0)

  decreasing from 0 to +∞ (not including 0)

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At x=0, the function is neither increasing nor decreasing, so x=0 is not part of either interval.

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I need help fast! I’m taking the test now!
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Given the below sequence:-1, -3, -5, -7, . . .
vekshin1

Answer:

A. The next 3 terms are —9, —11, —13

B. The sequence is Arithmetic

C. The sequence has a common difference of —2

Common difference = T2 — T1 or = T3 — T2

=T2 — T1 = —3 —(—1) = —2 or

= T3 — T2 = —5 —(—3) = —2

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a = first term = —1

d = Common difference = —2

n = 27

T27 = —1 + —2(27—1)

T27 = —1 + —2(26)

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