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kow [346]
4 years ago
10

As the moon revolves around the earth, the side that faces the earth is usually just partially illuminated by the sun. The phase

s of the moon describe how much of the surface appears to be in sunlight. An astronomical measure of phase is given by the fraction F of the lunar disc that is lit. When the angle between the sun, the earth, and the moon is θ(0<=θ<=360∘), then
F=1/2(1−cosθ)
Determine the angles θ, that correspond to the following phases:

(a) F = 0 (new moon)
(b) F = 0.25 (a crescent moon)
(c) F = 0.5 (first or last quarter)
(d) F = 1 (full moon)
Mathematics
1 answer:
lys-0071 [83]4 years ago
7 0

Answer:

a)   0∘ and  360∘

b)   300∘ and  60∘

c)   90∘ and  270∘

d)   180∘

Step-by-step explanation:

θ(0<=θ<=360∘)

then

a)

F=1/2(1−cosθ)

Putting F= 0

we get

0 = 1/2 (1−cosθ)

(1−cosθ) = 0

cosθ = 1

θ = cos^-^1 (1)

 = 0∘ and  360∘

b) If F = 0.25

then putting values

1/4 = 1/2 (1−cosθ)

(1−cosθ) = 1/2

cosθ = 1/2

θ = cos^-^1 (1/2)

 = 300∘ and  60∘

c) If F = 0.5

then  putting values we get

1/2 = 1/2 (1−cosθ)

(1−cosθ) = 1

cosθ = 0

θ = cos^-^1 (0)

 = 90∘ and  270∘

d) If F = 1

then  putting values we get

1 = 1/2 (1−cosθ)

(1−cosθ) = 2

cosθ = -1

θ = cos^-^1 (-1)

 = 180∘

So after these calculation we determine the vales of angles that are given uper.

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A school has 1080 students with a male to female ratio of 5:4. how many male students are there?
wariber [46]

Answer:

600 male students

Step-by-step explanation:

1080/5 + 4

1080/9 = 120

Male students ratio is 5 so

120 * 5 = 600

If my answer is incorrect, pls correct me!

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5 0
3 years ago
A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in
Vlada [557]

Answer:

0.001%

Step-by-step explanation:

Given that a recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes to help the public schools

n = 1500

favour x = 622

Sample proportion p = 622/1500 = 0.4147

H_0: p = 0.66\\H_a: p >0.66

(right tailed test)

Assume H0 to be true.

Std error = \sqrt{\frac{0.66*0.34}{1500} } \\=0.01223

p difference = -0.2453

Test statistic Z = \frac{-0.2453}{0.01223} \\=-20.05

p value <0.00001

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5 0
4 years ago
Evaluate (7² - 9 ) ÷ ( 55 - 35 ). <br> A: -34<br> B: 48<br> C: -4<br> D: 2
Marina86 [1]
This answer is D, 2. Hope this helps 
8 0
3 years ago
Read 2 more answers
Hubert cut a piece of yarn into pieces that are each 2/3 foot long. If the yarn is 6 feet long, how many pieces of yarn did he c
kompoz [17]
2/3 of a foot is 8 inches
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72/8 is 9

the answer is 9 pieces of yarn
8 0
3 years ago
Please help solve, Thank you. - Which expression is equivalent to t + 4 +3 - 2t?
OverLord2011 [107]
<h3>Answer: Choice B)  -t+7</h3>

Explanation

The like terms are ones that have the same variable in them, or that dont have a variable at all attached. One pair of like terms is t and -2t, which combine to t+(-2t) = t-2t = -t

The other pair of like terms are 4 and 3 which add to 7

So t+4+3-2t simplifies fully to -t+7, which is the same as 7+(-t) = 7-t

We cannot simplify any further from here as the 7 and -t are not like terms.

6 0
3 years ago
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