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Vedmedyk [2.9K]
2 years ago
8

A Cepheid star is a type of variable star, which means its brightness is not constant. The relationship between the brightness o

f a Cepheid star and its period, or length of its pulse, is given by M = –2.78(log P) – 1.35, where M is the absolute magnitude, or brightness, of the star, and P is the number of days required for the star to complete one cycle. What is the absolute magnitude of a star that has a period of 45 days? Use a calculator. Round your answer to the nearest hundredth. –5.95 –4.60 3.25 4.60
Mathematics
2 answers:
White raven [17]2 years ago
8 0

Answer:

The absolute brightness of the Cepheid star after a period of 45 days is -5.95

Step-by-step explanation:

Since the absolute magnitude or brightness of a Cepheid star is related to its period or length of its pulse by

M = –2.78(log P) – 1.35 where M = absolute magnitude and P = period or length of pulse.

From our question, it is given that P = 45 days.

So, M = –2.78(log P) – 1.35

M = –2.78(log 45) – 1.35

M = –2.78(1.6532) – 1.35

M = -4.60 - 1.35

M = -5.95

So, the absolute magnitude or brightness M of a Cepheid star after a period P of 45 days is -5.95

BaLLatris [955]2 years ago
7 0

Answer:

A

Step-by-step explanation:

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Eighteen 2.5 gallon buckets are needed to fill a cistern with water. Find the constant of variation. Please help! Thank you!
Allushta [10]

Given:

Eighteen 2.5 gallon buckets are needed to fill a cistern with water.

To find:

The constant of variation.

Solution:

If y is directly proportional to x, then

y\propto x

y=kx

Where, k is constant of variation.

In the given problem, water in cistern (w) is directly proportional to number of buckets (n).

w\propto n

w=2.5n        (Capacity of each bucket is 2.5 gallons)

Therefore, the constant of variation is 2.5.

6 0
1 year ago
Read 2 more answers
Find the value of X and Y in the following parallelogram.AD =X+8 D=2y +13 C=16-x CB=5y+4 AB=o​
vlada-n [284]

Answer:

The answer is below

Step-by-step explanation:

AD = X + 8 ∠D = 2y +13 ∠C = 16 - x CB = 5y+4

In a parallelogram, consecutive angles are supplementary and opposite sides are equal.

Therefore for parallelogram ABCD, AB = CD, CB = AD

Since AD = CB (opposite sides of a parallelogram are equal):

x + 8 = 5y + 4

5y - x = 8 - 4

5y - x = 4             (1)

∠C + ∠D= 180° (consecutive angles of a parallelogram are supplementary). Therefore:

16 - x + 2y + 13 = 180

2y - x + 29 = 180

2y - x = 180 -29

2y - x = 151             (2)

To find x and y, subtract equation 1 from equation 2:

3y = -147

y = -49

Put y = -49 in equation 2

2(-49) - x = 151

x = -98 - 151

x = -249

6 0
1 year ago
The terms of the binomial expansion are written below using the patterns. (m + 2)4 = (1)(m4)(20) + (4)(m3)(21) + (6)(m2)(22) + (
lorasvet [3.4K]

Answer:

(m + 2)^4 = m^4+ 8 m^3 + 24 m^2 + 32 m + 16

Step-by-step explanation:

(m + 2)^4 = (1)(m^4)(2^0) + (4)(m^3)(2^1) + (6)(m^2)(2^2) + (4)(m^1)(2^3) + (1)(m^0)(2^4)

2^0 is 1 also m^0 is 1

2^2= 4, 2^3= 8 , 2^4= 16

(m + 2)^4 = (1)(m^4)(1)+ (4)(m^3)(2) + (6)(m^2)(4) + (4)(m^1)(8) + (1)(1)(16)

(m + 2)^4 = m^4+ 8 m^3 + 24 m^2 + 32 m + 16


4 0
1 year ago
The equation for a projectile's height versus time is h(t)=-16t^2+Vt+h. A tennis ball machine serves a ball vertically into the
Artist 52 [7]

Answer:

The maximum height  is 191.063 ft

Step-by-step explanation:

We can easily solve this question by plotting the graph of the equation below

h(t)=-16t^2+Vt+h

Where

h = initial height = 2ft

V = initial speed = 110 ft/s

t = time in seconds

Please, see attached image below

The maximum height corresponds to

191.063 ft

7 0
2 years ago
In ΔPQR, p = 220 inches, q = 890 inches and ∠R=121°. Find the length of r, to the nearest inch.
Veronika [31]

Answer:

1021

Step-by-step explanation:

delta math said it was right

6 0
1 year ago
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