To approximate the distance from the Earth to stars relatively close by. astronomers often use the method of parallax. Parallax is the apparent displacement of an object caused by a change in the observer's point of view. As the Earth orbits the Sun, a nearby star will appear to move against the more distant background stars. Astronomers measure a star's position at times exactly 6 months apart when the Earth is at opposite points in its orbit around the Sun. The Sun, Earth, and star form the vertices of a right triangle with ∠ P S E = 90 ° . The length of is the distance between the Earth and Sun. approximately 92 , 900 , 000 mi . The parallax angle (or simply parallax) is denoted by p . Use this information for Exercises 31-32. a. Find the distance between the Earth and Barnard's Star if the parallax angle is 0.547 arcseconds. Round to the nearest hundred billion miles. b. Write the distance in part (a) in light-years. Round to 1 decimal place. (Hint 1 light-year is the distance that light travels in 1 yr and is approximately 5.878 × 10 12 mi .)
To approximate the distance from the Earth to stars relatively close by. astronomers often use the method of parallax. Parallax is the apparent displacement of an object caused by a change in the observer's point of view. As the Earth orbits the Sun, a nearby star will appear to move against the more distant background stars. Astronomers measure a star's position at times exactly 6 months apart when the Earth is at opposite points in its orbit around the Sun. The Sun, Earth, and star form the vertices of a right triangle with ∠ P S E = 90 ° . The length of is the distance between the Earth and Sun. approximately 92 , 900 , 000 mi . The parallax angle (or simply parallax) is denoted by p . Use this information for Exercises 31-32. a. Find the distance between the Earth and Barnard's Star if the parallax angle is 0.547 arcseconds. Round to the nearest hundred billion miles. b. Write the distance in part (a) in light-years. Round to 1 decimal place. (Hint 1 light-year is the distance that light travels in 1 yr and is approximately 5.878 × 10 12 mi .)
Solution Summary: The author calculates the distance between the earth and Barnard's star, if the parallax angle is 0.547arcseconds.
To approximate the distance from the Earth to stars relatively close by. astronomers often use the method of parallax. Parallax is the apparent displacement of an object caused by a change in the observer's point of view. As the Earth orbits the Sun, a nearby star will appear to move against the more distant background stars. Astronomers measure a star's position at times exactly
6
months apart when the Earth is at opposite points in its orbit around the Sun. The Sun, Earth, and star form the vertices of a right triangle with
∠
P
S
E
=
90
°
. The length of is the distance between the Earth and Sun. approximately
92
,
900
,
000
mi
. The parallax angle (or simply parallax) is denoted by
p
. Use this information for Exercises 31-32.
a. Find the distance between the Earth and Barnard's Star if the parallax angle is
0.547
arcseconds. Round to the nearest hundred billion miles.
b. Write the distance in part (a) in light-years. Round to
1
decimal place. (Hint
1
light-year is the distance that light travels in
1
yr
and is approximately
5.878
×
10
12
mi
.)
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and
use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three
investment?
STEP 1: The formula for compound interest is
A =
nt
= P(1 + − − ) n²,
where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to
A = Pert
Find r and n for each model, and use these values to write A in terms of t for each case.
Annual Model
r=0.10
A = Y(t) = 1150 (1.10)*
n = 1
Quarterly Model
r = 0.10
n = 4
A = Q(t) = 1150(1.025) 4t
Continuous Model
r=0.10
A = C(t) =…
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