Kepler's third law states that the square of the time T required for a planet to complete one orbit around the Sun is directly proportional to the cube of the average distance d of the planet to the Sun. For the Earth assume that d = 9.3 × 10 7 mi and T = 365 days . a. Find the period of Mars, given that the distance between Mars and the Sun is 1.5 times the distance from the Earth to the Sun. Round to the nearest day. b. Find the average distance of Venus to the Sun, given that Venus revolves around the Sun in 223 days. Round to the nearest million miles.
Kepler's third law states that the square of the time T required for a planet to complete one orbit around the Sun is directly proportional to the cube of the average distance d of the planet to the Sun. For the Earth assume that d = 9.3 × 10 7 mi and T = 365 days . a. Find the period of Mars, given that the distance between Mars and the Sun is 1.5 times the distance from the Earth to the Sun. Round to the nearest day. b. Find the average distance of Venus to the Sun, given that Venus revolves around the Sun in 223 days. Round to the nearest million miles.
Solution Summary: The author explains how Kepler's third law states that the square of time required for a planet to complete one orbit around the Sun is directly proportional to the cube of the average distance.
Kepler's third law states that the square of the time T required for a planet to complete one orbit around the Sun is directly proportional to the cube of the average distance d of the planet to the Sun. For the Earth assume that
d
=
9.3
×
10
7
mi and
T
=
365
days
.
a. Find the period of Mars, given that the distance between Mars and the Sun is 1.5 times the distance from the Earth to the Sun. Round to the nearest day.
b. Find the average distance of Venus to the Sun, given that Venus revolves around the Sun in 223 days. Round to the nearest million miles.
Let f be a function whose graph consists of 5 line segments and a semicircle as shown in the figure below.
Let g(x) = √ƒƒ(t) dt .
0
3
2
-2
2
4
5
6
7
8
9
10
11
12
13
14
15
1. g(0) =
2. g(2) =
3. g(4) =
4. g(6) =
5. g'(3) =
6. g'(13)=
The expression 3 | (3+1/+1)
of the following integrals?
A
Ов
E
+
+
+ +
18
3+1+1
3++1
3++1
(A) √2×14 dx
x+1
(C) 1½-½√ √ ² ( 14 ) d x
(B) √31dx
(D) So 3+x
-dx
is a Riemann sum approximation of which
5
(E) 1½√√3dx
2x+1
2. Suppose the population of Wakanda t years after 2000 is given by the equation
f(t) = 45000(1.006). If this trend continues, in what year will the population reach 50,000
people? Show all your work, round your answer to two decimal places, and include units. (4
points)
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