The prefix of a unit could give you a hint on its extent with respect to the base unit. In this case, the base unit is money in terms of dollars. When you say kilodollars, that would be 1,000 times as large as a dollar. Hence,
33,200 dollars * 1 kilodollar/ 1,000 dollars = 33.2 kilodollars
When you say megadollars, that would be a million times as large as a dollar. Hence,
33,200 dollars * 1 megadollar/1,000,000 dollars = 0.0332 megadollars
Answer:
(c) The planet must have a mass about the same as the mass of Jupiter,
(d) The planet must be closer to the star than Earth is to the Sun.
Explanation:
Astrometry is the ideal method to detect high-mass planets that are close to their star. That is because the gravitational effect that it will have the planet over its host star will be greater. This effect can be seen as a wobble in the star as a consequence of how they orbit a common center of mass¹. The center of mass will be closer to the most massive object, So, in the case of an extrasolar planet with masses like Jupiter (Jovian), this point will be a little bit farther from the star, making the wobble more notable than in a system with a low-mass planet.
Key terms:
Astrometry: study of the position of the stars over time in the sky.
¹Center of mass: a geometrical point in which the mass from a whole system is summed.
Answer:
θ = 225 rad
Explanation:
given data
angle = 25 rad
to find out
angular velocity after 3t?
solution
let angular acceleration α in t
θ = ω × t + 0.5 × α × t² ........................1
here ω = 0 (initial velocity )
so put this value here
25 = 0 + 0.5 × α × t² ..........................2
α = 25 ÷ (0.5 t²)
α = 50 ÷ t² .........................3
now here we take in 3t
θ = ω × 3t + 0.5 × α × (3t)²
for ω = 0
θ = 0 + 0.5 × α × 9t²
now put value in eq 2
so
θ = (0.5) × (50 ÷ t²) × (3t)²
θ = 25 × 9
θ = 225 rad
Let's convert the distance in meters first:
The sound wave travels at speed
So we can use the basic relationship between space, time and velocity to calculate the time it takes for the sound to reach our ears:
460 meters per second, or about 1,000miles per hour.
