Given the equation p2 = a3, what is the orbital period, in days, for the planet venus? (venus is located 0.72 au from the sun?)

Mathematics

2 answers:

Gelneren [198K]4 years ago

5 0

Hello,
P=0.72^(3/2)=0.610940...years=223.1398...days

pantera1 [17]4 years ago

4 0

Answer: 223 days

Step-by-step explanation:

From Kepler's third law, the orbital period of planet around the sun is related with the semi-major axis of the orbit as:

p² = a³

where p is the orbital period in years and a is the semi-major axis/ distance to the star in AU.

It is given for Venus, a = 0.72 AU, then

p = √(0.72 AU)³ = 0.61 years

1 year = 365 days 222.9 days ≈ 223 days

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Tom bought 4 cans of pineapple and 11 bottle of mayonnaise. The mayonnaise cost $2.89. He paid with a ten-dollar bill ($10 ) and

eimsori [14]

Answer:

a. $44(p) + 2.89 = (10 - 0.35)$

b. $0.15 per can of pineapple

Step-by-step explanation:

a. 1. Here we need to make a variable ( $p$ ) that represents the unknown cost of one single can of pineapple, then multiply $p$ by the total number of cans, which we are told is 44.

2. The second term is the cost of the 11 bottes of mayonnaise, which we know to be $2.89. We add this to the first term.

3. We know that the total of these two numbers should be equal to the total amount of money that Tom spent. This number will be the amount he gave the cashier ($10) MINUS the change the cashier gave back to him ($0.35)

4. Now that we have formed an equation, we just need to solve for $p$ .

$44(p) + 2.89 = (10 - 0.35)$ Equation

$44(p) = 9.65 - 2.89$ Simplify parentheses on the right and subtract 2.89 from both sides.