The amount of gold in decigrams if 450 micrograms is needed is 4.5 × 10-³ decigrams.
<h3>How to convert micrograms to decigrams?</h3>
According to this question, 450 micrograms of a sample of gold is needed but we only have a mass balance that measures in decigrams.
This means that we are to convert the amount of gold you need to decigrams by comparing the exponents.
The conversion factor of micrograms to decigrams is as follows:
1 micrograms = 1 × 10-⁵ decigrams
This means 450 micrograms is equivalent to 450 × 1 × 10-⁵ = 4.5 × 10-³ decigrams
Therefore, the amount of gold in decigrams if 450 micrograms is needed is 4.5 × 10-³ decigrams.
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Answer:
The tension is 
Explanation:
The free body diagram of the question is shown on the first uploaded image From the question we are told that
The distance between the two poles is 
The mass tied between the two cloth line is 
The distance it sags is 
The objective of this solution is to obtain the magnitude of the tension on the ends of the clothesline
Now the sum of the forces on the y-axis is zero assuming that the whole system is at equilibrium
And this can be mathematically represented as

To obtain
we apply SOHCAHTOH Rule
So 
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Answer:
the work done by friction on the car is 524,582 J.
Explanation:
Given;
mass of the roller coaster, m = 800 kg
distance moved by the coaster, d = 225 ft = 68.58 m
final velocity of the coaster, v = 80 mi/h = 35.76 m/s
The time taken for the coaster to drop down the hill is calculated as;

The work done by friction on the car is calculated as;

Therefore, the work done by friction on the car is 524,582 J.
Answer:
Explanation:
We know that,
Neptune is 4.5×10^9 km from the sun
And given that,
Earth is 1.5×10^8km from sun
Then,
Let P be the orbital period and
Let a be the semi-major axis
Using Keplers third law
Then, the relation between the orbital period and the semi major axis is
P² ∝ a³
Then,
P² = ka³
P²/a³ = k
So,
P(earth)²/a(earth)³ = P(neptune)² / a(neptune)³
Period of earth P(earth) =1year
Semi major axis of earth is
a(earth) = 1.5×10^8km
The semi major axis of Neptune is
a (Neptune) = 4.5×10^9km
So,
P(E)²/a(E)³ = P(N)² / a(N)³
1² / (1.5×10^8)³ = P(N)² / (4.5×10^9)³
Cross multiply
P(N)² = (4.5×10^9)³ / (1.5×10^8)³
P(N)² = 27000
P(N) =√27000
P(N) = 164.32years
The period of Neptune is 164.32years