Which expression best estimates 6 and three-fourths divided by 1 and two-thirds?
1 answer:
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Answer:
Approximately 22.97 years
Step-by-step explanation:
Use the equation for continuously compounded interest, which uses the exponential base "e":
Where P is the principal (initial amount of the deposit - unknown in our case)
A is the accrued value (value accumulated after interest is compounded), in our case it is not a given value but we know that it triples the original deposit (principal) so we write it as: 3 P (three times the principal)
k is the interest rate : 5% which translates into 0.05
and t is the time in the savings account to triple its value (what we need to find)
The formula becomes:
To solve for "t" we divide both sides of the equation by P (notice it cancels P everywhere), and then to solve for the exponent "t" we use the natural logarithm function:
Answer:
The man will take 64 seconds to reach to the south shore of the frozen pond.
Step-by-step explanation:
Given:
Weight of the man = 748 N Mass of the man, =
=
kg
Radius of the pond = 4 m
Mass of the textbook = 1.2 kg
Velocity at which the textbook is thrown = 4 ms^1
We have to find the velocity of the man after the throw.
Let the velocity is .
Now using law of conservation of momentum we can find the value.
Considering
And initial velocity of both the man and book i.e
So,
⇒
⇒ Plugging the values.
⇒
⇒
⇒ ms^-1
Here the negative velocity is meant for opposite direction of the throw.
Numerically we will write,
With this velocity the man will move towards south.
We have to calculate the time taken by the man to move to its south shore.
And we know
Let the time taken be and
and
then,
Then
⇒
⇒ Plugging the values.
⇒
⇒ sec
The man will take 64 seconds to reach to the south shore of the frozen pond (circular).