HELP ME PLEASE !!!!!!!!
2 answers:
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Answer:
After 20 months
Step-by-step explanation:
This is a compound growth problem which has the formula:
Where
F is future value
P is present amount
r is the rate of growth
t is the time (in months)
Future amount is $65, what he needs at-least
P is the initial amount, that is $10
r is the rate of growth, which is 10% or 10/100 = 0.1
t is time in months, what we need to find
Substituting and solving we get:
<u>He would need 19.64 months to save up at-least 65. So, that means, he would need 20 months</u>
Answer:
Step-by-step explanation:
This is a related rates problem from calculus using implicit differentiation. The main equation is going to be Pythagorean's Theorem and then the derivative of that. Pythagorean's Theorem is
where c is the hypotenuse and is a constant. Therefore, the derivative of this with respect to time, and using implicit differentiation is
and dividing everything by 2 to simplify a bit:
. Upon analyzing that equation, it looks like we need values for x, y,
, and
. And here's what we were given:
and
In the greater realm of things, that's nothing at all.
BUT we can use the right triangle and the angle we were given to find both x and y. The problem we are looking to solve is to
Find at the instant that
= .5.
Solving for x and y:
and
6tan45 = x ( and since this is a 45-45-90 triangle, y = x):
so
and now we can fill in our derivative. Remember the derivative was found to be
so
and
and
and multiplying by the reciprocal of the left gives us:
so