<span>The answer to what you are looking for is 3x(3x+2)</span>
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
Noah is doing a math problem, 1.39+4.45. Then, his friend Michael comes over and tells him the answer, 5.84.
Let's say the savings in your account are given by $V, the number of weeks by n and the starting balance by $x:
V = x + 200n
Now if after saving for 4 weeks you have $1700 in your account, then:
1700 = x + 200*4
1700 = x + 800
x = 900, thus your starting balance is $900
Using this information we can now write up the general equation for the savings at the end of each week:
V = 900 + 200n
