Answer:
Step-by-step explanation:
This is a super simple problem. I'm going to walk through it as I do when I teach this to my students for the first time.
We are given a rectangle. We are told to find how fast the area is changing under certain conditions. That tells us that the main equation for this problem is the area formula for a rectangle which is
. If we are looking for the rate at which the rectangle's area is changing, that means that we need to find the derivative of the area implicitly. This derivative is found using the product rule because the length is being multiplied by the width:
. If our unknown is the rate at which the area is changing, , that means that everything else has to have a value (because you can only have one unknown in an equation). Here's what we're told:
The length of the rectangle is increasing at a rate of 7 cm/s, so that satisfies our ;
the width is increasing at a rate of 6 cm/s, so that satisfies our ;
and all of this is going on when the length = 12 and the width = 8. It looks like everything will have a value except for our unknown. Filling in:
and
so
Answer:
Simplified = 64.
Step-by-step explanation:
81-8 & 5 + 4 = 73-9 = 64.
Answer: it will take 36 years for the account balance to reach $1,200.
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 70
A = 1200
r = 1.5% = 1.5/100 = 0.015
n = 1 because it was compounded once in a year.
Therefore,.
1200 = 700(1 + 0.015/1)^1 × t
1200/700 = (1.015)^t
1.714 = 1.015^t
Taking log of both sides,
Log 1.714 = log 1.015^t
0.234 = tlog 1.015 = t × 0.0065
t = 0.234/0.0065
t = 36 years
Answer:
The answer is 24
Step-by-step explanation: