Answer:
It'll take approximately 9.1 minutes
Step-by-step explanation:
The decay of this element can be modeled by the following expression:
m(t) = 540*(1 - 0.179)^t
Where m is the mass of the element in a given minute t. This expression comes from a compounded interest formula, with negative rate, since they will work in the same manner. Therefore to find how long until it reaches 90 g, we need to make m = 90 and solve for t.
90 = 540*(0.821)^t
(0.821)^t = 90 / 540
(0.821)^t = 1/6
ln(0.821^t) = ln(1/6)
t*ln(0.821) = ln(1) - ln(6)
t*ln(0.821) = - ln(6)
t = -ln(6)/ln(0.821) = 9.08452
It'll take approximately 9.1 minutes
Answer:
27 inches
Step-by-step explanation:
We are using the Pythagorean theorem
a^2 +b^2 = c^2 where c is the hypotenuse
We are given the diagonal, which is the hypotenuse and a leg
36^2 + b^2 = 45^2
Subtract 36^2 from each side
36^2 + b^2 - 36^2 = 45^2 - 36^2
b^2 = 45^2 - 36^2
b^2 =2025-1296
b^2 =729
Take the square root of each side
sqrt(b^2) = sqrt(729)
b =27
Answer: $183.71
<u>Step-by-step explanation:</u>
Original amount is $5,175.00
1st year: Increase of 9%
→ $5175(1 + 0.09)
= $5175(1.09)
= $5640.75
2nd year: Decrease of 5%
→ $5640.75(1 - 0.05)
= $5640.75(0.95)
= $5358.71
Gain: 2nd year - Original
→ $5358.71 - $5175.00
= $183.71
V=2 if you need a more in depth explanation let me know
