Answer:
M(t) = 741·(1/2)^(t/5730)
Step-by-step explanation:
One way to write an exponential function is this:
value at time t = (initial value) · (multiplier over period)^(t/period)
Here, the initial value is given as 741 grams, and the time period is 5730 years. The multiplier over that period is 1/2, since half of the quantity remains after that time. The problem statement tells us that "value at time t" is M(t), so we have ...
M(t) = 741·(1/2)^(t/5730) . . . . . t in years; M(t) in grams
Answer:
60
Step-by-step explanation:
List factors of each:
60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
45: 1, 3, 5, 9, 15, 45
The largest common value is 15
The greatest possible length of each is 15 cm
Answer: 15 cm.
Hello!
First, we must calculate the area of the base by using the formula, which is 3.14 × r × r × h
(I cannot access symbols on my device right now, otherwise I would've used the pi symbol and squared. Sorry, dude/dudette!)
Substitue:
A = 3.14 × 9 × 9
A = 28.26 × 9
A = 254.34 cm squared
Next, we must multiply the area of the base by the height to find the volume:
V = 9 × 254.34 squared
V = 2,289.06
Since there is no option for 2,289.06,the volume for the figure above is D. None of the above.
Answer: The central angle measures 135 degrees
Step-by-step explanation: We have been given an arc with length 9pi/2 feet and a radius of 6 feet. The arc is shown in the attached diagram (please see attachment). The central angle subtended by this arc is at point O and has been labeled angle X.
So if the diagram shows arc AB with length 9pi/2 and radius AO with length 6, we can use the formula to compute “Length of an arc” to arrive at the missing angle.
Length of an arc = X/360 x 2pi x radius
Substituting for the known values, our formula can now be re-written as
9pi/2 = X/360 x 2pi x6
By cross multiplication we now have
9pi/2pi x 6 = 2X/360
We simplify as much as possible by dividing all like terms, hence pi divides pi on the left side of the equation. Also 2 divides 360 on the right side of the equation.We now arrive at,
9/12 = X/180
Simplify even further and we have
3/4 = X/180
By cross multiplication we now have
(3 x 180)/4 = X
540/4 = X
135 = X
Therefore the central angle that intercepts the arc measures 135 degrees.