A circular oil spill continues to increase in size. The radius of the oil spill, in miles, is given by the function r(t) = 0.5 + 2t, where t is the time in hours. The area of the circular region is given by the function A(r) = πr2, where r is the radius of the circle at time t.Explain how to write a composite function to find the area of the region at time t.
Answers
Answer:
The area at time t is given by
Step-by-step explanation:
We know the radius of the oil spill as a function of time, and we know the area
as a function of radius, and we want the area at time t. In other words we are looking for area as a function of time
We find by putting
into
as a substitute to r:
Which is our answer.
Final answer:
To find the composite function for the area of the oil spill over time, replace 'r' in A(r) = πr2 with the function r(t). The function becomes A(t) = π(0.5 + 2t)2.
Explanation:
In order to find the function that represents the area of the oil spill over time, we need to write a composite function. This means we plug the function r(t) into A(r). Since r(t) = 0.5 + 2t, you can replace every instance of 'r' in A(r) = πr2 with (0.5 + 2t) to get the area as a function of time 't'. So, the composite function becomes A(t) = π(0.5 + 2t)2. Now we have a composite function that represents the area of the oil spill, denoted by A(t), as a function of time. The function is: A(t) = π(0.5 + 2t)2.
Learn more about Composite Functions here:
#SPJ12
Related Questions
Fourteen less than five times number is three times a number. Define a variable, write an equation, and solve to find the number. PLEASE SOLVE! I NEED IT 2 MIN FROM NOW!
What is The answer when a subtraction problem is performed
You are planning to make and sell three different sizes if cylindrical candles. You buy 1 cubic foot of candle wax for $20 to make 8 candles of each size.a.)design the candles. What are the dimensions of each size of candle? b) You want to make a profit of $100. Decide on a price for each size of candle. c) Did you set the prices so that they are proportional to the volume of each size of candle? Why or why not?
The diameter of a bysicle tires is 2.5 ft. How many revolutions of the tires does it take to travel 1 mile?Use 5280 ft=1 mile.Round to the nearest tenth ....plss help me...tnx
B.30
C.80
D.480
need the answer asap
Answers
Answer:
B
Step-by-step explanation:
Putting x=5 in the above eq
y=2(5)^2-4(5)
y=2(25)-20
y=50-20
y=30
Answer:i literally have no clue humy
Step-by-step explanation:
this is bull i got to get the f out of here
Answers
a² + b² = c²
a is the long leg of the triangle
b is the short leg of the triangle
c is the hypotenuse
side lengths ; 3 inches, 4 inches, 5 inches of a right triangle.
a = 4 inches
b = 3 inches
c = 5 inches
4² + 3² = 5²
16 + 9 = 25
25 = 25
Possible Answer:
The base of a right triangle is shorter then the hypotenuse due to the diagnal of the line being the longest line we can conclude that 5 is the Hypotenuse (C). That would mean that the longest line thats not the hypotenuse(4) is B and the shortest line(3) is A.
Possible Answer Two:
Since the hypotenuse is the longest line in a right triangle we can conclude its length is 5 and the base is 4 and the side length is 3.
Answers
Answer:
Step-by-step explanation:
πd = 25 inches
= 8.0 inches
Answer:
Step-by-step explanation:
Circumference= 25 inches
Circumference of the circular stone=
As,
Putting the values in the formula:
As,
Answers
Answer:
The best could describe Anita's race from minute 3 to minute 5, She was standing, not moving, she could have been in an accident.
Step-by-step explanation:
See the attached figure.
As shown in the figure, we can note that the distance from minute 3 to minute 5 is constant which is equal to the distance at minute 3.
So, the average distance from minute 3 to minute 5 will be zero and hence the speed of Anita will be zero
So, From minute 3 to minute 5, She was standing, not moving.
Note: speed of Anita from minute 3 to minute 5
= ( distance difference) / (time difference) = zero / (5-3) = 0/2 = 0
Final answer:
To describe the race from minute 3 to 5, analyze the graph paying attention to the x and y axis and the slope of the curve. A straight line suggests constant speed, an upward line implies acceleration, and a downward line denotes deceleration.
Explanation:
To describe Anita's race from minute 3 to minute 5, we need to analyze the provided graph which depicts the distance from the start as a function of time for both racers. In this case, we do not have the actual graph so it's important that when you are presented with a graph you pay attention to the
x and y axis
, which in this instance are time and distance. It's vital to also look at the slope of the curve during those minutes 3 to 5 for Anita. If it's a straight line, it means Anita was biking at a
constant speed
. If the line is going upward, Anita was accelerating, and if the line is going downward, she was decelerating. Without the graph itself, it's hard to provide a definitive answer. But the basic method of reading the graph will help you understand the function of time and distance in the context of a race.
Learn more about Analyzing Graphs
Answers
First you add 9k to both sides
k/3 + 4 -2k = -9k
+9k +9k
k/3 + 4 + 7k = 0
Now subtract 4 from both sides
k/3 + 4 + 7k = 0
-4 -4
k/3 + 7k = -4
Now multiply 3 by both sides
k/3 + 7k = -4
x3 x3 x3
k +21k = -12
Now add k + 21k
22k = -12
Now divide both sides by 22
22k = -12
----- -----
22 22
k = -6/11
Answers
2000 * 6 = 12000
There are 12,000 lbs in 6 tons.
Hope that helped! =)
Well, first things first!
1 ton=2,000 pounds
So, you need 6 tons, right?
Now, all you got to do is simply do 2,000*6
Last but not least, you will get 12,000 pounds.
I hope this helps:)
(Please Pick Me As Brainliest!)
THANK YOU SO MUCH!