A forest fire leaves behind an area of grass burned in an expanding circular pattern. If the
Question:
A forest fire leaves behind an area of grass burned in an expanding circular pattern. If the radius of the circle of burning grass is increasing with time according to the formula r(t) = 2t + 1, express the area burned as a function of time, t (minutes).
Step by Step Answer:
rt 2t 1 for c...View the full answer
Related Video
The area of a circle is given by the formula: A = ?r^2 Where A is the area, ? is a mathematical constant (approximately 3.14), and r is the radius of the circle. The radius is the distance from the center of the circle to the edge. So for example, if the radius of a circle is 5 units, the area would be: A = ?(5^2) = ?(25) = 78.5 square units Here three friends went out to a restaurant and decided to have pizza for lunch. While they were waiting for their order, one of them stepped out to take a call but promised to return in two minutes. The waiter came and presented them with the menu, and they decided to order two 10-inch pepperoni pizzas. The waiter took their order and left. Just then, the third friend returned and asked what they had ordered. They explained that they had ordered two small pepperoni pizzas as they were only three of them and it would be enough for them. However, the third friend suggested that for the same price, they could get a large pizza that would be much bigger than the two small ones. He asked the waiter for a pen and paper and proceeded to calculate the area of the two small pizzas and compared it to the area of one large pizza. The friends were amazed at how the circle measurements worked and decided to change their order from two small pizzas to one large pizza.
Students also viewed these Mathematics questions
-
Suppose you are traveling on business to a foreign country for the first time. You do not have a bus schedule or a watch with you. However, you have been told that buses stop in front of your hotel...
-
The current in a wire varies with time according to the relationship I = 55 A - (0.65 A/S2)t2. (a) How many coulombs of charge pass a cross section of the wire in the time interval between t = 0 and...
-
If the radius of a circle is doubled, by what factor will the area change? 2r
-
The functions in Exercises 1128 are all one-to-one. For each function, a. Find an equation for f -1 (x), the inverse function. b. Verify that your equation is correct by showing that f( f -1 (x)) = x...
-
Which of the following are true? If false, explain briefly. a) A very high P-value is strong evidence that the null hypothesis is false. b) A very low P-value proves that the null hypothesis is...
-
Eximco Corporation (based in Champaign, Illinois) has a number of transactions with companies in the country of Mongagua, where the currency is the mong. On November 30, 2011, Eximco sold equipment...
-
Using the same sort of reasoning as in the derivation of the formula for the hypergeometric distribution, we can derive a formula which is analogous to the multi-nomial distribution but applies to...
-
Assume a corporation has earnings before depreciation and taxes of $100,000, depreciation of $40,000, and that it has a 40 percent tax bracket. a. Compute its cash flow using the following format....
-
You are evaluating a project with the following cash flows: initial investment is $ - 1 1 , and the expected cash flows for years 1 - 3 are $ 6 , $ 1 4 and $ 1 1 ( all cash flows are in millions of...
-
The Northshire Hospital Trust operates two types of specialist X-ray scanning machines, XR1 and XR50. Details for the next period are estimated as follows: A brain scan is normally carried out on...
-
A rain drop hitting a lake makes a circular ripple. If the radius, in inches, grows as a function of time in minutes according to r(t) = 25 t + 2, find the area of the ripple as a function of time....
-
Use the function you found in the previous exercise to find the total area burned after 5 minutes.
-
Think of a situation at work or school where somebody clearly used politics in a negative way. What could have been done to prevent this from happening?
-
You release three balls simultaneously from the same height above the floor. The balls all carry the same quantity of surplus positive charge, but they have different masses: \(1 \mathrm{~kg}, 2...
-
What orientation of an electric dipole in a uniform electric field has the greatest electric potential energy? What orientation has the least? (Let the system comprise both the electric dipole and...
-
What is the magnitude of the electric field \(200 \mathrm{~mm}\) away from a particle carrying \(3.0 \mu \mathrm{C}\) of charge?
-
Points \(A\) and \(B\) are on the same electric field line. If the potential difference between \(A\) and \(B\) is positive, is the field directed from \(A\) to \(B\) or from \(B\) to \(A\) ?
-
A proton moves from point \(A\) to point \(B\) under the influence of an electrostatic field in which the potential difference between A and B is negative. (a) If your system includes both the proton...
-
Show that when 0 4z
-
On April 29, 2015, Auk Corporation acquires 100% of the outstanding stock of Amazon Corporation (E & P of $750,000) for $1.2 million. Amazon has assets with a fair market value of $1.4 million (basis...
-
In problem, graph each polynomial function. f(x) = x 4 + x 2 - 2
-
In problem, analyze each polynomial function by following Steps 1 through 6. f(x) = 4x - x 3
-
In problem, graph each polynomial function. f(x) = 2x 3 + x 2 + 2x + 1
-
6. Consider the following algorithm. Give a function with one term and coefficient 1 g(n) such that the running time of this algorithm is (g(n)), and briefly explain. public static int funkySum...
-
In the diagram, let U = {all objects}, B = {all students who live in Hartford}, = {students majoring in math}, and R = {students taking a course with Professor Antonio} B M 1 2 3 5 + 6 7 8 R In which...
-
Risk Identification: Disruption Disruption Assessment: Assessment: Risk Risk Probability Risk 1: Cyberwarfare 1 Consequence 5 Risk 2: Natural 1 5 Diaster Risk 3: Supplier 2 2 closure Risk 4:...
Study smarter with the SolutionInn App