Mathematics, 21.11.2020 05:40 anthony983

The area of a circular wave expands across a still pond such that its radius increases by 14 cm each second. Write a formula for the area A of the circle as a function of time t since the wave begins: A=

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Answer from: eriks7779

We want to get the area function given that we know how the radius increases with time.

The function is:

A(t) = (615.44 cm^2)*t^2

Here we know that the radius of a circular wave increases by 14cm each second.

Then we can write the radius as a function of time as:

r(t) = 14cm*t

where t is the time, in seconds, since the wave begins.

Now, remember that the area of a circle of radius r is given by:

A = pi*r^2

where pi = 3.14

Replacing r by the radius function, we get:

A(t) = 3.14*(14cm*t)^2 = (615.44 cm^2)*t^2

This is the area function we wanted to get.

if you want to learn more, you can read:

link

Answer from: lakinbacon4

A = π(14t)²

Step-by-step explanation:

The radius is increasing at the rate of 14 cm per second.

We need to find the formula for the area A of the circle as the function of time t.

Initial area of the circle,

A = πr², where r is the radius of the circle

Area as a function of t will be :

A = π(14t)²

Here, 14t is the radius of the wave.

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

Answer from: Quest

steve should create a type of business report called a business plan. the correct option among the options that are already given in the question is the last or the fourth option. this business report created by steve will actually influence the investors about investing their money in steve's business. this business report will have all the details about the business, the amount of investment required and the amount of expected profit.