Lynette needs to make 2 birthday cards. Ellen needs to make 3 times as many. If y represents the number of cards Lynette need to
1 answer:
You might be interested in
Answer:
105th term of given series is
Step-by-step explanation:
Given series is
As we can see,
Also,
hence, we can say given series is in arithmetic progression,
with common difference,
As given in question the nth term in A.P is given by
since we have to find the 105th term, so we can write
Hence, the 105th term of given series of A.P is .
Answer:
Recursive: f(1) = 1; f(n) = f(n-1)/3
Equation: f(x) = 5/3·(1/3)^(x-1)
Step-by-step explanation:
You know this is an exponential function because sequential lines in the table have a common ratio of f(x) values:
f(2)/f(1) = (5/9)/(5/3) = 3/9 = 1/3
f(3)/f(2) = (5/27)/(5/9) = 9/27 = 1/3
and it continues like that.
Besides telling you the function is exponential, it also tells you that each term is 1/3 of the previous term.
<h3>Recursive formula</h3>The value of f(1) is read from the table. For x = 1, that value is ...
f(1) = 5/3
As we noticed above, each term is 1/3 the previous term, so the recursive relation is ...
f(n) = (1/3)·f(n-1)
<h3>Equation</h3>The general form of the equation for a geometric (exponential) relation is ...
f(x) = f(1)·r^(x-1) . . . . . . where f(1) is the first term, and r is the common ratio
For this function, we have f(1) = 5/3 and r = 1/3, so the equation is ...
f(x) = 5/3·(1/3)^(x-1)
__
<em>Additional comment</em>
When given values of x that count from 1, we often express the equation in terms of (x-1). That equation can be simplified so the exponent is x.
f(x) = 5·(1/3)^x
Let's assume the frequency of sound be f and wave length is w.
Given that, the frequency of sound varies inversely as the wavelength.
So, we can set up an equation as following:
f*w = k Where k= constant of variation.
Other information is, the frequency of a musical note is 276 cycles per second when the wavelength is 1.2m.
So, next step is to plug in f = 276 and w = 1.2 in the above equation to get the value of k.
276 * 1.2 = k
So, k = 331.2
Next step is to plug in k = 331.2 in the above equation. So,
f * w = 331.2
Now we need to find the wave length : w when frequency : f = 600.
Therefore,
600 * w = 331.2
So, w = 0.552
Hence, the wave length is 0.552 m.
Hope this helps you!.