30 is the answer to your question
Answer:
93
Step-by-step explanation:
First differences increase by 4 each time. The given numbers are a quadratic sequence that can be described by 2n² -2n +9. The 7th term would be 93.
_____
First differences are ...
13-9 = 4, 21-13 = 8, 33-21 = 12, 49-33 = 16, 69-49 = 20
Second differences are ...
8-4 = 4, 12-8 = 4, 16-12 = 4, 20-16 = 4
When second differences are constant, the sequence can be represented by a second-degree polynomial function. The leading coefficient is half the value of the second differences.
Answer:
The speed of a wave depends on the characteristics of the medium. For example, in the case of a guitar, the strings vibrate to produce the sound. The speed of the waves on the strings, and the wavelength, determine the frequency of the sound produced. The strings on a guitar have different thickness but may be made of similar material. They have different linear densities, where the linear density is defined as the mass per length,
μ
=
mass of string
length of string
=
m
l
.
In this chapter, we consider only string with a constant linear density. If the linear density is constant, then the mass
(
Δ
m
)
of a small length of string
(
Δ
x
)
is
Δ
m
=
μ
Δ
x
.
For example, if the string has a length of 2.00 m and a mass of 0.06 kg, then the linear density is
μ
=
0.06
kg
2.00
m
=
0.03
kg
m
.
If a 1.00-mm section is cut from the string, the mass of the 1.00-mm length is
Δ
m
=
μ
Δ
x
=
(
0.03
kg
m
)
0.001
m
=
3.00
×
10
−
5
kg
.
The guitar also has a method to change the tension of the strings. The tension of the strings is adjusted by turning spindles, called the tuning pegs, around which the strings are wrapped. For the guitar, the linear density of the string and the tension in the string determine the speed of the waves in the string and the frequency of the sound produced is proportional to the wave speed.
Answer:
Matthew travels 0.0161 meters per second.
Step-by-step explanation:
Given that Matthew travels 42/50 meters In 26/30 minutes, to find the speed of Mathew in meters per second the following calculation must be performed:
42/50 = 0.84
26/30 = 0.86
0.86 x 60 = 52
0.84 meters in 52 seconds
0.84 / 52 = 0.01615
Therefore, Matthew travels 0.0161 meters per second.
-3.5(2 - 3n) - 2.5n
= -7 + 10.5n - 2.5n
= -7 + 8n