Answer:
<u>Recursive:</u>
![a_n=a_{(n-1)}+18\\ \\ a_1=82](https://tex.z-dn.net/?f=a_n%3Da_%7B%28n-1%29%7D%2B18%5C%5C%20%5C%5C%20a_1%3D82)
<u>Explicit:</u>
![a_n=64+18n](https://tex.z-dn.net/?f=a_n%3D64%2B18n)
Explanation:
<u>1. Sequence:</u>
![a_1=82\\ \\ a_2=82+18=100\\ \\ a_3=100+18=118\\ \\ a_4=118+18=136\\ \\ ...](https://tex.z-dn.net/?f=a_1%3D82%5C%5C%20%5C%5C%20a_2%3D82%2B18%3D100%5C%5C%20%5C%5C%20a_3%3D100%2B18%3D118%5C%5C%20%5C%5C%20a_4%3D118%2B18%3D136%5C%5C%20%5C%5C%20...)
<u>2. Recursive formula</u>
The recursive formula permits to calculate the value of the nth term in the sequence using the (n-1)th term in the sequence.
![a_n=a_{(n-1)}+18\\ \\ a_1=82](https://tex.z-dn.net/?f=a_n%3Da_%7B%28n-1%29%7D%2B18%5C%5C%20%5C%5C%20a_1%3D82)
<u>3. Explicit formula</u>
The explicit formula permits to calculate any value of a term in the sequence:
![a_n=a_1+(n-1)d\\ \\ a_n=82+(n-1)18\\ \\ a_n=82+18n-18\\ \\ a_n=64+18n](https://tex.z-dn.net/?f=a_n%3Da_1%2B%28n-1%29d%5C%5C%20%5C%5C%20a_n%3D82%2B%28n-1%2918%5C%5C%20%5C%5C%20a_n%3D82%2B18n-18%5C%5C%20%5C%5C%20a_n%3D64%2B18n)
Answer:
448 cubes
Step-by-step explanation:
Volume of cubes fitted in the box will be equal to the cumulative volume of the cubes.
Since, volume of a cube = (Side)³
Side of the cube =
inch
Therefore, volume of the cube =
inches
Volume of the storage box = 56 cubic inches
Since, number of cubes fitted in the storage box = ![\frac{\text{Volume of the storage box}}{\text{Volume of one cube}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BVolume%20of%20the%20storage%20box%7D%7D%7B%5Ctext%7BVolume%20of%20one%20cube%7D%7D)
= ![\frac{56}{\frac{1}{8}}](https://tex.z-dn.net/?f=%5Cfrac%7B56%7D%7B%5Cfrac%7B1%7D%7B8%7D%7D)
= 56 × 8
= 448 cubes
Therefore, number of cubes fitted in the storage box = 448
The minimum distance will be along a perpendicular line to the river that passes through the point (7,5)
4x+3y=12
3y=-4x+12
y=-4x/3+12/3
So a line perpendicular to the bank will be:
y=3x/4+b, and we need it to pass through (7,5) so
5=3(7)/4+b
5=21/4+b
20/4-21/4=b
-1/4=b so the perpendicular line is:
y=3x/4-1/4
So now we want to know the point where this perpendicular line meets with the river bank. When it does y=y so we can say:
(3x-1)/4=(-4x+12)/3 cross multiply
3(3x-1)=4(-4x+12)
9x-3=-16x+48
25x=51
x=51/25
x=2.04
y=(3x-1)/4
y=(3*2.04-1)/4
y=1.28
So now that we know the point on the river that is closest to Avery we can calculate his distance from that point...
d^2=(x2-x1)^2+(y2-y1)^2
d^2=(7-2.04)^2+(5-1.28)^2
d^2=38.44
d=√38.44
d=6.2 units
Since he can run at 10 uph...
t=d/v
t=6.2/10
t=0.62 hours (37 min 12 sec)
So it will take him 0.62 hours or 37 minutes and 12 seconds for him to reach the river.
Question is Incomplete;Complete question is given below;
Jerry sold 7/20 of the total number of tickets that were sold for the spring band concert. What percent of the total number of tickets did jerry sell.
Answer:
Jerry sold 35 % of the total tickets.
Step-by-step explanation:
Given:
Jerry sold tickets =
of total number of tickets
We need to find the percent of the total number of tickets Jerry sold.
Solution:
to find the percent of the total number of tickets Jerry sold we need to multiply the fraction by 100 we get;
framing in equation form we get;
Percent of the total number of tickets Jerry sold = ![\frac{7}{20}\times100 = 35\%](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B20%7D%5Ctimes100%20%3D%2035%5C%25)
Hence Jerry sold 35 % of the total tickets.