The number of cars that sold on the third week is (P3=26)
The number of cars that sold on the first week is (P4=33)
<u>Step-by-step explanation:</u>
<u>Given:</u>
- The number of cars that sold on the first week is (P0=7)
- The number of cars that sold on the second week is (P0=12)
We have to find the number of cars being sold on the upcoming week
From the data given above, frame the equation
Pn = Pn −1+7 ( 12-5=7 it denotes the cars sold in the first and the second week)
Pn=5+7n (cars in the first week and the cars sold in the second week into "n" n is used to find the cars sold in the upcoming weeks)
(If n=3)
Pn=5+7(3)
Pn=26
The number of cars that sold on the third week is (P3=26)
(If n=4)
Pn=5+7(4)
Pn=33
The number of cars that sold on the first week is (P4=33)
Part I
We have the size of the sheet of cardboard and we'll use the variable "x" to represent the length of the cuts. For any given cut, the available distance is reduced by twice the length of the cut. So we can create the following equations for length, width, and height.
width: w = 12 - 2x
length: l = 18 - 2x
height: h = x
Part II
v = l * w * h
v = (18 - 2x)(12 - 2x)x
v = (216 - 36x - 24x + 4x^2)x
v = (216 - 60x + 4x^2)x
v = 216x - 60x^2 + 4x^3
v = 4x^3 - 60x^2 + 216x
Part III
The length of the cut has to be greater than 0 and less than half the length of the smallest dimension of the cardboard (after all, there has to be something left over after cutting out the corners). So 0 < x < 6
Let's try to figure out an x that gives a volume of 224 in^3. Since this is high school math, it's unlikely that you've been taught how to handle cubic equations, so let's instead look at integer values of x. If we use a value of 1, we get a volume of:
v = 4x^3 - 60x^2 + 216x
v = 4*1^3 - 60*1^2 + 216*1
v = 4*1 - 60*1 + 216
v = 4 - 60 + 216
v = 160
Too small, so let's try 2.
v = 4x^3 - 60x^2 + 216x
v = 4*2^3 - 60*2^2 + 216*2
v = 4*8 - 60*4 + 216*2
v = 32 - 240 + 432
v = 224
And that's the desired volume.
So let's choose a value of x=2.
Reason?
It meets the inequality of 0 < x < 6 and it also gives the desired volume of 224 cubic inches.
Answer:
geometric
arithmetic
arithmetic
Step-by-step explanation:
1.
4/9,4/3,4,12,36
Multiply each term by 3 to get the next term. There is a common ratio between terms, so it geometric.
2.
0,1,2,3,4,5,6
Add 1 to each term to get the next term. Since there is a common difference between terms, it is an arithmetic sequence.
3.
-10,-6,-2,2,6,10
Add 4 to each term to get the next term. Since there is a common difference between terms, it is an arithmetic sequence.
Answer:
0
Step-by-step explanation:
21(3) +2(7) - 11(7) because the absolute value of -11 is 11
63+14-77
=0
75+ 15x ≥ 140
⇒ 15x ≥ 140-75
⇒ 15x ≥ 65
⇒ x ≥ 65/15
⇒ x ≥ 13/3
⇒ x ≥ 4 1/3
Final answer: x ≥ 4 1/3~
