Answer:
Sequence: 13, 20, 27
Rule: Tn = 7n + 6
Step-by-step explanation:
The 3 other numbers that can form an arithmetic progression is 13, 20, 27...
The nth term of an arithmetic progression is expressed as;
Tn = a + (n-1)d
a is the first term = 13
n is the number of terms
d is the common difference = 20 - 13 = 27 - 20
d = 7
Substitute
Tn = 13 + (n-1)(7)
Tn = 13 + 7n - 7
Tn = 7n+13-7
Tn = 7n + 6
This gives the required rule
Answer:
w =< 70
(width is less or equal to 70 inches)
Step-by-step explanation:
Let l = length, w = width, h = height
Restrictions given in this question:
'sum of perimeter of the base and the height cannot exceed 130 inches'
perimeter of the base is 2 width and 2 length of the box
perimeter = 2w + 2l
Therefore, inequality involves here is
2w + 2l + h =< 130
(Note that =< here means less or equal)
Then a new condition given with
height, h = 60 in
and length is 2.5 times the width
l = 2.5w
Substitute this new condition into the equation will give us the following:
2w + 2(2.5w) + 60 =< 130
2w + 5w + 60 =< 130
7w + 60 =< 130
7w =< 130-60
7w =< 70
w =< 10
The y intercept is where the line hits the verticals line of the graph. Hope this helps!
Answer:

General Formulas and Concepts:
<u>Calculus</u>
Limits
Limit Rule [Variable Direct Substitution]: 
Limit Rule [Variable Direct Substitution Exponential]: 
Limit Property [Multiplied Constant]: 
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>

<u>Step 2: Solve</u>
- Rewrite [Limit Property - Multiplied Constant]:
![\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4} \lim_{x \to 0} [f(x)]^4](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B1%7D%7B4%7D%5Bf%28x%29%5D%5E4%20%3D%20%5Cfrac%7B1%7D%7B4%7D%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Bf%28x%29%5D%5E4)
- Evaluate limit [Limit Rule - Variable Direct Substitution Exponential]:
![\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4}(4^4)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B1%7D%7B4%7D%5Bf%28x%29%5D%5E4%20%3D%20%5Cfrac%7B1%7D%7B4%7D%284%5E4%29)
- Simplify:
![\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = 64](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B1%7D%7B4%7D%5Bf%28x%29%5D%5E4%20%3D%2064)
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Book: College Calculus 10e