Answer:
aₙ = 4(5)ⁿ⁻¹
Explanation:
To identify a geometric series: second term = √(first term * third term)
Here given:
check ============
20 = √(100*4)
20 = √400
20 = 20 Hence its a geometric term.
Find common difference (r):
20/4 = <u>5</u> or 100/20 = <u>5</u>
Geometric term formula:
aₙ = a₁(r)ⁿ⁻¹ [where a1 is the 1st term, r is common difference]
<u>insert values found</u>
aₙ = 4(5)ⁿ⁻¹ ......this is the nth term.
Answer: 16
Step-by-step explanation:
Total number of laptops ordered= 650
Number of laptops tested= 40
Number of laptops that takes more than 30 seconds to start up= 1
To get the number of laptops that will take 30 seconds to start in the whole shipment goes thus:
Let the number of laptops that will take more than 30 seconds be represented by y.
1 : 40 = y : 650
1/40 = y/650
Cross multiply
40y = 650
y= 650/40
y= 16.25 which approximately gives 16.
There are expected to be 26 laptops that takes more than 30 seconds to start.
Answer:
Area of square = 100 inches
Step-by-step explanation:
Diameter = 14 inches
Diagonal of the square = diameter= 14 inches
Area of Square = (1/2) * (diagonal)^2
=(1/2) * 14 * 14 = 7 * 14 = 98
= 100 inches ( rounded to nearest tenth)
Answer:
b.
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Functions
- Function Notation
- Exponential Rule [Rewrite]:
- Exponential Rule [Root Rewrite]: <u>
</u>
<u>Calculus</u>
Derivatives
Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Chain Rule]:
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
<em /><em />
<em />
<u>Step 2: Differentiate</u>
- Rewrite function [Exponential Rule - Root Rewrite]:
- Chain Rule:
- Basic Power Rule:
- Simplify:
- Rewrite [Exponential Rule - Rewrite]:
<u>Step 3: Evaluate</u>
- Substitute in <em>x</em> [Derivative]:
- Substitute in function values:
- Exponents:
- Multiply:
- Simplify:
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
Answer:
<h2>x = 8m</h2>
Step-by-step explanation:
Let the two triangles be represented as A and B.
Given two triangles with sides 12m 20m 16m and 6m 10m x.
Lengths of sides of triangle A = 12m, 20m, 16m
Lengths of sides of triangle B = 6m, 10m, x
It can be seen that each length of triangle A are twice that of B i.e triangle B dilated by a factor of 1/2.
A = 2B
<u>Considering the 16m length in triangle A and comparing it with the 'x'm length in triangle B, we can get the unknown length x as shown;</u>
16 = 2x
x = 16/2
x = 8m