Answer:
The factors of x² - 3·x - 18, are;
(x - 6), (x + 3)
Step-by-step explanation:
The given quadratic expression is presented as follows;
x² - 3·x - 18
To factorize the given expression, we look for two numbers, which are the constant terms in the factors, such that the sum of the numbers is -3, while the product of the numbers is -18
By examination, we have the numbers -6, and 3, which gives;
-6 + 3 = -3
-6 × 3 = -18
Therefore, we can write;
x² - 3·x - 18 = (x - 6) × (x + 3)
Which gives;
(x - 6) × (x + 3) = x² + 3·x - 6·x - 18 = x² - 3·x - 18
Therefore, the factors of the expression, x² - 3·x - 18, are (x - 6) and (x + 3)
Well the first thing you need to do is set up a proportion.
8 girls 56 girls
-------- = -----------
7 boys x
Now what we have to do is find out what we multiplied by 8 to get 56.
Simply divide.
56 ÷ 8 = 7
So, we figured out that the magic number is 7!
So we multiply the boy number by 7
7 x 7 = 49
So this means that there are 49 boys on the field trip.
Answer:
General Formulas and Concepts:
<u>Algebra I</u>
<u>Calculus</u>
Antiderivatives - integrals/Integration
Integration Constant C
U-Substitution
Integration Property [Multiplied Constant]:
Trig Integration:
Step-by-step explanation:
<u>Step 1: Define</u>
<u /><u />
<u />
<u>Step 2: Integrate Pt. 1</u>
- [Integral] Factor fraction denominator:
- [Integral] Integration Property - Multiplied Constant:
<u>Step 3: Identify Variables</u>
<em>Set up u-substitution for the arctan trig integration.</em>
<u>Step 4: Integrate Pt. 2</u>
- [Integral] Substitute u-du:
- [Integral] Trig Integration:
- [Integral] Simplify:
- [integral] Multiply:
- [Integral] Back-Substitute:
Topic: AP Calculus AB
Unit: Integrals - Arctrig
Book: College Calculus 10e
Answer:
Below
Step-by-step explanation:
● cos O = 2/3
We khow that:
● cos^2(O) + sin^2(O) =1
So : sin^2 (O)= 1-cos^2(O)
● sin^2(O) = 1 -(2/3)^2 = 1-4/9 = 9/9-4/9 = 5/9
● sin O = √(5)/3 or sin O = -√(5)/3
So we deduce that tan O will have two values since we don't khow the size of O.
■■■■■■■■■■■■■■■■■■■■■■■■■
●Tan (O) = sin(O)/cos(O)
● tan (O) = (√(5)/3)÷(2/3) or tan(O) = (-√(5)/3)÷(2/3)
● tan (O) = √(5)/2 or tan(O) = -√(5)/2