Answer: x = 8/3 ; or, write as: 2 2/3; or, write as, 2.66666667 .
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Explanation:
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Given: 5 − 1/2 x = 5/8 x + 2 ;
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Change the 1/2 x to "4/8 x" ;
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Since "1/2" = "(1*4)/(2*4)" = "(4/8)"; and rewrite:
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→ 5 − (4/8)x = (5/8)x + 2 ;
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Subtract "5"; and add "(5/8)x" to EACH side of the equation:
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5 − (4/8)x − 5 + (5/8)x = (5/8)x + 2 − 5 + (5/8)x ;
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to get:
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(1/8) x = (10/8)x − 3
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Multiply the entire equation (BOTH SIDES) by "8"; to get rid of the fraction:
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8 * { (1/8) x = (10/8)x − 3 };
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to get:
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x = 10x − 24 ;
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Subtract "x" ; and add "24" ; to EACH side of the equation:
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→ x − x + 24 = 10x − 24 − x + 24 ;
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to get:
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→ 24 = 9x ; ↔ 9x = 24 ;
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→ Divide EACH side of the equation by "9" ; to isolate "x" on one side of the equation; and to solve for "x" ;
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→ 9x / 9 = 24 / 9 ;
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→ x = 24/9 = (24÷3)/ (9÷3) = 8/3
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→ x = 8/3 ; or, write as: 2 2/3; or, write as, 2.66666667.
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We are integrating f(x) = 9cos(9x) + 3x²: 
a) Apply the sum rule

b) Calculate each antiderivative
<u>First integral</u>

1. Take out the constant

2. Apply u-substitution, where u is 9x

3. Take out the constant (again)

4. Take the common integral of cos, which is sin

5. Substitute the original function back in for u and simplify
6. Always remember to add an arbitrary constant, C, at the end

<u>Second integral</u>

1. Take out the constant

2. Apply the power rule,
, where <em>a</em> is your exponent
⇒ 
3. Add the arbitrary constant

c) Add the integrals
sin(9x) + C + x³ + C = sin(9x) + x³ + C
Notice the two arbitrary constants. Since we do not know what either constant is, we can combine them into one arbitrary constant.
<h3>
Answer:</h3>
F(x) = sin(9x) + x³ + C
It diverges; it does not have a sum. the sum of a geometric series is given by a /(1-r) where a is the first term and the r is the ratio between the terms. r=3 in the series you have given . The absolute value of r must be less then 1 for a geometric series to converge.
Answer:
(-3, 4)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
<u>Algebra I</u>
- Terms/Coefficients
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
y = -x + 1
2x + 3y = 6
<u>Step 2: Solve for </u><em><u>x</u></em>
<em>Substitution</em>
- Substitute in <em>y</em>: 2x + 3(-x + 1) = 6
- Distribute 3: 2x - 3x + 3 = 6
- Combine like terms: -x + 3 = 6
- Isolate <em>x</em> terms: -x = 3
- Isolate <em>x</em>: x = -3
<u>Step 3: Solve for </u><em><u>y</u></em>
- Define equation: y = -x + 1
- Substitute in <em>x</em>: y = -(-3) + 1
- Simplify: y = 3 + 1
- Add: y = 4
21:30 and 35: and 50 this is because 7 times 3 is 21, 10 times 3 is 30, and 7 times 5 is 35, and lastly 10 times 5 is 50