Answer:
2 5/9
Step-by-step explanation:
6 1/9 = 55/9
3 5/9 = 32/9
55/9-32/9
23/9 or 2 5/9
Answer:
z = -3
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
Distributive Property
Terms/Coefficients
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify.</em>
42 = -7(z - 3)
<u>Step 2: Solve for </u><em><u>z</u></em>
- [Distributive Property] Distribute -7: 42 = -7z + 21
- [Subtraction Property of Equality] Subtract 21 on both sides: 21 = -7z
- [Division Property of Equality] Divide -7 on both sides: -3 = z
- Rewrite: z = -3
Answer:
-30√(t/a) cos(√(at)) + 30/a sin(√(at)) + C
Step-by-step explanation:
∫ 15 sin(√(at)) dt
Use substitution:
If x = √(at), then:
dx = ½ (at)^-½ (a dt)
dx = a / (2√(at)) dt
dx = a/(2x) dt
dt = (2/a) x dx
Plugging in:
∫ 15 sin x (2/a) x dx
30/a ∫ x sin x dx
Integrate by parts:
If u = x, then du = dx.
If dv = sin x dx, then v = -cos x.
∫ u dv = uv − ∫ v du
= 30/a (-x cos x − ∫ -cos x dx)
= 30/a (-x cos x + ∫ cos x dx)
= 30/a (-x cos x + sin x + C)
Substitute back:
30/a (-√(at) cos(√(at)) + sin(√(at)) + C)
-30√(t/a) cos(√(at)) + 30/a sin(√(at)) + C
Answer:
x=4
Step-by-step explanation:
