Answer:
A. 34°
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Trigonometry</u>
- [Right Triangles Only] SOHCAHTOA
- [Right Triangles Only] tanθ = opposite over adjacent
- Inverse Trig
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify variables</em>
Angle θ = <em>x</em>
Opposite leg AC = 24
Adjacent leg CB = 35
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute in variables [Tangent]:
- Inverse Trig [Tangent]:
- Evaluate:
- Round:
The fractions 25/100 and 50/200 are both equivalent to 1/4.
If there are 400 silver dollars in all, and there are 275 in one bag, to find the amount in the other bag, just subtract:
400-275=125
There are 125 in the other bag.
Answer:
n = 19/18
Step-by-step explanation:
11/6 = n + 7/9
-n + 11/6 = 7/9
-n = 7/9 - 11/6
-n = -19/18
n = 19/18
The characteristic solution follows from solving the characteristic equation,
so that
A guess for the particular solution may be
, but this is already contained within the characteristic solution. We require a set of linearly independent solutions, so we can look to
which has second derivative
Substituting into the ODE, you have
Therefore the particular solution is
Note that you could have made a more precise guess of
but, of course, any solution of the form
is already accounted for within
.