Answer:
Step-by-step explanation:
The total area of a circle (πR²) Is to be proportional to the population's State.
If proportionality to be maintained then Populations should be in
the ratio R²₁ / R²₂
The population of NY is represented by an area of πR² = π.25 (R=5 Given)
CA/NY =37,691,000 / 19,465,000 = R²₁ / R²₂ = 1.936
==> √(R²₁/R²₂)=√1.936 = R₁/R₂ =1.4 ==> R₁/5 = 1.4 & R(ca) = 7
Same logic for Texas: 25,675,000/19,465,000 = R²(tx)/25 =1.319
==> R(tx) =6.6
Answer: 1200pi cubic cm per sec
========================================
Work Shown:
dr/dt = 3 is the rate of change of the radius
V = (4/3)pi*r^3 ..... volume of a sphere
dV/dt = (4/3)*3*pi*r^2*dr/dt ... chain rule
dV/dt = 4*pi*r^2*dr/dt
dV/dt = 4*pi*r^2*3
dV/dt = 12*pi*r^2
dV/dt = 12*pi*10^2 ... plug in r = 10
dV/dt = 1200pi
Answer:
x = -8
m∠BDC = 68°
General Formulas and Concepts:
<u>Pre-Algebra
</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Geometry
</u>
- Definition of a Line: A line is 180°
Step-by-step explanation:
<u>Step 1: Set up Equation</u>
m∠BDC + m∠CDA = 180°
(-7x + 12)° + (-8x + 48)° = 180°
<u>Step 2: Solve for x
</u>
- Combine like terms: -15x + 60 = 180
- Isolate x term: -15x = 120
- Isolate x: x = -8
<u>Step 3: Find m∠BDC
</u>
- Define: m∠BDC = (-7x + 12)°
- Substitute in x: m∠BDC = (-7(-8) + 12)°
- Multiply: m∠BDC = (56 + 12)°
- Add: m∠BDC = 68°
Let x = number of students then by proportion:-
5/7 = 185 / x
x = (7 * 185) / 5
= 259 Answer
