<span>Since each population is represented by the area then the area is equal to the population of whatever city. So the are of the Texas circle is 28,240,245 and that rounded of to the nearest tenth is 28,240,250. To find the radius of whatever city you must use the formula for find area of a circle which is A = πr^2, where r is the radius. Make the r the subject of the formula, to do that you divide both sides of the equation by π, this will make the π on the right side cancel out and the final equation will be
A/Ď€ = r^2, then square root both sides to get rid of the squared exponent on the r then the final equation will be sqr(A/Ď€) = r. So you replace the A with the area or the population of the city want in this case Texas, you will end up with this equation, sqr(28,240,250/Ď€) = r. The radius of the Texas circle is 2998.19 but that rounded to the nearest tenth is 3,000.</span>
Answer:
10
Step-by-step explanation:
X = 10.7
Answer:
Number of people who order chicken dinner = 1
Number of people who order the steak dinner = 5
Step-by-step explanation:
Let
x = number of people who order chicken dinner
y = number of people who order the steak dinner
x + y = 6 (1)
14x + 17y = 99 (2)
From (1)
x = 6 - y
Substitute into (2)
14x + 17y = 99 (2)
14(6 - y) + 17y = 99
84 - 14y + 17y = 99
- 14y + 17y = 99 - 84
3y = 15
y = 15/3
y = 5
Substitute y = 5 into (1)
x + y = 6 (1)
x + 5 = 6
x = 6 - 5
x = 1
Number of people who order chicken dinner = 1
Number of people who order the steak dinner = 5
58/1000 which reduces to 29/500 when you pull a two out of both numbers
Answer:
<h3>#1</h3>
The normal overlaps with the diameter, so it passes through the center.
<u>Let's find the center of the circle:</u>
- x² + y² + 2gx + 2fy + c = 0
- (x + g)² + (y + f)² = c + g² + f²
<u>The center is:</u>
<u>Since the line passes through (-g, -f) the equation of the line becomes:</u>
- p(-g) + p(-f) + r = 0
- r = p(g + f)
This is the required condition
<h3>#2</h3>
Rewrite equations and find centers and radius of both circles.
<u>Circle 1</u>
- x² + y² + 2ax + c² = 0
- (x + a)² + y² = a² - c²
- The center is (-a, 0) and radius is √(a² - c²)
<u>Circle 2</u>
- x² + y² + 2by + c² = 0
- x² + (y + b)² = b² - c²
- The center is (0, -b) and radius is √(b² - c²)
<u>The distance between two centers is same as sum of the radius of them:</u>
<u>Sum of radiuses:</u>
<u>Since they are same we have:</u>
- √(a² + b²) = √(a² - c²) + √(b² - c²)
<u>Square both sides:</u>
- a² + b² = a² - c² + b² - c² + 2√(a² - c²)(b² - c²)
- 2c² = 2√(a² - c²)(b² - c²)
<u>Square both sides:</u>
- c⁴ = (a² - c²)(b² - c²)
- c⁴ = a²b² - a²c² - b²c² + c⁴
- a²c² + b²c² = a²b²
<u>Divide both sides by a²b²c²:</u>
Proved