Given:
plot of land doubles in size.
original plot area 200 by 300 meters
Area = 200m * 300m
A = 60,000 m² original plot area
60,000m² x 2 = 120,000 m²
(200m + x)(300m + x) = 120,000 m²
60,000m² + 200m*x + 300m * x + x² = 120,000 m²
x² + 500x + 60,000 = 120,000
x² + 500x + 60,000 - 120,000 = 0
x² + 500x - 60,000 = 0
x = -b <u>+</u> (√b² - 4ac)/2a
a = 1 ; b = 500 ; c = -60,000
x = -500 + (√500² - 4(1)(-60,000)) / 2(1)
x = (-500 + (√250,000 + 240,000)) / 2
x = (-500 + 700)/ 2
x = 200 / 2
x = 100 meters
(200 + x)(300 + x) = 120,000
(200 + 100)(300 + 100) = 120,000
300 * 400 = 120,000
120,000 = 120,000
A little Algebra, and we're home free!
We are given R = 20 and r2 = 75. We need to find r1.
The formula is 1/R = 1/r1 + 1/r2. Plug-in:
1/20 = 1/r1 + 1/75
1/20 - 1/75 = 1/r1
0.0366 = 1/r1
r1 = 1/0.03666
r1 = 27.272
Our answer is r1 = 27 ohms.
Answer: a. Positive, because the products (3)(-3) and (-2)(4) are negative, and the product of two negative numbers is positive
Step-by-step explanation: It is also possible to rearrange the factors.
(3)(4) = 12 a positive number.
(-3)(-2) = 6, a positive number. Again "a negative times a negative is a positive" --Jaime Escalante, <em>Stand and Deliver</em>
Now you have two positive numbers: 12×6 = 72
The product is positive either way.
