Answer:
The numbers are 19 and 71.
Step-by-step explanation:
Let x and y represent the two numbers. Then x + y = 90.
Also, if we assume that the larger number is y, then y = 3x + 14.
We must solve this system of linear equations. Since we already have the result of solution for y (y = 3x + 14), let's use the substitution method to find the solution:
x + y = 90 becomes x + 3x + 14 = 90, or:
4x = 76. Thus, x = 76/4, or 19. If x = 19, then y = 3(19) + 14, or y = 71.
The numbers are 19 and 71.
Note that these add up to 90, as they must, and that 71 is 14 more than 3 times 19.
Answer: 16.33 feet/s
Explanation:
1) Data:
a) circular motion
b) revolutions: 12 rpm
c) r = 15 feet
d) v = ?
2) Formulae:
angular velocity: ω = number of rpm × 2π / 60 seconds
linear velocity: v = ω × r
3) Solution:
ω = 12 × 2π / 60 s = 0.4π rad / s
v = 0.4π rad / s × 13 feet = 5,2 π feet / s ≈ 5,2 (3.14159) feet / s = 16.33 feet/s.
That is the answer.
We can form two ratios to help us solve this:
(2x+6):10 = (x+6):8
(2x+6) (x+6)
--------- = --------
10 8
Cross multiply:
8(2x+6) = 10(x+6)
Foil:
16x + 48 = 10x + 60
Move like variables to the same side:
16x - 10x = 60 - 48
6x = 12
x = 2
Line AE = 2x+6
Plug 2 for x into the equation: 2(2) + 6 = 10
Hope this helps, and May the Force Be With You!
-Jabba
