Answer: The three numbers are 8, 12 and 20.
Explanation:
Let k be the ratio of the numbers
The numbers: 2k, 3k, 5k
(2k)^2 + (3k)^2 (5k)^2 = 608
4k^2 + 9k^2 + 25k^2 = 608
38k^2 = 608
k^2 = 16
k = 4
Hence, the three numbers are 8, 12 and 20.
The freight train speed = 22 mph
The passenger train speed = 28 mph
Step-by-step explanation:
Assign the speed of the freight train as; <em>x </em>mph
Since the passenger train travels 6 mph faster than the freight train, its speed will be; (<em>x + 6</em>) mph
In 2 hours, the freight and passenger trains will have traveled (distance = speed * time);
2<em>x</em> and 2(<em>x + 6</em>) miles respectively
Both add up to 100 miles. Therefore;
2x + 2(x +6) = 100
4x + 12 = 100
4x = 88
x = 22
x + 6 = 28
The freight train speed = 22 mph
The passenger train speed = 28 mph
Answer: 502 Bad Gateway
Step-by-step explanation:
Answer:
Length of the trail = 39473.68 ft
Step-by-step explanation:
Let x be the length of the trail.
Given:
Lodge Elevation = 700 ft
Mountain elevation = 8200 ft
Inclination of trail = 11°
We need to find the length of the trail.
Solution:
Total ascent is difference between mountain elevation and lodge elevation.
Length of the trail is the length of the hypotenuse of right angle triangle where the length of the shortest side is the right angle triangle is 7500 ft and opposite angle is 11°.
Using cosine rule.
Therefore, the length of the trail is equal to 39473.68 ft.
Answer:
a = 2
Step-by-step explanation:
given x = - 1 is a zero then f(- 1) = 0 , that is
a(- 1)³ - (- 1)² - 1 + 4 = 0
- a - 1 - 1 + 4 = 0
- a + 2 = 0 ( subtract 2 from both sides )
- a = - 2 ( multiply both sides by - 1 )
a = 2