One airplane is at 7,000 feet and is descending 50 feet every second. Another plane is at
1 answer:
Given:
One airplane is at 7,000 feet and is descending 50 feet every second.
Another plane is at 1,000 feet and is climbing at a rate of 70 feet per second.
To find:
The time taken by planes to reach at the same height.
Solution:
Let x be the number of seconds after which the planes be at the same height.
One airplane is at 7,000 feet and is descending 50 feet every second.
Change in 1 second = -50 feet (Here negative sign means decrease)
Change in x second = -50x feet
Height of first airplane after x seconds is
...(i)
Another plane is at 1,000 feet and is climbing at a rate of 70 feet per second.
Change in 1 second = 70 feet
Change in x second = 70x feet
Height of first airplane after x seconds is
...(ii)
Equate (i) and (ii), to find the time after which both planes are on the same height.
Divide both sides by 120.
Therefore, both planes are at the same height after 50 seconds.
You might be interested in
Answer:
5 trees should be planted to maximize the yield per acre,
The maximum yield would be 1250
Step-by-step explanation:
Given,
The original number of trees per acre = 20,
Average pounds of nuts by a tree = 60,
Let x be the times of increment in number of trees,
So, the new number of trees planted per acre = 20 + x
∵ for each additional tree planted per acre, the average yield per tree drops 2 pounds,
So, the new number of pounds of nut = (60 - 2x)
Thus, the total yield per acre,
Differentiating with respect to t ( time ),
Again differentiating with respect to t,
For maxima or minima,
⇒ 20 - 4x = 0
⇒ 20 = 4x
⇒ x = 5,
For x = 5, Y''(x) = negative,
Hence, Y(x) is maximum for x = 5,
And, maximum value of Y(x) = (20+5)(60 - 10) = 25(50) = 1250,
i.e. 5 trees should be planted to maximize the yield per acre,
and the maximum yield would be 1250 pounds
9514 1404 393
Answer:
-361
Step-by-step explanation:
Your calculator can tell you the result. It is -361.
Start with the inner parentheses and work outward. Do multiplication and division in the order shown, left to right, before addition or subtraction.
-3[2/6+8{-9/3(8-5*3)-6}]
= -3[2/6+8{-9/3(8-15)-6}]
= -3[2/6+8{-9/3(-7)-6}]
= -3[2/6+8{-3(-7)-6}]
= -3[2/6+8{21-6}]
= -3[2/6+8{15}]
= -3[1/3+8{15}]
= -3[1/3+120]
= -3[361/3]
= -361
