The rate of change of the size of the diagonal is; 25.2 ft/s
By Pythagoras theorem;
The length, l of a diagonal of a rectangle whose sides have lengths x and y is;
In essence; the length of the diagonal is dependent on the length, x and y of the sides.
Therefore;
(dl/dt)² = (dx/dt)² + (dy/dt)²
where;
- (dx/dt) = 19 ft/s
- (dy/dt) = -15 ft/s
Therefore,
(dl/dt)² = 19² + (-15)²
(dl/dt)² = 361 + 225
dl/dt = √586
dl/dt = 25.2
Therefore, the size of the diagonal is changing at a rate of; 25.2 ft/s.
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brainly.com/question/12559989
Answer:
5x-3p
Step-by-step explanation:
(1/3)(3x-6p) + 4x - p
Distribute the 1/3 to the variables in parenthesis.
x - 2p +4x - p
Combine the like variables.
5x - 3p
Hope this helps!
Answer:
Part A: -3x^8 + 2x^5 + 4x^3
Part B: 8
Part C: 3
Part D: -3x^8
Part E: -3
Answer:
T > -9/28
Step-by-step explanation:
A quadratic has two real solutions when the discriminant (b² - 4ac) is positive.
b² - 4ac > 0
3² - 4(T)(-7) > 0
9 + 28T > 0
28T > -9
T > -9/28
Answer:
- 3.9 hours
- 90 mph
Step-by-step explanation:
<h3>1.</h3>
The sum of the rates of painting, in fences per hour, is ...
1/9 + 1/7 = (9+7)/63 . . . . fences per hour
The total rate in hours per fence is the inverse of that:
63/16 = 3 15/16 ≈ 3.9 . . . hours to paint the fence
__
<h3>2.</h3>
The relevant relationship is ...
distance = speed × time
Let t represent Tom's speed in miles per hour. Then George's speed is (t-36). They both have traveled the same total distance at the point where Tom catches up.
(2+3)(t-36) = 3t
2t = 180 . . . . . . . add 180-3t
t = 90 . . . . . . divide by 2
Tom's average speed is 90 miles per hour.
