Answer:
13 ft/s
Step-by-step explanation:
t seconds after the boy passes under the balloon the distance between them is ...
d = √((15t)² +(45+5t)²) = √(250t² +450t +2025)
The rate of change of d with respect to t is ...
dd/dt = (500t +450)/(2√(250t² +450t +2025)) = (50t +45)/√(10t² +18t +81)
At t=3, this derivative evaluates to ...
dd/dt = (50·3 +45)/√(90+54+81) = 195/15 = 13
The distance between the boy and the balloon is increasing at the rate of 13 ft per second.
_____
The boy is moving horizontally at 15 ft/s, so his position relative to the spot under the balloon is 15t feet after t seconds.
The balloon starts at 45 feet above the boy and is moving upward at 5 ft/s, so its vertical distance from the spot under the balloon is 45+5t feet after t seconds.
The straight-line distance between the boy and the balloon is found as the hypotenuse of a right triangle with legs 15t and (45+5t). Using the Pythagorean theorem, that distance is ...
d = √((15t)² + (45+5t)²)
Answer:
320 messages
Step-by-step explanation:
20 messages per dollar,
20 x 16 equals 320
Answer:
g = 55
f = 55
h = 55
Step-by-step explanation:
g = 180 - 25 = 55
this is because angle on a straight line is equal to 180 degrees
f = 55
alternate angles are equal. f alternates g
h = 55
opposite angels are equal
Answer:
128
Step-by-step explanation:
You would multiply 79 by 1.62 to get the answer.
This would give you 127.98 which you would round up to 128.
Answer:
the correct for this question is be over the y-axis (x,y)=(-x,y)
