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:
-281.25
Step-by-step explanation:
Answer:
The horizontal component of the force is 48 N.
Step-by-step explanation:
The angle that the rope makes with with the horizontal is 15°, that means, the horizontal component of the force 
is
Answer:
if you are trying to find the rest of A it would be adding by 1 because of the slope so: 5,6,7,8,9,10. The slope of B wouldbe .8 because it is increasing by .8 everytime so: 3.8,4.6,5.4,6.2,7.0
Step-by-step explanation:
B) 4.6-3.8= .8
5.4-4.6= .8
slope is .8
5.4+.8=6.2
6.2+ .8= 7.0
