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)
2 BBC’s if that’s what the council agrees as fair punishment for lying cheating and spreading evil i just want to die
84+92+87+104=367
500-367=133
He needs to plant 133 shrubs on Friday
Thank you for posting your question here. Please see below answers for the problem above:
a. to find the circumference of the tire you need to multiply 3.14 by 2.5:
= 3.14 x 2.5
= 7.85 to round of it will be 8
b. to get the number of times the tire have to rotate to travel 1 mile:
1 mile = 5,280 ft
1 rotation is 7.85
5,280/7.85 = 672.611465
Answer:
ans x=4
Step-by-step explanation:
- 5x + 7 = -13
- 5x = -13 -7
- 5x= -20
- x = -20/5
- x = -4
- so the answer is x= -4
