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)
They have the same slope, but g(x) intercepts the y axis higher.
In this question, it is given that
Walter wants computer software that cost $129. He has $57 saved.
he saves a maximum of $15 a week, the following inequality can be used to find how many weeks it will take Walter to save enough money to buy the software.
And we have to solve this inequality for x.
First we subtract 57 to both sides. And on doing so , we will get
Dividing both sides by 15.
\
Correct option is A.
Answer:
Steps shown below
Step-by-step explanation:
We will simplify this using definitions and identities. Let's start.
Using 
, we have:
Using 
, we have:
Hence, proved.
