Answer:
No Answer
Step-by-step explanation:
cancel out same on both sides
N/A
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:
It takes 30 minutes
Step By Step:
The rate of Glenn in finishing a job would be equivalent to:
Rate (G) = 1
job / 20 minutes
While the rate of Veronika is:
Rate (V) = 1
job / x---> x is the unknown
Where 1 job for Glenn means completely cleaning his room while 1 job for Veronika means pulling out everything. Therefore the equation to use would be:
1 / 20 – 1 /
x = 1 / 60
The rate of
Veronika is subtracted from the rate of Glenn since Veronika is slowing Glenn
down. Solving for x:
Multiply both
sides by 60 x
(1 / 20 – 1 /
x = 1 / 60) * 60 x
3 x – 60 = x
2 x = 60
x = 30
Therefore it
takes 30 minutes for Veronika to pull everything out.
1a) f(x) = I x+2 I. This is a piece-wise graph ( V form)
x = 0 →f(x) =2 (intercept y-axis)
x = -2→f(x) = 0 (intercept x-axis)
x = -3→f(x) = 1 (don't forget this is in absolute numbers)
x = -4→f(x) = 2 (don't forget this is in absolute numbers)
Now you can graph the V graph
1b) Translation: x to shift (-3) units and y remains the same, then
f(x-3) = I x - 3 + 2 I = I x-1 I
the V graph will shift one unit to the right, keeping the same y. Proof:
f(x) = I x-1 I . Intercept x-axis when I x-1 I = 0, so x= 1
4,000. subtract the numbers, then round to the nearest thousand.
