Answer:
1
Step-by-step explanation:
(f+g)(1) = f(1) +g(1) = -1 + 2 = 1
__
The pair (1, -1) in the definition of f tells you f(1) = -1.
The pair (1, 2) in the definition of g tells you g(1) = 2.
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:
3
Step-by-step explanation:
Because you can see there was one cube length in figure A and there was 3 cubes length in figure B.
Substract by 12 from 42, and keep going down until you hit -54, which is 8 hours!
Answer:
Araceli would have used 2.25 (or 2 1/4) yards of fabric for each bag.
Step-by-step explanation:
First, you have the 9 bags you are making and they all must be the same because they are identical, so you divide the nine bags by the four yards and I got an answer of 2.25 yards per bag. The answer can also be 2 1/4 as well.
