Answer:
h( x) = 4^x + x - 2
Step-by-step explanation:
h(x)=f(x)+g(x)=4^x+2+x-4=<u>4^x+x-2</u>
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:
x < -3 or x > 3
second answer choice
Step-by-step explanation:
The symbol "∨" between p and q represents a disjunction and can be replaced with the word "or" to turn p ∨ q into p or q.
Plug in x < -3 in for p and x > 3 for q, and now you have:
x < -3 or x > 3
which is the same as the second answer choice.
So, the answer is x < -3 or x > 3, or the second answer choice.
I hope you find my answer helpful.
Answer:
x=75
Step-by-step explanation:
The triangle is isosceles, meaning that the angles V and U are congruent
