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:
the first one
Step-by-step explanation:
y = 3x/3
y = x
Answer:
6.25%
Step-by-step explanation:
Total = 1 ; as a decimal
1/2 = skittles
1/4 = M&Ms
Skittles +M&Ms = 1/2 + 1/4 = 3/4
Remainder = 1 - 
Remainder = 
Sour patch = 
As a percentage , multiply 1/16 by 100 and it becomes 6.25%
Answer:
Step By Step Explanation:
Area Of Rhombus: 
Identify 'p'
5 + 5 = 10
p = 10
Identify 'q'
10 + 10 = 20
q = 20
➤ 
5 * (2 + 4)
5 * 2 + 5 * 4 (the distributive property)
5 * 6 (order of operations)
