<span>-7 • (a4 - 81a2 - 162)27
-------------------------------- hope it helps
27</span>
Use the distributive property.
1/7(105 + r) = 20
15 + (1/7)r = 20
Then subtract each side of the equation by 15.
15 + (1/7)r = 20
(1/7)r = 5
Divide both sides by 1/7.
(1/7)r = 5
r = 35
So, the answer to this question is r is equal to 35.
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)
Well... we know that... there are 365 days in a year, unless is a leap-year, but we'll use 365 anyway
and each day has 24hrs, each hr has 60 minutes
so. let us use those ratios

so.. multiply and simplify, cancelling out any like-units atop and bottom
notice, all we do, is use the ratios, in a way, that if we need one unit to be changed, we flip the ratio
for example, to toss away "year" unit, since in the first fraction is at the bottom, then we put it on the top on the ratio, year/year = 1, effectively cancelling the unit