Answer:
5.4
Explanation:
a²+b²=c²
2²+5²= 4+25
4+25=29
Now we have to square root the 29 which would make the answer 5.4
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)
Step-by-step explanation:
£480 = 120% (after adding the 20% VAT).
we want to know how much 100% is.
he do we get from 120% to 100% ?
first the formal long way
£480 = 120%
1% = 120%/120 = 480/120 = £4
100% = 1% × 100 = 4×100 = £400
once you understand this mechanism, you can apply the direct shortcut :
£480 / 1.2 = £400
as a multiplication with 100/120 is the same as a division by 120/100, which is 1.2.
and what we did at the beginning in long form was nothing else than
£480 × 100/120 = 480 × 10/12 = 480 × 5/6 = £400
55 - 3 = 52
52 - 3 = 49
49 - 3 = 46
46 - 3 = 43
43 is your answer
I believe it would be 2 units to the right
and 4 units down
