6. Jake jumped 3 feet. Marco jumped

Mathematics

1 answer:

cestrela7 [59]3 years ago

4 0

They jumped 2 feet more as Jake + Peter = 7 so 7-5=2

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Magnus purchased a new car for $35,865. It depreciates about 3.6% each year. What is the value of the car after 10 years?

Naddik [55]

1 year = 3.6 % depreciation
100-3.6=96.4

so you do 35,865 ×0.964 = 34,573.86

so the price after a year is £34,573.86

to find out what the price is after 10 years you do 34,573.86 (0.964) to the power of 10
which equals £23961.73

I hope that was helpful :)

5 0

4 years ago

Suppose a ball is dropped from a height of 16 feet. Each time it drops h feet, it rebounds 0.81h feet. Find the total distance t

Roman55 [17]

When the ball is first dropped, it falls $h$ feet. On the first bounce, it rebounds $0.81h$ feet, which means on the second "drop" it must travel $0.81h$ feet again. On the second bounce, the ball rebounds $0.81(0.81h)=0.81^2h$ feet, and on the third drop falls the same distance. And so on.

So there are two directions to track:

$\text{downward: }\displaystyle h+0.81h+0.81^2h+\cdots=\sum_{n=0}^\infty 0.81^nh$
$\text{upward: }\displaystyle 0.81h+0.81^2h+\cdots=\sum_{n=1}^\infty 0.81^nh$

The total distance is the sum of these two:

$\displaystyle\sum_{n=0}^\infty 0.81^nh+\sum_{n=1}^\infty 0.81^nh=h+2h\sum_{n=1}^\infty 0.81^n$

Recall that for an infinite geometric sum, you have

$\displaystyle\sum_{n=0}^\infty r^n=1+\sum_{n=1}^\infty r^n=\frac1{1-r}$

provided that $|r|$ . So the total distance traveled by the ball is

$h+2h\left(\dfrac1{1-0.81}-1\right)\approx9.53h$

Starting with a height of $h=16$ means the total distance is about 152.42 ft.