Help a girl out please ???

Mathematics

2 answers:

Andreas93 [3]3 years ago

8 0

Answer:

1.) y= 41

2.) y=34

3.) y= -19

Step-by-step explanation:

1.) y= (15 x 3) - 40

y= 45-40

y= 41

2.) y= (2/3 x 21) +20

y= 14+20

y= 34

3.) y= (3* -2)² +17

y= -6² +17

y= -36 +17

y= -19

Gnoma [55]3 years ago

4 0

Answer:

1.)

y= (15 x 3) - 40

y= 45-40

y= 41

2.)

y= (2/3 x 21) +20

y= 14+20

y= 34

3.)

y= (3* -2)² +17

y= -6² +17

y= -36 +17

y= -19

SRY I DID NOT ANSWER BEFORE

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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.