(c) what is the probability that jeanie remembers the first errand but not the second or third?

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.

4 0

3 years ago

6. Which expression is equivalent to the

slava [35]

What is the algebraic expression?

4 0

3 years ago

Write the equation of a line that is parallel to y=1/2x−4y and that passes through the point (9,−6)

lara [203]

Answer:

the desired equation is

y = (1/2)x - 21/2

Step-by-step explanation:

Looks as tho' you may have typed in an extra 'y' here. I will proceed under the assumption that you meant y = (1/2)x - 4. This line has a slope of 1/2.

Any line parallel to it also has a slope of m = 1/2.

Start by replacing y, x, m and b in y = mx + b with the knowns:

y = mx + b becomes -6 = (1/2)(9) + b.

Clear this of fractions by multiplying all 3 terms by 2:

-12 = 9 + 2b, or:

-21 = 2b. Dividing both sides by 2 results in b = -21/2.

Thus, the desired equation is

y = (1/2)x - 21/2

8 0

3 years ago

For every $50.00. Michael earns, he saves $5. for the future. How much money will he have saved when he earns a total of $500.

xeze [42]

The answer is D

This is because if for every $50 he saves $5, and he has saved a total of $500, you can set up a proportion to find out how much money he has saved at that point.

The proportion is as follows:

50/5 == 500/x

x is equivalent to the amount of money he has saved

You can cross multiply to get the following equation:

50x == 2500

To isolate x, you must divide both sides by 50, giving you an answer of:

x = 50

This is the same as option D

4 0

4 years ago

Read 2 more answers

Haleiwa takes all stuckers

miss Akunina [59]

Answer:

What does this mean, and what are we looking for?

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers