25.04.2021

*Suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 12 feet, then hits the floor and rebounds to 9.6 feet. Write an explicit formula for the sequence.
Also, How high will the ball rebound after its fourth bounce?

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Step-by-step answer

09.07.2023, solved by verified expert
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The explicit formula is *Suppose you drop a tennis ball from a height, №18010863, 25.04.2021 04:25.

Step-by-step explanation:

First, we need to find the common ratio. We know this is a geometric sequence because the decrease from one term to the next is not a constant number.

To find the constant ratio, we can take the *Suppose you drop a tennis ball from a height, №18010863, 25.04.2021 04:25 term and divide by the *Suppose you drop a tennis ball from a height, №18010863, 25.04.2021 04:25 term:

*Suppose you drop a tennis ball from a height, №18010863, 25.04.2021 04:25

So, our common ratio is *Suppose you drop a tennis ball from a height, №18010863, 25.04.2021 04:25.

We already know our initial term, *Suppose you drop a tennis ball from a height, №18010863, 25.04.2021 04:25 is 15, so we get:

*Suppose you drop a tennis ball from a height, №18010863, 25.04.2021 04:25

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Mathematics
Step-by-step answer
P Answered by Master

The explicit formula is a_n=15(\frac{4}{5})^{n-1}.

Step-by-step explanation:

First, we need to find the common ratio. We know this is a geometric sequence because the decrease from one term to the next is not a constant number.

To find the constant ratio, we can take the 2^{nd} term and divide by the 1^{st} term:

\frac{2nd}{1st}=\frac{12}{15}=\frac{4}{5}

So, our common ratio is r=\frac{4}{5}.

We already know our initial term, a_0 is 15, so we get:

a_n=a_0(r)^{n-1}\\a_n=15(\frac{4}{5})^{n-1}

Mathematics
Step-by-step answer
P Answered by PhD
The answer is in the image 

The answer is in the image 

Mathematics
Step-by-step answer
P Answered by PhD

Here,

tip=18%of $32

tip=(18/100)*32

=0.18*32

=$5.76

Total payment=32+5.76=$37.76

Mathematics
Step-by-step answer
P Answered by PhD

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Mathematics
Step-by-step answer
P Answered by PhD

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

Mathematics
Step-by-step answer
P Answered by PhD

30% of 420 are first year students

first year students = (30/100 )*420

=126 students

Student who are not in first year = 420-126

=294 students  

Mathematics
Step-by-step answer
P Answered by PhD

Let the father's age be x and son's be y

10 years before-

Father age=x-10

sons age=y-10

Given,

x-10=10(y-10)

x-10=10y-100

Given present age of father=40

therefore,

x=40

40-10=10y-100

10y-100=30

10y=130

y=130/10

y=13

Therefore present age of son=13years

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