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nirvana33 [79]
3 years ago
11

Wild Water Park

Mathematics
2 answers:
telo118 [61]3 years ago
6 0
Answer:
$44.00

Explanation:

Because you including three friends
Make up 4 people and if you multiply the prices my 4 and then add them up and subtract by $100 then you will get $44.00 dollars back
hram777 [196]3 years ago
4 0

Answer: your change is $44

Step-by-step explanation:

The cost of each water rides at the

Wild Water Park are

The Slip $2.00

The Slide $5.50

The Splash $6.50

You and three friends are going to Wild Water Park. Your group plans to ride each water ride one time. This means 4 of you will ride each water ride one time. Therefore,

Cost of riding the slip = 4 × 2 = $8

Cost of riding the slide = 4 × 5.5 = $22

Cost of riding the splash = 4 × 6.5 = $26

Total cost of riding the 3 water rides is

8 + 22 + 26 = $56

Amount of change that you would get back from a $100 bill is

100 - 56 = $44

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A mass of 3.25 kg is attached to the end of a spring that is stretched 22 cm by a force of 15 N. It is set in motion with an ini
mylen [45]

Answer:

Step-by-step explanation:

Given that,

Mass of object=3.25kg

The extension e=22cm=0.22m

Force applied to cause extension F=15N

Initial position Xo=0

Initial velocity Vo=-12m/s

We can get the spring constant from Hooke's law

F=ke

Then, k=F/e

k=15/0.22

k=68.182N/m

Also our natural frequency w is given as

w=√(k/m)

Therefore,

w=√(68.182/3.24)

w=√20.98

w=√21

w=4.58rad/s

w=4.6rad/s

There is no damping in this situation, no outside force acting on the system and the equation that governs the system is

mx''+kx=0

3.25x''+68.182x=0

Divide through by 3.25

x''+20.98x=0

We can approximate 20.98 to 21

x"+21x=0

The solution to this differential equation using D operator

D²+21=0

D²=-21

D= ±√-21

D=±√21 •i

Then the solution is

x(t)=A•Sinwt +B•Coswt

x(t)=A•Sin√21 t +B•Cos√21 t

Note that x'(t)=v(t)

and at t=0 Vo=-12m/s

x(t)=A•Sin√21 t +B•Cos√21 t

x'(t)=v(t)=A√21•Cos√21 t - B√21•Sin√21 t

v(t)=A√21•Cos√21 t - B√21•Sin√21 t

Then, using the two initial conditions

v(0)=-12

And X(0)=0

x(t)=A•Sin√21 t +B•Cos√21 t

X(0)=A•Sin√21•0 +B•Cos√21•0

X(0)=A•Sin0+B•Cos0

0=B

B=0

Also,, V(0)=-12m/s

v(t)=A√21•Cos√21 t - B√21•Sin√21 t

V(0)=A√21•Cos√21•0- B√21•Sin√21•0

V(0)=A√21•Cos0- B√21•Sin0

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A=-12/√21

A=-2.62

Therefore the general equation becomes

x(t)=A•Sin√21 t +B•Cos√21 t

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x(t)=-2.62Sin√21 t

a. The amplitude

Comparing x(t) to wave equations

x(t)=-Asin(wt+2λ/t)

Then,

A=2.62m

b. We know the natural frequency already to be

w=√21

w=4.58rad/s

c. Period

Comparing the equation again

wt=√21t

Given that w=2πf

Therefore, 2πft=√21t

Then, f=√21t / 2πt

f=√21/2π

f=0.73Hz

Then, period is the reciprocal of frequency

T=1/f

T=1/0.73

T=1.37seconds

The period is 1.37sec,

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You went for a run on Monday.

You then went on a run on Tuesday as well. On this day you ran 2.41 km and it is said that you ran the same distance on both days which means you ran for 2.41 km on Monday as well.

The total distance you ran is therefore:

= 2.41 + 2.41

= 4.82 km

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Step-by-step explanation:

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