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Vika [28.1K]
2 years ago
14

1) A 1.5 kg apple pie is sitting on the kitchen counter . If it has 13.44 J of gravitational potential energy, how tall is the c

ounter it sits on?
2) A suitcase weighing 120 N sits on a counter 1.8 m high in the airport. How much energy does it have?

plsss answer 1&2 and also show work
Mathematics
1 answer:
vampirchik [111]2 years ago
8 0

a)

Answer: 0.91 m

Explanation:

We know that,

P.E. = m g h

Where,

P.E = Potential energy

m = Mass of the object

g = acceleration due to gravity (9.8 m/s²)

It is given that, m = 1.5 kg

P.E. = 13.44 J

⇒ 13.44 = 1.5 kg × 9.8 m/s² × h

⇒ h = 0.91 m

Hence, apple sits om 0.91 m tall counter.

b)

Answer: 216 J

Explanation:

P.E. = m g h

Weight, mg = 120 N ( given)

height, h = 1.8 m ( given)

The energy possessed by the suitcase is due to virtue of its position (gravitational potential energy)

P.E. = 120 N × 1.8 m = 216 J

Hence, the energy possessed by the suitcase sitting on the counter is 216 J.

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Suppose that public opinion in a large city is 55% in favor of increasing taxes to support renewable energy and 45% against such
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Answer:

The approximate probability that more than 360 of these people will be against increasing taxes is P(Z> <u>0.6-0.45)</u>

                                              √0.45*0.55/600

The right answer is B.

Step-by-step explanation:

According to the given data we have the following:

sample size, h=600

probability against increase tax p=0.45

The probability that in a sample of 600 people, more that 360 people will be against increasing taxes.

We find that P(P>360/600)=P(P>0.6)

The sample proposition of p is approximately normally distributed mith mean p=0.45

standard deviation σ=√P(1-P)/n=√0.45(1-0.45)/600

If x≅N(u,σ∧∧-2), then z=(x-u)/σ≅N(0,1)

Now, P(P>0.6)=P(<u>P-P</u>   >     <u>0.6-0.45)</u>

                             σ          √0.45*0.55/600

=P(Z> <u>0.6-0.45)</u>

       √0.45*0.55/600

8 0
2 years ago
In 2013, the national debt was
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Answer:

You can use a calculator for the decimal operations, but practice some by hand because on the quiz and the test you will not have a calculator.

Step-by-step explanation:

7 0
2 years ago
what is the simplified form of the following expression? Assume x is greater than or equal to 0 and y is greater than or equal t
yarga [219]

the given expression is :

2(4√16x) - 2(4√2y) + 34√81x - 4(4√32y)

⇒ 8(√16x) - 8(√2y) + 34√81x - 16√32y  

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⇒32√x - 8√2y + 306√x - 16×4√2y

⇒(32√x + 306√x) - 8√2y  - 16×4√2y      

⇒338√x -72√2y

4 0
2 years ago
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The function D(t) defines a traveler's distance from home, in miles, as a function of time, in hours. D(t) = StartLayout enlarge
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- At 2 hours, the traveler is 725 miles from home.

- At 3 hours, the distance is constant, at 880 miles. --> TRUE.

- The total distance from home after 6 hours is 1,062.5 miles --> TRUE.

Step-by-step explanation:

The function D(t) is defined as follows:

D(t) = 300t+125 for t< 2.5

D(t) = 880 for 2.5 \leq 3.5

D(t) = 75t+612.5 for t\leq 6

Where

t is the time in hours

D(t) is the distance covered, in miles, after t hours

Now let's analyze the different statements:

- The starting distance, at 0 hours, is 300 miles. --> FALSE. In fact, if we substitute t = 0 into the 1st equation, we get

D(0) = (300)(0)+125 = 125

So, the distance at t = 0 is 125 miles.

- At 2 hours, the traveler is 725 miles from home. --> TRUE. In fact, if we substitute t = 2 into the 1st equation,

D(2) = (300)(2)+125 = 725

- At 2.5 hours, the traveler is 875 miles from home. --> FALSE. In fact, for t=2.5 we have to use the 2nd equation, which states that the distance is:

D(t) = 880

So, not 875 miles.

- At 3 hours, the distance is constant, at 880 miles. --> TRUE. This is clearly visible from the 2nd equation: for t between 2.5 and 3.5 (so, in this case), the distance is

D(t) = 880

- The total distance from home after 6 hours is 1,062.5 miles --> TRUE. In fact, if we replace t = 6 into the last equation,

D(6)) = 75(6)+612.5=1062.5

Learn more about functions:

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Learn more about  distance:

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S(t) =  -4.9t^2 + 19.6t + 24.5

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so we have -4.9t^2 + 19.6t + 24.5 = 0

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(t + 1)(t - 5) = 0

so required time t = 5 seconds  

answer 5 seconds

5 0
2 years ago
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