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seraphim [82]
3 years ago
7

A balloon lifts off the ground and reaches a height of 200m. The total mass of the balloon is 1000 kg. What is the GPE of the ba

lloon?
Mathematics
1 answer:
raketka [301]3 years ago
4 0

Answer:

1,960,000Joules

Step-by-step explanation:

Gravitational Potential Energy is expressed as;

GPE = mgh

m is the mass

g is the acceleration due to gravity

h is the height

Given

m = 1000kg

h = 200m

g = 9.8m/s

Substitute;

GPE  = 1000 * 9.8 * 200

GPE = 9800 * 200

GPE = 1,960,000Joules

Hence the GPE of the balloon is 1,960,000Joules

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Determine formula of the nth term 2, 6, 12 20 30,42​
nalin [4]

Check the forward differences of the sequence.

If \{a_n\} = \{2,6,12,20,30,42,\ldots\}, then let \{b_n\} be the sequence of first-order differences of \{a_n\}. That is, for n ≥ 1,

b_n = a_{n+1} - a_n

so that \{b_n\} = \{4, 6, 8, 10, 12, \ldots\}.

Let \{c_n\} be the sequence of differences of \{b_n\},

c_n = b_{n+1} - b_n

and we see that this is a constant sequence, \{c_n\} = \{2, 2, 2, 2, \ldots\}. In other words, \{b_n\} is an arithmetic sequence with common difference between terms of 2. That is,

2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2

and we can solve for b_n in terms of b_1=4:

b_{n+1} = b_n + 2

b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2

b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2

and so on down to

b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)

We solve for a_n in the same way.

2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)

Then

a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)

a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))

a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))

and so on down to

a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2

\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}

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2 years ago
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Step-by-step explanation:

5 0
3 years ago
Who failed to support civil rights for freed slaves? (wrong category by mistake, not mathematics)
dangina [55]

Answer:

The Supreme Court.

Step-by-step explanation:

After the end of the Civil War and the enactment of the Thirteenth Amendment in 1865, slavery was officially abolished in the United States. Thus, the millions of African American slaves that inhabited the southern states of the country won their freedom and equality before the law against whites.

Now this situation began to dismember in 1877, when federal troops left the southern states and Reconstruction officially came to an end. From then on, Democratic governors and legislators began to sanction the Black Codes and Jim Crow Laws, aimed at curtailing the civil and political rights of African-Americans.

This situation was tested before the Supreme Court in 1896 in the case Plessy v. Ferguson. But in the ruling of said case, the Supreme Court established that racial segregation was constitutional and therefore neglected African Americans and their rights.

8 0
4 years ago
Are the points U, H, and L collinear?<br> U<br> E<br> S<br> H
butalik [34]

Answer:

Yes

Step-by-step explanation:

Collinear means points are lying on the same straight line. U, H, and L are all lying on the line l.

4 0
3 years ago
Which are true about the area of a circle? Check all that apply. The diameter is used in the formula. The units are always squar
jenyasd209 [6]

Answer:

selected the correct ones in bold

Step-by-step explanation:

The diameter is used in the formula. The units are always squared. The area can be found when given the diameter by first finding the radius. The area is the distance around the circle. Circumference can be used to find area.

8 1
4 years ago
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