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Oliga [24]
3 years ago
8

For alln∈N≥1(son≥1), and usingweakinduction, prove that:n∑i=1i3=[n(n+ 1)2]2Note that this result means that the sum of t

he third powers of the first strictly positive integers is equal to the sum of the same integers, squared=

Mathematics
1 answer:
kirill [66]3 years ago
8 0

Answer:

Step-by-step explanation:

hello,

the question is not really clear. i believe the intended equation would be

\sum_{k=1}^{k=n} k^3=\frac{(n(n+1))}{4}

please check the attached file for the step by step proof.

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What is 19.6 divided by 7
Lemur [1.5K]
19 divided by 7 = 2.8
7 0
3 years ago
200 kg of brass is melted down and cast into ornamental frogs, each weight 3/20kg. How many frogs are made?
Savatey [412]

Answer:

1,333 frogs

Step-by-step explanation:

okay so we know that mass remains conserved no matter where you are.

same here ^^

if the total mass of brass is 200 kg

the total mass of the new frogs formed from it when put together will be the same :)

and if there were n such frogs formed

we have,

total mass = n × mass of each frog

200 = n × 3/ 20

n = 4000/ 3

so it becomes something like 1,333.33

that is nearly 1,333 frogs can be made out of 200 kg of brass each weighing 3/ 20kg (the last ones a bit less to make upto 200kg)

5 0
3 years ago
A boat travels 32 miles on 4 gallons of fuel. How many miles per half gallon is that?
Firdavs [7]
The answer is 4 miles
7 0
3 years ago
Whats the rate if 13 inches of snow in 7 hours
dem82 [27]

Answer:

1.86 (rounded to nearest hundredth) inches of snow in 1 hour

Step-by-step explanation:

Divide 13 inches of snow by 7 hours

The answer is 1.8571428571428571428571428571429

Round to the nearest hundredth

1.86

Hope this helped :)

5 0
3 years ago
Read 2 more answers
Solve the equation by completing the square round to the nearest hundredth is necessary x^2-x-7=0
masha68 [24]

The answers are 3.19 or -2.19.

In order to complete the square, you must first get the constant to the other side of the equation. WE do that by adding 7 to both sides.

x^2 - x - 7 = 0

x^2 - x = 7

Now we must take half of the x coefficient (-1), which would be -.5. Then we square it and add it to both sides. This is the second step to any completing the square problem.

x^2 - x = 7

x^2 - x + .25 = 7.25

Now that we have done that, the left side will be a perfect square so that, we can factor it.

x^2 - x + .25 = 7.25

(x - .5)^2 = 7.25

After having done that, we can take the square root of both sides

(x - .5)^2 = 7.25

x - .5 = +/-\sqrt{7.25}

Now we can take the value of that square root and solve.

x - .5 = +/-\sqrt{7.25}

x - .5 = +/-2.69

x = .5 +/- 2.69

And with the + and - both there, we need to do both to get the two answers.

.5 + 2.69 = 3.19

.5 - 2.69 = -2.19

4 0
3 years ago
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