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antiseptic1488 [7]
2 years ago
13

Can you see an easy way to work out the value of

3%20%2B%204%5E3%20%2B%205%5E3" id="TexFormula1" title="\sqrt{ 1^3 + 2^3 + 3^3 + 4^3 + 5^3" alt="\sqrt{ 1^3 + 2^3 + 3^3 + 4^3 + 5^3" align="absmiddle" class="latex-formula"> ? if so, describe it.
Mathematics
1 answer:
Lina20 [59]2 years ago
5 0

We have the sum of cubes identity

a^3 + b^3 = (a + b) (a^2 - ab + b^2)

and observing that 1 + 4 = 2 + 3, we have

1^3 + 4^3 = (1 + 4) (1^2 - 4 + 4^2) = 5 \times 13

and

2^3 + 3^3 = (2 + 3) (2^2 - 6 + 3^2) = 5 \times 7

Then

\sqrt{1^3+2^3+3^3+4^3+5^3} = \sqrt{5\times13 + 5\times7 + 5\times5^2} = \sqrt{5 \times (20 + 25)} \\\\ ~~~~~~~~ = \sqrt{5^2 \times (4 + 5)} = \sqrt{5^2\times9} = \sqrt{5^2\times3^2} = 5\times3 = \boxed{15}

Alternatively, we have the well-known sum of cubes formula

\displaystyle \sum_{i=1}^n i^3 = \frac{n^2(n+1)^2}4

The sum under the square root is this sum with n=5. Then

1^3+2^3+3^3+4^3+5^3 = \dfrac{5^2\times6^2}4 = 225 = 15^2

and so the square root again reduces to 15.

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mafiozo [28]

Answer:

140

Step-by-step explanation:

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2 years ago
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cestrela7 [59]
What do you need help with
6 0
3 years ago
Please help! will give brainlist
Alchen [17]

Answer:

C. Slope is 2

Step-by-step explanation:

Since this equation is written in the y=mx+b equation, 2 would be the slope, because any number that comes before x (AKA "m") is always the slope. For example, if you were trying to find the slope for the equation y=4x+19, 4 would be the slope.

5 0
3 years ago
Can someone help me with these
Trava [24]
Short answer
For 6: 72 ft^2
For 7: 650 m^2

Six
The base is a square. It's measurement is s = 4
Base = 4^2 
Base = 16 ft^2

One triangle 
A = 1/2 * b * h
A = 1/2 * 4 * 7
A = 14 tt^2

Four triangles
A = 4 * 14
A = 56 ft^2

Total Area = 56 + 16 = 72 ft^2
Answer 72 square feet

Seven
Triangles
Area of 1 triangle = 1/2 * 10 * 13
Area of 1 triangle = 65


Area of 6 triangles
Area of 6 triangles = 6 * area of 1 triangle
Area of 6 triangles = 390

Base
As near as I can tell, the base is a hexagon. It's using a rather out of the way method of drawing it. I will assume it is a regular hexagon. The area of a regular hexagon is 3 sqrt(3)/2 * S^2 where s is the side of the hexagon.

Area = 3sqrt(3)/2 s^2
s = 10
Area = 3sqrt(3)/2 10^2
Area = 5.1962 * 100 /2
Area = 259.81

Total area
Total area = area of the base + area of the triangles
Total area = 259.81 + 390
Total area (rounded ) = 650

Answer C <<<< answer 

I'll do one more in this batch and then you'll need to repost again.

Eight

If you draw two diagonals on the base of the figure, the intersection point will meet the base of the height. Read that a couple of times.
Join the intersection to the midpoint of the length of the square bottom.  You should get 3.5

x is found by using the pythagorean theorem.
h = 6
s = 3.5
x = ????

x^2 = 6^2 + 3.5^2
x^2 = 36 + 12.25
x^2 = 48.25
x = sqrt(48.25)
x = 6.95 

C <<<< answer

 


8 0
3 years ago
What is an equation of the line that passes through the points (4,4) and (8.1)
andrey2020 [161]

Answer:

  • y = - 3/4x + 7

Step-by-step explanation:

<u>Use both points and find the slope:</u>

  • m = (1 - 4) / (8 - 4) = - 3/4

<u>Find the line, using point-slope form and point (4, 4):</u>

  • y - 4 = - 3/4(x - 4)
  • y - 4 = - 3/4x + 3
  • y = - 3/4x + 7
5 0
2 years ago
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