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Jlenok [28]
3 years ago
6

Srinivasa Ramanujan, the great East Indian mathematician, was invited to Cambridge University in England in 1914 by the English

mathematician G. H. Hardy. One day Ramanujan was ill in the hospital, and Hardy came to visit him. Hardy remarked that he had come in taxicab #1729, and said that he thought that this was an entirely uninteresting number. Ramanujan instantly replied, "Oh no! 1,729 is the smallest number that can be written as the sum of two cubes in two different ways."
The table below shows two patterns of numbers. The pattern in the top row represents the counting numbers. The pattern in the second row consists of the cubes of the counting numbers.

Which two pairs of numbers have cubes that add up to 1,729? Because there are two pairs of numbers to find, you should select a total of four numbers from the list below.

A. 8
B. 7
C. 12
D. 11
E. 10
F. 9
G. 1
H. 2
I. 3
J. 4
K. 5
L. 6
Mathematics
2 answers:
ale4655 [162]3 years ago
6 0

Answer:

1,10,9,12 for APEX

Step-by-step explanation:


kotegsom [21]3 years ago
3 0
(12,1):12³+1³=1728+1=1729
(10,9): 10³+9³=1000+729=1729
☺☺☺☺
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11Alexandr11 [23.1K]
W² - v + 1

(-2)² - (-8) + 1

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B.13 is your answer

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-20x+27

Step-by-step explanation:

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On a coordinate plane, parallelogram R S T U has points (negative 4, 4), (2, 6), (6, 2), and (0, 0). What is the area of paralle
Ad libitum [116K]

Answer:

The area of the parallelogram is;

32 square units

Step-by-step explanation:

The given parameters are;

The coordinates of the parallelogram RSTU = R(-4, 4), S(2, 6), T(6, 2), and U(0, 0)

We note that the area of a parallelogram = Base length × Height

From the drawing of the parallelogram RSTU, we have;

The base length = The length of \overline {TU} = The length of \overline {SR} = √((2 - (-4))² + (6 - 4)²) = 2·√10

The height of a parallelogram is perpendicular to its base length = The line \overline {VT}

∴ Where, the slope of the base length = m, the slope of the height = -1/m

The slope, 'm' of \overline {SR} = (6 - 4)/(2 - (-4)) = 1/3

Therefore, the slope of the height = -1/(1/3) = -3

We note that a point on the height is the point 'T', therefore, the equation of the line in point and slope form is therefore;

y - 0 = -3·(x - 0)

∴ y = -3·x

Therefore, the coordinates of the point 'V' is given by the simultaneous solution of the equations of \overline {SR} and \overline {VT}

The equation of the line \overline {SR} in point and slope form from the point 'R' and the slope 'm = 1/3' is given as follows;

y - 4 = (1/3) × (x - (-4)) = (1/3) × (x + 4)

y = x/3 + 4/3 + 4 = x/3 + 16/3

y = x/3 + 16/3

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x = -1.6

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y = 4.8

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The height of the parallelogram = 8/5·√10

The area of the parallelogram, A = Base length × Height

∴ A = 2·√(10) × 8/5·√(10) = (16/5) × 10 = 32

The area of the parallelogram, A =  32 square units.

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