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4 years ago

If you could find answers to both questions that would be great thx

Mathematics

1 answer:

mario62 [17]4 years ago

8 0

Answer:

3) -5 and 5

4) 17 and - 17

Step-by-step explanation:

y^2 - 1 = 24

y = 25

y = √25

y = - 5 and y = 5

x^2 = 289

x = √289

x = 17 and x = - 17

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A sculpture is in the shape of a square pyramid. The sculpture has a height of 6 meters and a volume of 50 cubic meters. Find th

Anton [14]

Answer : a link for your answer<em> https://quizlet.com/140197143/surface-area-and-volume-surface-area-of-rectangular-pyramids-flash-cards/</em>

<em>Step-by-step explanation:</em>

4 0

3 years ago

Read 2 more answers

Prove that if x is an positive real number such that x + x^-1 is an integer, then x^3 + x^-3 is an integer as well.

Shkiper50 [21]

Answer:

By closure property of multiplication and addition of integers,

If $x + \dfrac{1}{x}$ is an integer

∴ $\left ( x + \dfrac{1}{x} \right) ^3 = x^3 + \dfrac{1}{x^3} +3\cdot \left (x + \dfrac{1}{x} \right )$ is an integer

From which we have;

$x^3 + \dfrac{1}{x^3}$ is an integer

Step-by-step explanation:

The given expression for the positive integer is x + x⁻¹

The given expression can be written as follows;

$x + \dfrac{1}{x}$

By finding the given expression raised to the power 3, sing Wolfram Alpha online, we we have;

$\left ( x + \dfrac{1}{x} \right) ^3 = x^3 + \dfrac{1}{x^3} +3\cdot x + \dfrac{3}{x}$

By simplification of the cube of the given integer expressions, we have;

$\left ( x + \dfrac{1}{x} \right) ^3 = x^3 + \dfrac{1}{x^3} +3\cdot \left (x + \dfrac{1}{x} \right )$

Therefore, we have;

$\left ( x + \dfrac{1}{x} \right) ^3 - 3\cdot \left (x + \dfrac{1}{x} \right )= x^3 + \dfrac{1}{x^3}$

By rearranging, we get;

$x^3 + \dfrac{1}{x^3} = \left ( x + \dfrac{1}{x} \right) ^3 - 3\cdot \left (x + \dfrac{1}{x} \right )$

Given that $x + \dfrac{1}{x}$ is an integer, from the closure property, the product of two integers is always an integer, we have;

$\left ( x + \dfrac{1}{x} \right) ^3$ is an integer and $3\cdot \left (x + \dfrac{1}{x} \right )$ is also an integer

Similarly the sum of two integers is always an integer, we have;

$\left ( x + \dfrac{1}{x} \right) ^3 + \left(- 3\cdot \left (x + \dfrac{1}{x} \right ) \right )$ is an integer

$\therefore x^3 + \dfrac{1}{x^3} = \left ( x + \dfrac{1}{x} \right) ^3 - 3\cdot \left (x + \dfrac{1}{x} \right )= \left ( x + \dfrac{1}{x} \right) ^3 + \left(- 3\cdot \left (x + \dfrac{1}{x} \right ) \right )$ is an integer

From which we have;

$x^3 + \dfrac{1}{x^3}$ is an integer.

4 0

3 years ago

Simplify the expression. 1/2 (-sin2x - cos 2x)

maria [59]

Answer:

1/2 (-sin2x - cos 2x)

Step-by-step explanation:

Distribute 1/2 to every term in the parentheses

4 0

3 years ago

Solve the equation x/3-5=y for x

Annette [7]

X/3-5=y
add 5 to both sides
x/3=y+5
now multiply both sides by 3
x=3(y+5)
which means
x=3y+15

6 0

3 years ago

What number is 0.001 more than 437.999

sergij07 [2.7K]

Answer:

437.999 + 0.001 = 438

Step-by-step explanation:

8 0

3 years ago