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Degger [83]
3 years ago
14

The Palace of Peace and Accord in Astana, Kazakhstan, was built in 200620062006. The building has a square right pyramid structu

re. The length of a side of the square base is 62\,\text{m}62m62, start text, m, end text, and the vertical height of the pyramid is also 62\,\text{m}62m62, start text, m, end text.
What is the height, hhh, of one of the triangular faces?

Round your answer to the nearest tenth.
Mathematics
1 answer:
Anastaziya [24]3 years ago
3 0

Answer: h= 69.3m

Step-by-step explanation:

The correct values in the question are:

year : 2006, length 62, vertical height 62.

So, the measure asked is called slant height . we have to apply the formula:

sh = √(vh^2 + [L/2]^2)

Where:  

vh= vertical height

L= length of a side of the square base

Replacing with the values given:

sh= √(62^2 + [62/2]^2)

sh = √(3,844 + 31^2)

sh= √(3,844 + 961)

sh = √4,805

hs= 69.31 =69.3 m (nearest tenth)

Since in the question that height is called h, h= 69.3

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Find the solutions to 2x^5-5x^3-3x=0. What are the x-intercepts of the graph of the function f(x)=2x^5-5x^3-3x?
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Answer:

Solution

roots: ((-\sqrt{3} )   (0,0)   (\sqrt{3})

domain X∈3

vertical intercept (0,0)

x = {0, -1.732050808, 1.732050808}  

Please, find attached images equation graphs

Step-by-step explanation:

Simplifying

2x5 + -5x3 + -3x = 0

Reorder the terms:

-3x + -5x3 + 2x5 = 0

Solving

-3x + -5x3 + 2x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.

x(-3 + -5x2 + 2x4) = 0

Factor a trinomial.

x((-1 + -2x2)(3 + -1x2)) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve:

Simplifying

x = 0

Solving

x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying

x = 0

Subproblem 2

Set the factor '(-1 + -2x2)' equal to zero and attempt to solve:

Simplifying

-1 + -2x2 = 0

Solving

-1 + -2x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.

-1 + 1 + -2x2 = 0 + 1

Combine like terms: -1 + 1 = 0

0 + -2x2 = 0 + 1

-2x2 = 0 + 1

Combine like terms: 0 + 1 = 1

-2x2 = 1

Divide each side by '-2'.

x2 = -0.5

Simplifying

x2 = -0.5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3

Set the factor '(3 + -1x2)' equal to zero and attempt to solve:

Simplifying

3 + -1x2 = 0

Solving

3 + -1x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.

3 + -3 + -1x2 = 0 + -3

Combine like terms: 3 + -3 = 0

0 + -1x2 = 0 + -3

-1x2 = 0 + -3

Combine like terms: 0 + -3 = -3

-1x2 = -3

Divide each side by '-1'.

x2 = 3

Simplifying

x2 = 3

Take the square root of each side:

x = {-1.732050808, 1.732050808}

Solution

x = {0, -1.732050808, 1.732050808}

3 0
3 years ago
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