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The statements that are true about the pyramid are
- The base of the pyramid is a square with four sides, each measuring 756 feet.
- The slant height of the pyramid is 612 feet.
- All four triangular faces are congruent.
- The pyramid has four lateral faces.
From the question, we are to determine the statements that are true about the pyramid
The diagram shows a square pyramid,
The length of a side of its base is 756 ft
and
The height / altitude of a triangular face is 612 ft
Since the pyramid is a square pyramid,
Then, the base must be a square with each side measuring 756 feet
∴ The first statement is true
Since the height of a triangular face is 612 ft,
Then,
∴ The slant height of the pyramid is 612 feet
NOTE: Slant height of a pyramid is the altitude of the triangle comprising a lateral face
Thus, the second statement is true
Since the triangular faces each have a base of 756ft and a height of 612 ft,
Then,
All four triangular faces are congruent
∴ The fourth statement is true
NOTE: Lateral sides of a solid are the faces on the <u>sides</u> of the shape
The pyramid has four lateral faces which are each a triangle
∴ The last statement is true
Hence, the statements that are true about the pyramid are
- The base of the pyramid is a square with four sides, each measuring 756 feet.
- The slant height of the pyramid is 612 feet.
- All four triangular faces are congruent.
- The pyramid has four lateral faces.
Learn more on Pyramid here: brainly.com/question/10042135
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Answer:
<u>Volume = 1.535</u>
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Step-by-step explanation:
The region R is bounded by the equations:
y = √sin⁻¹x
y = √(π/2)
y = √(π/3)
x = 0
R is revolved around the x-axis so we will need f(y) for finding out the volume. We need to make x the subject of the equation and then replace it with f(y).
f(x) = √sin⁻¹x
y = √sin⁻¹x
Squaring both sides we get:
y² = sin⁻¹x
x = sin (y²)
f(y) = sin (y²)
Using the Shell Method to find the volume of the solid when R is revolved around the x-axis:
The limits a and b are the equations y = √(π/2) and y = √(π/3) which bound the region R. So, a = √(π/2) and b = √(π/3).
V = 2π sin (y²) dy
Integrating sin (y²) dy, we get:
-cos(y²)/2y
So,
V = 2π [-cos(y²)/2y] with limits √(π/2) and √(π/3)
V = 2π [(-cos(√(π/2) ²)/2*√(π/2)] - [(-cos(√(π/3) ²)/2*√(π/3)]
V = 2π [(-cos(π/2)/ 2√(π/2)) - ((-cos(π/3)/ 2√(π/3))]
V = 2π [ 0 - (-0.5/2.0466)]
V = 2π (0.2443)
V = 1.53499 ≅ 1.535
Answer:
4n+2
Step-by-step explanation:
The common difference between the terms is 4 which means that the sequence is an arithmetic sequence.
The general formula for arithmetic sequence is:
where a_n is the nth term, a_0 is the first term and d is the common difference between them.
We know that
Putting the value in general formula:
So the generalized pattern is 4n+2 ..