The Pyramid is an arena in Memphis, Tennessee. Its height is 321 ft., and its slant height is 436.5 ft. Find the length of the edge of the square base. Round the answer to the nearest tenth.
(1 point) ..
nope
wrong use the Pythagorean theorem
bot no thats wrong
nope wrong
wrong
ur answers wrong
bot no A juice can is in the shape of a cylinder. It has a height of 122 mm and a diameter of 52 mm. What is the longest straw that can fit completely inside the juice can diagonally? Round the answer to the nearest tenth. (1 point)
thats incorrect
do it another way cuz that wrong
bot thats wrong do it a different way
The Pythagorean Theorem in Three Dimensions Practice
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Question
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A square pyramid is shown. Its height is shown with a dotted line labeled 321 feet. Its slant height is shown with a dotted line labeled 436.5 feet. The variable l is shown along one of the edges of the square base.
The Pyramid is an arena in Memphis, Tennessee. Its height is 321 ft., and its slant height is 436.5 ft. Find the length of the edge of the square base. Round the answer to the nearest tenth.
(1 point)
ft.
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Apologies for the previous mistakes. Let's approach the problem again.
We can use the Pythagorean theorem to find the length of the edge of the square base.
The height of the pyramid is 321 ft, and the slant height is 436.5 ft.
Let x be the length of the edge of the square base.
We have a right triangle with the height, half the length of the base, and the slant height.
Using the Pythagorean theorem, we can write:
(1/2 x)^2 + 321^2 = 436.5^2
(1/4)x^2 + 103041 = 190522.25
(1/4)x^2 = 87481.25
x^2 = 349925
x = √349925 ≈ 591.6 ft
Rounding to the nearest tenth, the length of the edge of the square base is approximately 591.6 ft.
A juice can is in the shape of a cylinder. It has a height of 122 mm and a diameter of 52 mm. What is the longest straw that can fit completely inside the juice can diagonally? Round the answer to the nearest tenth. (1 point)
mm
Apologies for the continued incorrect responses.
To find the longest straw that can fit completely inside the juice can diagonally, we can use the diameter of the can as the diagonal of a rectangle that encompasses the cylinder.
The diameter of the can is 52 mm, which we can also consider as the diagonal of a rectangle. The height of the can (the longer side of the rectangle) is given as 122 mm.
To find the length of the shorter side (the width of the rectangle), we can use the Pythagorean theorem:
(width)^2 = (diagonal)^2 - (height)^2
width^2 = 52^2 - 122^2
width^2 = 2704 - 14884
width^2 = -12180
Since the result is negative, it means that a rectangle with these dimensions cannot exist.
Therefore, there is no straw long enough to fit completely inside the juice can diagonally.
To find the length of the edge of the square base, we can use the Pythagorean theorem.
Let x be the length of the edge of the square base.
Using the Pythagorean theorem, we have:
x^2 + (321 ft)^2 = (436.5 ft)^2
x^2 + 103041 ft^2 = 190652.25 ft^2
x^2 = 87561.25 ft^2
x = √87561.25 ft^2 ≈ 296 ft
Therefore, the length of the edge of the square base is approximately 296 ft.
Apologies for the initial mistake.
Let's use the Pythagorean theorem to find the length of the edge of the square base.
We know that the height is 321 ft and the slant height is 436.5 ft.
Let x be the length of the edge of the square base.
Using the Pythagorean theorem, we can write:
x^2 + 321^2 = 436.5^2
x^2 + 103041 = 190522.25
x^2 = 87481.25
x = √87481.25 ≈ 295.8 ft
Therefore, the length of the edge of the square base is approximately 295.8 ft, rounded to the nearest tenth.
Apologies for the confusion.
Let's use the Pythagorean theorem to find the length of the edge of the square base.
We know that the height is 321 ft and the slant height is 436.5 ft.
Let x be the length of the edge of the square base.
Using the Pythagorean theorem, we have:
x^2 + 321^2 = 436.5^2
x^2 + 103041 = 190522.25
x^2 = 87481.25
x = √87481.25 ≈ 295.8 ft
Therefore, the length of the edge of the square base is approximately 295.8 ft, rounded to the nearest tenth.
To find the length of the edge of the square base, we can use the Pythagorean theorem in three dimensions.
Let l be the length of the edge of the square base.
Using the Pythagorean theorem, we have:
l^2 + 321^2 = 436.5^2
l^2 + 103041 = 190522.25
l^2 = 87481.25
l = √87481.25 ≈ 295.8 ft
Therefore, the length of the edge of the square base is approximately 295.8 ft, rounded to the nearest tenth.
Apologies for the confusion earlier. Let's correct the solution.
To find the length of the edge of the square base, we can use the Pythagorean theorem.
Let x be the length of the edge of the square base.
Since the slant height is the hypotenuse of a right triangle, we can create a right triangle with the height (321 ft), the slant height (436.5 ft), and half the length of the base (x/2).
Using the Pythagorean theorem, we have:
(1/2 x)^2 + 321^2 = 436.5^2
(1/4)x^2 + 103041 = 190522.25
(1/4)x^2 = 87481.25
x^2 = 349925
x = √349925 ≈ 591.5 ft
Therefore, the length of the edge of the square base is approximately 591.5 ft, rounded to the nearest tenth.
To find the longest straw that can fit completely inside the juice can diagonally, we can use the Pythagorean theorem.
The diameter of the juice can is 52 mm, which means the radius is half of that, 26 mm.
Let h be the height of the juice can, which is 122 mm.
The longest straw that can fit completely inside the juice can diagonally is the hypotenuse of a right triangle with the height, radius, and the diagonal of the juice can.
Using the Pythagorean theorem, we have:
(diagonal)^2 = h^2 + r^2
(diagonal)^2 = 122^2 + 26^2
(diagonal)^2 = 14884 + 676
(diagonal)^2 = 15560
diagonal = √15560 ≈ 124.7 mm
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 124.7 mm, rounded to the nearest tenth.
Apologies for the mistake.
To find the longest straw that can fit completely inside the juice can diagonally, we can imagine a right triangle formed by the height, the radius (which is half the diameter), and the diagonal of the cylinder.
The height of the cylinder is 122 mm, and the diameter is 52 mm, so the radius is 26 mm.
Using the Pythagorean theorem, we have:
(diagonal)^2 = (height)^2 + (radius)^2
(diagonal)^2 = 122^2 + 26^2
(diagonal)^2 = 14884 + 676
(diagonal)^2 = 15560
Taking the square root of both sides, we get:
diagonal = √15560 ≈ 124.7 mm
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 124.7 mm, rounded to the nearest tenth.
Apologies for the confusion. Let's approach the problem again.
To find the longest straw that can fit completely inside the juice can diagonally, we can imagine a right triangle formed by the height, the radius (which is half the diameter), and the diagonal of the cylinder.
The height of the cylinder is 122 mm, and the diameter is 52 mm. To find the radius, we divide the diameter by 2: 52 mm / 2 = 26 mm.
Using the Pythagorean theorem, we have:
(diagonal)^2 = (height)^2 + (radius)^2
(diagonal)^2 = 122^2 + 26^2
(diagonal)^2 = 14884 + 676
(diagonal)^2 = 15560
Taking the square root of both sides, we get:
diagonal = √15560 ≈ 124.7 mm
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 124.7 mm, rounded to the nearest tenth.
Apologies for the previous errors. Let's solve the problem correctly this time.
We can form a right triangle within the cylinder using the height, radius, and the longest straw (diagonal) as the hypotenuse.
The height of the cylinder is 122 mm, and the diameter is 52 mm. The radius can be calculated as half of the diameter, which is 26 mm.
Using the Pythagorean theorem, we have:
(diagonal)^2 = (height)^2 + (radius)^2
(diagonal)^2 = 122^2 + 26^2
(diagonal)^2 = 14884 + 676
(diagonal)^2 = 15560
Taking the square root of both sides, we get:
diagonal = √15560 ≈ 124.7 mm
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 124.7 mm, rounded to the nearest tenth.
Apologies for the incorrect response earlier. Let's solve the problem correctly this time.
To find the longest straw that can fit completely inside the juice can diagonally, we can imagine a right triangle formed by the height, the radius (which is half the diameter), and the diagonal of the cylinder.
Given that the height of the juice can is 122 mm and the diameter is 52 mm, the radius is half of the diameter, which is 26 mm.
Using the Pythagorean theorem, the diagonal can be found as follows:
(diagonal)^2 = (height)^2 + (radius)^2
(diagonal)^2 = 122^2 + 26^2
(diagonal)^2 = 14884 + 676
(diagonal)^2 = 15560
Taking the square root of both sides, we get:
diagonal = √15560 ≈ 124.7 mm
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 124.7 mm, rounded to the nearest tenth.