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AveGali [126]
1 year ago
13

Can someone help me with this question on Prodigy? ​

Mathematics
1 answer:
lions [1.4K]1 year ago
4 0

Answer:

  8 +(3/8)√53 in² ≈ 10.73 in²

Step-by-step explanation:

Given the net of a triangular pyramid with some of the dimensions filled in, you want to find the total surface area.

<h3>Triangle base</h3>

The triangle bases identified by dashed lines will have a length equal to the hypotenuse of the right triangles with legs shown as solid lines. The legs of each of those right triangles are ...

  a = (3 in)/2 = 1.5 in

  b = 2 in . . . . . . shown as the altitude of the triangle

Then the hypotenuse is found using the Pythagorean theorem:

  c² = a² +b²

  c² = 1.5² +2² = 2.25 +4 = 6.25

  c = √6.25 = 2.5

The dashed lines are 2.5 inches long.

<h3>Triangle altitude</h3>

The altitude from the solid horizontal line to the vertex at the bottom of the figure can be found using the fact that all of the outside edge lengths of the net are the same length. That edge length is found as the length of the hypotenuse of the right triangles in the left- and right-sides of the upper portion of the net. Each of those has a leg that is (2.5 in)/2 = 1.25 in and a leg marked as 2 in.

  c² = a² +b²

  c² = 1.25² +2² = 1.5625 +4 = 5.5625

  c = (√89)/4 ≈ 2.358 . . . in

The unmarked altitude of the bottom triangle is then ...

  b² = c² -a²

  b² = 89/16 -1.5² = 53/16

  b = (√53)/4 ≈ 1.820 . . . in

<h3>Surface area</h3>

The surface area of the figure is the sum of the areas of the four triangles that make up the net. Each triangle has an area given by the formula ...

  A = 1/2bh

The left and right triangles have b=2.5, h=2, so they each have an area of ...

  A = 1/2(2.5)(2) = 2.5 . . . . in²

The center triangle has dimensions of b=3, h=2, so an area of ...

  A = 1/2(3)(2) = 3 . . . . in²

The bottom triangle has dimensions of b=3, h=(√53)/4, so an area of ...

  A = 1/2(3)(√53/4) = (3/8)√53 ≈ 2.730 . . . . in²

The total surface area is the sum of the areas of these triangles, so is ...

  A = 2.5 in² +2.5 in² +3 in² +2.73 in² = 10.73 in²

The surface area of the triangular pyramid is (64+3√53)/8 ≈ 10.73 in².

__

<em>Additional comment</em>

Often we work with pyramids that are rotationally symmetrical about a vertical line through the peak. This one is not. The altitude of the bottom triangle in the net is less than the altitude of the other triangles. This short face of the pyramid will tend to be more vertical than the other two lateral faces.

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timama [110]

The prime factorization of 240 is 2^{4} . 3 . 5 ⇒ last answer

Step-by-step explanation:

Prime number is the number that has only 2 factors 1 and itself

{2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , ............}

In prime factorization we use only the prime numbers

Ex: The factors of 15 are 1 , 3 , 5 , 15,

      Then the prime factors of 15 are 3 and 5 only because they are

       prime numbers

So to find the prime factors of a number do that

1. Factorize the number by divide it using prime numbers only

2. Write the number as a product of its prime factors

∵ 240 divisible by first prime number 2

∴ 240 ÷ 2 = 120

∵ 120 ÷ 2 = 60

∵ 60 ÷ 2 = 30

∵ 30 ÷ 2 = 15

- We divided the number by 2 for 4 times

∴ 2^{4} is a prime factor of 240

∵ 15 is divisible by prime number 3

∴ 15 ÷ 3 = 5

∴ 3 is a prime factor of 240

∵ 5 is divisible by prime number 5

∴ 5 ÷ 5 = 1

∴ 5 is a prime factor of 240

∴ The prime factors of 240 are 2^{4} , 3 , 5

The prime factorization of 240 is 2^{4} . 3 . 5

Learn more:

You can learn more about factors in brainly.com/question/5194236

#LearnwithBrainly

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Sandra decided to bake blackberry pies to sell at the county fair. She had $180 in her savings
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Answer:

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Step-by-step explanation:

-5t-2(5t+10t)=100

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