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soldier1979 [14.2K]
3 years ago
13

A triangular pyramid is formed from three right triangles as shown below.

Mathematics
1 answer:
Lady bird [3.3K]3 years ago
7 0

ΔADC is a right angle triangle, we will use the Pythagorus Theorem to find the length CD.

Formula of the Pythagorus Theorem :  

⇒ a² + b² = c²

⇒ AD² + CD² = AC²

The value of AD is 54 and the value of AC is 90:

54² + CD² = 90²

Solve for CD:

54² + CD² = 90²

CD² = 90² - 54²

CD² = 5184

CD = √5184

CD = 72

ΔADC is also a right angle triangle, we will use the Pythagorus Theorem to find the length BD.

Formula of the Pythagorus Theorem :  

⇒ a² + b² = c²

⇒ BD² + CD² = BC²

The value of CD is 72 and the value of BC is 97:

BD² + 72² = 97²

Solve for BD:

BD² = 97² - 72²

BD² = 4225

BD = √4225

BD = 65

Answer: The length of BD is 65 units.

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Answer:

a) 0.145

b) 0.013

c) 0.783

d) 0.586

Step-by-step explanation:

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b) there are always 13 diamonds in a complete card

Pb = 13/52 × 12/51× 11/50 = 11/850 = 0.013

c) there are always 4 aces, and 48 that are not aces

Pc = 48/52 × 47/51 × 46/50 = 4324/5525 = 0.783

d) there are 13 hearts,to get at least one heart we have.

Pd = 1 - p

Where p is the probability of no hearts

p = 39/52 × 38/51 × 37/50 = 703/1700 = 0.414

Pd = 1 - 0.414

Pd = 0.586

4 0
4 years ago
Write equivalent fractions for 3^3 bottom 4 and 1^2 bottom 3
Rufina [12.5K]

\tt \dfrac{3^3}{4}=\dfrac{27}{4}\\\\\dfrac{1^2}{3}=\dfrac{1}{3}

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2 years ago
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A mother gives birth to triplets. The individual weights of the babies at birth are 4 lb 2 oz, 4 lb 5 oz, and 3 lb 13 oz. Find t
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Answer:

You mean just add them together?

Step-by-step explanation:

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3 years ago
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HELP ASAP
Sliva [168]

Answer: 13.74

Step-by-step explanation:

to find out the total cost we will:

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8 0
3 years ago
Luis made some trail mix .He mixed 4 2/3 cups of popcorn ,1 1/4 cups of peanuts ,1 1/3 cups of raisins ,and 3/4 cup of sunflower
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So you have to add all the fractions together and then divide by five. When dealing with mixed fractions i like to add the whole numbers first, then add the fractions:
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the whole numbers:  4 + 1 + 1 = 6
then we are left with 2/3, 1/4, 1/3, 3/4
add the ones with common denominators together to make it easiest: 2/3 + 1/3 = 3/3 = 1 (another whole number! add it to 6 to get 7)
now we are left with 1/4 + 3/4 = 4/4 = 1 (another whole number! add it to 7 to get 8)
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