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2 years ago

The sum of four odd integers is 296. What is the greatest of the four consecutive odd integers

Mathematics

1 answer:

exis [7]2 years ago

8 0

Answer: 77

Step-by-step explanation:

Let the four odd numbers be represented as a, b, c and d.

a + b + c + d = 296

b = a+2 ( since they are consecutive and odd)

c = a+4

d = a+6

Then, substitute the values gotten into the original equation. This will be:

a + (a+2) + (a+4) + (a+6) = 296

4a +2 +4 +6 = 296

4a +12 = 296

Then, collect like terms

4a + 12 = 296

4a = 296 - 12

4a = 284

Divide both sides by 4

4a/4 = 284/4

a = 71

If a is 71,

b = a + 2 = 71+ 2 = 73

c = a + 4 = 71 + 4 = 75

d = a + 6 = 71 + 6 = 77

The greatest of the four consecutive odd integers is 77.

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Answer:

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b. height of the building = 1384 ft

c. Angle of elevation from the surveyor to the top of the antenna = 38.31°

d. Height of antenna = 237.08 ft

Step-by-step explanation:

The picture above is a illustration of the described event.

a = the height of the flag

b = the height of the building

c = distance of the surveyor from the base of the building

the angle of elevation from the position of the surveyor on the ground to the top of the building = 34°

distance from her position to the top of the building = 2475 ft

distance from her position to the top of the flag = 2615 ft

(a) How far away from the base of the building is the surveyor located?

using the SOHCAHTOA principle

cos 34° = c/2475

c = 0.8290375726 × 2475

c = 2051.8679921

c = 2051.90 ft

(b) How tall is the building

The height of the building = b

sin 34° = opposite /hypotenuse

0.5591929035 = b/2475

b = 0.5591929035 × 2475

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(c) What is the angle of elevation from the surveyor to the top of the antenna?

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cos ∅ = 0.784665392

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∅ = 38.31°

(d) How tall is the antenna?

height of the antenna = a

sin 38.31° = opposite/hypotenuse

sin 38.31° = (a + b)/2615

sin 38.31° × 2615 = (a + b)

(a + b) = 0.6199159917 × 2615

(a + b) = 1621.0803182

(a + b) = 1621. 08 ft

Height of antenna = 1621. 08 - 1384.00 = 237.08031822 ft

Height of antenna = 237.08 ft

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