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4 years ago

Solve (2.5x10^-8)(9x10^-10)

Mathematics

1 answer:

aleksandrvk [35]4 years ago

6 0

(2.5×10⁻⁸)(9×10⁻¹⁰) = 2.5×9×10⁻⁸⁻¹⁰ = 22.5×10⁻¹⁸

= 2.25×10⁻¹⁷

_____

The rules of exponents apply.

... 10^a × 10^b = 10^(a+b)

... 22.5 = 2.25 × 10¹

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A man standing on the roof of a building 64.0 feet high looks down to the building next door. He finds the angle of depression t

8_murik_8 [283]

Answer:

The height of the next door building is 41.7 feet

Step-by-step explanation:

* Lets study the situation in the problem

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- The angle of depression to roof of the next door building is 34.7°

- The angle of depression to the bottom of the next door building

is 63.3°

- We need to find the height of the next door building

* Lets consider the height of the man building and the horizontal

distance between the two building formed a right triangle and the

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- Let the horizontal distance between the two buildings called x

# In the triangle

∵ The length of the side opposite to the angle of depression (63.3°)

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∵ The length of the horizontal distance is x which is adjacent to the

angle of depression (63.3°)

- Use the trigonometry function tanФ = opposite/adjacent

∴ tan 63.3° = 64.0/x ⇒ use cross multiplication

∴ x (tan 63.3°) = 64 ⇒ divide both sides by (tan 63.3°)

∴ x = 64.0/(tan 63.3°)

∴ x = 32.1886 feet

- Lets use this horizontal distance to find the vertical distance between

the roofs of the two buildings

* Lets consider the height of the vertical distance between the roofs

of the two buildings and the horizontal distance between the two

building formed a right triangle and the

angle of depression is opposite to the side which represented the

vertical distance between the roofs of the two buildings

- Let the vertical distance between the roofs of the two buildings

called y

# In the triangle

∵ The vertical distance between the roofs of the two buildings is y

and opposite to the angle of depression (34.7°)

∵ The horizontal distance x is adjacent to the angle of

depression (34.7°)

∴ tan (34.7°) = y/x

∵ x = 32.1886

∴ tan 34.7° = y/32.1886 ⇒ use the cross multiplication

∴ y = 32.1886 (tan 34.7°)

∴ y = 22.2884 ≅ 22.3 feet

∴ The vertical distance between the roofs of the two

buildings is 22.3 feet

- The height of the next door building is the difference between the

height of the man building and the vertical distance between the

roofs of the two buildings

∴ The height of the next door building = 64.0 - 22.3 = 41.7 feet

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