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3 years ago

A blimp is flying parallel to a road and is 2460 feet directly above it. The angles of depression of two parked

Mathematics

1 answer:

Nina [5.8K]3 years ago

4 0

Answer:

‭1419.42‬ feet

Step-by-step explanation:

Let y be the height of the blimp above the cars and x₁ be the distance from the blimp to the first car at an angle of depression of 34.99° and x₂ be the distance from the blimp to the second car at an angle of depression of 26.5°.

From trigonometric ratios,

tan34.99° = y/x₁ and tan26.5° = y/x₂

So, x₁ = yt/an34.99° and x₂ = y/tan26.5°

So, the distance between the cars is thus d = x₂ - x₁ = y/tan26.5° - y/tan34.99°= y(1/tan26.5° - 1/tan34.99°) = y(cot26.5° - cot34.99°)

Since y = height of blimp above the road = 2460 feet, substituting it into the equation, we have,

d = 2460(cot26.5° - cot34.99°)

d = 2460(2.0057 - 1.4287)

d = 2460(0.577)

d = ‭1419.42‬ feet

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Read 2 more answers

Consider the function below. g(x) = 4x − 1 Find the difference quotient below (where h ≠ 0) and simplify your answer. g(x + h) −

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Step-by-step explanation:

Given that:

$g(x) = 4x - 1$

To find:

Difference quotient = ?

where $h \neq 0$

Solution:

Formula for Difference quotient is given as:

$\dfrac{g(x+h)-g(x)}{h}$

First of all, let us find out $g(x+h)$

Replacing $x$ with $x+h$

$g(x+h) = 4(x+h)-1 \\\Rightarrow g(x+h) = 4x+4h-1$

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$g(x+h)-g(x) = (4x+4h-1 )-(4x-1)\\\Rightarrow g(x+h)-g(x) = 4x+4h-1 -4x+1\\\Rightarrow g(x+h)-g(x) = 4h$

Putting the above value in:

$\dfrac{g(x+h)-g(x)}{h} = \dfrac{4h}{h}$

We are given that, $h \neq 0$

$\therefore \dfrac{4h}{h} = 4$

So, the difference quotient is 4.

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