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Serjik [45]
3 years ago
11

2. How long does this lease last?

Mathematics
1 answer:
Tatiana [17]3 years ago
7 0

Answer:

akeijd

Step-by-step explanation:

kahshsarihaieie

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A right triangle has base x meters and height h meters, where h is constant and x changes with respect to time t, measured in se
aksik [14]

The relationship between dθ/dt, the rate of change of θ with respect to time, and dx/dt, the rate of change of x with respect to time is \frac{d\theta}{dt}  = \frac{h}{x\sqrt{x^2+y^2} }\frac{dx}{dt}

Given the following parameters:

  • Adjacent side = x
  • Opposite side = h
  • The angle of elevation = θ

According to SOH CAH TOA identity;

tan \theta =\frac{Opposite}{Adjacent}

Substitute the given values into the formula

tan \theta =\frac{h}{x}

\theta= tan^{-1}\frac{h}{x}

Differentiate with respect to x

\frac{d \theta}{dx} = \frac{h}{x\sqrt{x^2+y^2} }

According to the chain rule,

\frac{d\theta}{dt} =\frac{d\theta}{dx} \times \frac{dx}{dt}\\\frac{d\theta}{dt}  = \frac{h}{x\sqrt{x^2+y^2} }\frac{dx}{dt}

Hence the relationship between dθ/dt, the rate of change of θ with respect to time, and dx/dt, the rate of change of x with respect to time is \frac{d\theta}{dt}  = \frac{h}{x\sqrt{x^2+y^2} }\frac{dx}{dt}

Learn more on the rate of change here: brainly.com/question/11883878

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