Mathematics, 29.05.2021 20:20, Tylobones

A weather balloon is rising vertically at the rate of 10 ft s . An observer is standing on the ground 300 ft horizontally from the point where the balloon was released. At what rate is the distance between the observer and the balloon changing when the balloon is 400 ft height

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answered: babygirlqueen5588

The distance between the observer and the balloon is increasing at a rate 8 feet per second.

Step-by-step explanation:

Let be A the point at which the observer is located, O the initial location of the weather balloon and B is the current location above the ground. Since the weather balloon is rising vertically and the distance between its initial position and the position of the observer, we can represent all distances by the Pythagorean Theorem:

$r^{2} = h^{2} + (300\,ft)^{2}$ (1)

Where:

- Distance between observer and current position of the weather balloon, in feet.

- Current height of the weather balloon above ground, in feet.

By Differential Calculus, we derive an expression for the rate of change of the distance between observer and current position of the weather balloon ( $\dot r$ ), in feet per second:

$2\cdot r \cdot \dot r = 2\cdot h \cdot \dot h$

$\dot r = \frac{h\cdot \dot h}{r}$

$\dot r = \frac{h\cdot \dot h}{\sqrt{h^{2}+ (300\,ft)^{2}}}$ (2)

Where $\dot h$ is the rate of change of the height of the weather balloon, in feet per second.

If we know that $h = 400\,ft$ and $\dot h = 10\,\frac{ft}{s}$ , then the rate of change of the distance between the observer and the balloon is:

$\dot r = \frac{(400\,ft)\cdot \left(10\,\frac{ft}{s} \right)}{500\,ft}$

$\dot r = 8\,\frac{ft}{s}$

The distance between the observer and the balloon is increasing at a rate 8 feet per second.

A weather balloon is rising vertically at the rate of 10 ft s . An observer is standing on the groun

answered: Guest

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answered: Guest

whole numbers.

step-by-step explanation:

we are given the average monthly rainfall (in millimeters) model r(m) for the years 1900-2009 as a function of the month number m.

as we can see m is taken for the number of months for years 1900-2009.

we know that number of months can't be a negative number or decimal number or a fraction.

so, the number of months could be only positive whole numbers.

therefore, whole numbers is more appropriate for the domain of r.

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A weather balloon is rising vertically at the rate of 10 ft s . An observer is standing on the groun...