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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Answer from: 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

Answer from: Quest

Answer for 2: his profit would be $2.88 explanation: you have to first multiply 72 and 0.12 together to get $8.64 once you do that you know how much money the shopkeeper made from selling the candy bars individually. so you have to do 8.64-5.76=2.88 hope that ; )answer for 3: yeah i’m sorry i have no idea what number 3 is. i’m sorry i couldn’t with that.
I'm going to add u to plsss answer questions 2 n 3

I'm going to add u to plsss answer questions 2 n 3

Answer from: Quest

percentage - 25%

probability - 0.25

we know,

total amount of students in class = 20

total boys = 10

total girls = 10

no of girls who wear glasses = 10/2 = 5

probability of choosing a girl with glasses is =

number of girls wearing glasses/total number of students in the class = 5/20

thus, percentage of selecting a girl wearing glasses will be

= 5/20 × 100

= 5 × 5

25%

therefore,

probability will be 0.25

happy to

pls mark as brainliest

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