1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
d1i1m1o1n [39]
2 years ago
10

A hot air balloon hovers above its launch site at an altitude of 100 meters. The pilot of the balloon sights a parking lot at a

12˚ angle of depression. To the nearest meter, what is the horizontal distance between the parking lot and the launch site?
Mathematics
1 answer:
IgorLugansk [536]2 years ago
6 0

Answer:

The horizontal distance between the parking lot and the launch site is 470 meters

Step-by-step explanation:

Let

x----->  the horizontal distance between the parking lot and the launch site

we know that

The tangent of angle of 12 degrees is equal to divide the altitude of 100 meters by the horizontal distance

so

tan(12°)=100/x

Solve for x

x=100/tan(12°)=470 meters

You might be interested in
Solve by Factoring<br><br> 3b^4−6b^2+27b
Ganezh [65]

Answer:

Step-by-step explanation:

hello :

3b^4−6b^2+27b = 3b(b^3-2b+9)

8 0
2 years ago
420/98 rounded to the nearest integer?
trapecia [35]

Answer:

4

Step-by-step explanation:

420 divided by 98 is 4.28571428571, therefore rounding would make the answer 4!

6 0
2 years ago
5 is to 7 as is to 49
Ostrovityanka [42]
5 is to 7 as is to 49 is to 51
3 0
2 years ago
Given P = x^0.3 y^0.7 is the chicken lay eggs production function, where P is the number of eggs lay, x is the number of workers
lora16 [44]

Answer:

Part A)

\displaystyle \frac{dy}{dx}=-\frac{3}{7}P^\frac{10}{7}x^{-\frac{10}{7}}

Part B)

The daily operating cost decreases by about $143 per extra worker.

Step-by-step explanation:

We are given the equation:

\displaystyle P=x^{\frac{3}{10}}y^{\frac{7}{10}}

Where <em>P</em> is the number of eggs laid, <em>x</em> is the number of workers, and <em>y</em> is the daily operating budget (assuming in US dollars $).

A)

We want to find dy/dx.

So, let’s find our equation in terms of <em>x</em>. We can raise both sides to 10/7. Hence:

\displaystyle P^\frac{10}{7}=\Big(x^\frac{3}{10}y^\frac{7}{10}\Big)^\frac{10}{7}

Simplify:

\displaystyle P^\frac{10}{7}=x^\frac{3}{7}y

Divide both sides by<em> </em>the <em>x</em> term to acquire:

\displaystyle y=P^\frac{10}{7}x^{-\frac{3}{7}}

Take the derivative of both sides with respect to <em>x: </em>

\displaystyle \frac{dy}{dx}=\frac{d}{dx}\Big[P^\frac{10}{7}x^{-\frac{3}{7}}\Big]

Apply power rule. Note that P is simply a constant. Hence:

\displaystyle \frac{dy}{dx}=P^\frac{10}{7}(-\frac{3}{7})(x^{-\frac{10}{7}})

Simplify. Hence, our derivative is:

\displaystyle \frac{dy}{dx}=-\frac{3}{7}P^\frac{10}{7}x^{-\frac{10}{7}}

Part B)

We want to evaluate the derivative when <em>x</em> is 30 and when <em>y</em> is $10,000.

First, we will need to find <em>P</em>. Our original equations tells us that:

P=x^{0.3}y^{0.7}

Hence, at <em>x</em> = 30 and at <em>y</em> = 10,000, <em>P </em>is:

P=(30)^{0.3}(10000)^{0.7}

Therefore, for our derivative, we will have:

\displaystyle \frac{dy}{dx}=-\frac{3}{7}\Big(30^{0.3}(10000^{0.7})\Big)^\frac{10}{7}\Big(30^{-\frac{10}{7}}\Big)

Use a calculator. So:

\displaystyle \frac{dy}{dx}=-\frac{1000}{7}=-142.857142...\approx-143

Our derivative is given by dy/dx. So, it represents the change in the daily operating cost over the change in the number of workers.

So, when there are 30 workers with a daily operating cost of $10,000 producing a total of about 1750 eggs, the daily operating cost decreases by about $143 per extra worker.

5 0
2 years ago
Find where the function is increasing and decreasing. G(x)=1/x^2 +7
eduard
Inc on (-inf,0)
Dec on (0,inf)
3 0
3 years ago
Other questions:
  • This is the question​
    5·2 answers
  • Find area of a squares with a side lengths of 6 ft round to the nearest hundredth
    6·1 answer
  • Find the surface area of the regular pyramid shown to the nearest whole number. <br><br> Thank you.
    15·1 answer
  • Which of the following is the next number in the series 3,6,4,9,5,12,6,_
    11·1 answer
  • Find the complementary angle of 73.8 (Type an integer or a decimal.) is Enter your answer in the answer box
    5·1 answer
  • There are 25 prime numbers between 1 and 100. There are 46 prime numbers between 1 and 200. Which situation is more likely? Expl
    7·1 answer
  • Find the value of x. (Picture attached.)
    15·1 answer
  • PLZ HELP ME ITS DUE RIGHT NOW
    10·1 answer
  • If a man can weave 450m in 6 hours. How many metres of cloth can he weave in 12 hors
    9·1 answer
  • I have no clue how to start this problem,plz help
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!