AP CAL AB HELP!
A plane flying with a constant speed of 14 km/min passes over a ground radar station at an altitude of 11 km and climbs at an angle of 25 degrees. At what rate is the distance from the plane to the radar station increasing 4 minutes later?
The distance is increasing at equation editorEquation Editor____ km/min.

Answers

Answer 1

Answer:

[tex]\frac{dc}{dt}\approx13.8146\text{ km/min}[/tex]

Step-by-step explanation:

We know that the plane travels at a constant speed of 14 km/min.

It passes over a radar station at a altitude of 11 km and climbs at an angle of 25°.

We want to find the rate at which the distance from the plane to the radar station is increasing 4 minutes later. In other words, if you will please refer to the figure, we want to find dc/dt.

First, let's find c, the distance. We can use the law of cosines:

[tex]c^2=a^2+b^2-2ab\cos(C)[/tex]

We know that the plane travels at a constant rate of 14 km/min. So, after 4 minutes, the plane would've traveled 14(4) or 56 km So, a is 56, b is a constant 11. C is 90+20 or 115°. Substitute:

[tex]c^2=(56)^2+(11)^2-2(56)(11)\cos(115)[/tex]

Evaluate:

[tex]c^2=3257-1232\cos(115)[/tex]

Take the square root of both sides:

[tex]c=\sqrt{3257-1232\cos(115)}[/tex]

Now, let's return to our law of cosines. We have:

[tex]c^2=a^2+b^2-2ab\cos(C)[/tex]

We want to find dc/dt. So, let's take the derivative of both sides with respect to t:

[tex]\frac{d}{dt}[c^2]=\frac{d}{dt}[a^2+b^2-2ab\cos(C)][/tex]

Since our b is constant at 11 km, we can substitute this in:

[tex]\frac{d}{dt}[c^2]=\frac{d}{dt}[a^2-(11)^2-2a(11)\cos(C)][/tex]

Evaluate:

[tex]\frac{d}{dt}[c^2]=\frac{d}{dt}[a^2-121-22a\cos(C)][/tex]

Implicitly differentiate:

[tex]2c\frac{dc}{dt}=2a\frac{da}{dt}-22\cos(115)\frac{da}{dt}[/tex]

Divide both sides by 2c:

[tex]\frac{dc}{dt}=\frac{2a\frac{da}{dt}-22\cos(115)\frac{da}{dt}}{2c}[/tex]

Solve for dc/dt. We already know that da/dt is 14 km/min. a is 56. We also know c. Substitute in these values:

[tex]\frac{dc}{dt}=\frac{2(56)(14)-22\cos(115)(14)}{2\sqrt{3257-1232\cos(115)}}[/tex]

Simplify:

[tex]\frac{dc}{dt}=\frac{1568-308\cos(115)}{2\sqrt{3257-1232\cos(115)}}[/tex]

Use a calculator. So:

[tex]\frac{dc}{dt}\approx13.8146\text{ km/min}[/tex]

And we're done!

AP CAL AB HELP!A Plane Flying With A Constant Speed Of 14 Km/min Passes Over A Ground Radar Station At

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Answer:

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Step-by-step explanation:

Ok so, this question looks intimidating but I promise it's not that bad.

a) They're asking how much water (L - meaning liters) would be needed for 25 baths.

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Step-by-step explanation:

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Step-by-step explanation:

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THE DISTANCE BETWEEN LONDON AND CARDIFF IS 150 MILES WHAT IS THE DISTANCE IN KILOMETER

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Answers

Answer: x = 10

Step-by-step explanation:

The value of unknown variable x for the parallel lines AB and CD with given angles is equal to 15°.

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Answer:

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Hi there.

Glad to see you using Brainly!

Equation:

a^2-b^2c^2

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After:

a^2 - (b c)^2

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[tex] {a}^{2} - {b}^{2} {c}^{2} = (a - bc)(a + bc) [/tex]

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Answer:

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Step-by-step explanation:

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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

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Answers

Answer:

Three fourths of the theater that is 500 seats is 375 seats.

Your answer is 375 seats.

Step-by-step explanation:

Okay, so to find 3/4 of 500 the first thing you want to do is set up an equation. To find 3/4 of 500 you want to multiply 500 by 3/4 so here's your equation.

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

If the marked price of an article is Rs.x, discount amount is
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Answer:

The marked price of an article is Rs. x, and selling price is Rs. y

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Answers

Answer:

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Stephanie took a science exam that had two parts.

Part 1: She got 16 questions correct, which was 4/5 of the number of part 1 questions.
Part 2: She got 16 questions correct, which was 2/3 of the number of part 2 questions.
What was the total number of questions on Stephanie’s exam?

Answers

Answer:

44 questions

Step-by-step explanation:

Part 1: She got 16 questions correct, which was 4/5 of the number of part 1 questions.

Let x = total number of questions in part 1

4/5x = 16

Divide both sides by 4/5

x = 16 ÷ 4/5

= 16 × 5/4

= 20

x = 20

There are 20 questions in part 1

She got 16 questions correct, which was 2/3 of the number of part 2 questions.

Let y = number of questions in part 2

2/3y = 16

Divide both sides by 2/3

y = 16 ÷ 2/3

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simplifying radicals
[tex] \sqrt{20m {}^{4} } n {}^{3} [/tex]

Answers

Answer: 2m^2n.\sqrt{5}  

Step-by-step explanation: Factor 20 into its prime factors

          20 = 22 • 5  

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

Factors which will be extracted are :

          4 = 22  

Factors which will remain inside the root are :

          5 = 5  

To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :

          2 = 2  

At the end of this step the partly simplified SQRT looks like this:

        2 • sqrt (5m4n3)  

Rules for simplifing variables which may be raised to a power:

  (1) variables with no exponent stay inside the radical

  (2) variables raised to power 1 or (-1) stay inside the radical

  (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

     (3.1) sqrt(x8)=x4

    (3.2) sqrt(x-6)=x-3

   (4) variables raised to an odd exponent which is  >2  or  <(-2) , examples:

     (4.1) sqrt(x5)=x2•sqrt(x)

    (4.2) sqrt(x-7)=x-3•sqrt(x-1)

Applying these rules to our case we find out that

     SQRT(m4n3) = m2n • SQRT(n)

sqrt (20m4n3) =

       2 m2n • sqrt(5n)  

2 m2n • sqrt(5n)

solve equation 2(4b-6)=4(3b-7)

Answers

Answer:

2(4b - 6) = 4(3b - 7)

This is

8b - 12 = 12b - 28

Now,

16 = 4b

This means that b = 4 :)

Answer:

[tex]\boxed {b = 4}[/tex]

Step-by-step explanation:

Solve for the value of [tex]b[/tex]:

[tex]2(4b - 6) = 4(3b - 7)[/tex]

-Use Distributive Property:

[tex]2(4b - 6) = 4(3b - 7)[/tex]

[tex]8b - 12 = 12b - 28[/tex]

-Take [tex]12b[/tex] and subtract it from [tex]8b[/tex]:

[tex]8b - 12 - 12b = 12b - 12b - 28[/tex]

[tex]-4b - 12 = -28[/tex]

-Add [tex]12[/tex] to both sides:

[tex]-4b - 12 + 12 = -28 + 12[/tex]

[tex]-4b = -16[/tex]

-Divide both sides by [tex]-4[/tex]:

[tex]\frac{-4b}{-4} = \frac{-16}{-4}[/tex]

[tex]\boxed {b = 4}[/tex]

So. therefore, the value of [tex]b[/tex] is [tex]4[/tex].

What is the value of x in the equation 3 x minus 4 y equals 65, when y equals 4?

A. x equals 13 and one-fourth
B. x equals 21 and two-thirds
C. x= 23
D. x=27

Answers

Answer:

x = 27

Step-by-step explanation:

3x-4y = 65

Let y = 4

3x - 4*4 = 65

3x -16 = 65

Add 16 to each side

3x-16+16 = 65+16

3x  = 81

Divide each side by 3

3x/3 = 81/3

x = 27

X=27 Is the answer the rest of them are wrong.

Please help this is in pre algebra

Answers

Answer:

2nd Option

Step-by-step explanation:

Exponent Rule: [tex]b^{-m} =\frac{1}{b^m}[/tex]

Daniel is buying a video game that costs $52.99. The sales tax is found by multiplying the cost of the video game by 0.07. How much is the sales tax for the video game?

Answers

i got $3.70 for sales tax

Answer:

$3.71

Step-by-step explanation:

52.99*1.07=56.6993

56.6993-52.99=3.7093

3.7093 rounded to the nearest hundredth is 3.71

So therefore, the sales tax is $3.71

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