If x is increasing at a
rate of 2 units per second,
find the rate of change of theta
at the instant when x= 12 units.

If X Is Increasing At Arate Of 2 Units Per Second,find The Rate Of Change Of Theta At The Instant When

Answers

Answer 1

Answer:

[tex]\frac{d\theta}{dt}=-\frac{2}{5}[/tex] at [tex]x=12[/tex]

Step-by-step explanation:

[tex]\frac{dx}{dt}=2[/tex]

[tex]\frac{d\theta}{dt}=?[/tex]

[tex]x=12[/tex]

[tex]cos(\theta)=\frac{adjacent}{hypotenuse}[/tex]

[tex]cos(\theta)=\frac{x}{13}[/tex]

[tex]\frac{d}{dt}cos(\theta)=\frac{d}{dt}\frac{x}{13}[/tex]

[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{1}{13}\frac{dx}{dt}[/tex]

[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{1}{13}(2)[/tex]

[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{2}{13}[/tex]

[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(\theta)}[/tex]

[tex]cos(\theta)=\frac{x}{13}[/tex]

[tex]cos(\theta)=\frac{12}{13}[/tex]

[tex]\theta=cos^{-1}(\frac{12}{13})[/tex]

[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(\theta)}[/tex]

[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(cos^{-1}(\frac{12}{13}))}[/tex]

[tex]\frac{d\theta}{dt}=\frac{2}{-13(\frac{5}{13})}[/tex]

[tex]\frac{d\theta}{dt}=\frac{2}{-5}[/tex]

[tex]\frac{d\theta}{dt}=-\frac{2}{5}[/tex]

Answer 2

The value of θ is given by the inverse sine function, from which the rate of

change of θ with respect to x can be derived.

The rate of change of θ at the instant when x = 12 units is -0.4 rad/s

Reasons:

[tex]\displaystyle \frac{dx}{dt} = \mathbf{2 \ units \ per \ second}[/tex]

[tex]\displaystyle cos(\theta) = \frac{x}{13}[/tex]

[tex]\displaystyle \theta = arccos \left(\frac{x}{13}\right)[/tex]

[tex]\displaystyle \frac{d}{dx} \theta = \frac{d\left(arccos \left(\frac{x}{13}\right)\right)}{dx} = \mathbf{\frac{\sqrt{169-x^2} }{x^2-169}}[/tex]

Using chain rule of differentiation, we have;

[tex]\displaystyle \frac{d\theta}{dt} = \mathbf{ \frac{d\theta}{dx} \times \frac{dx}{dt}}[/tex]

Therefore;

[tex]\displaystyle \frac{d\theta}{dt} =\frac{\sqrt{169-x^2} }{x^2-169}\times \frac{dx}{dt} = \mathbf{\frac{\sqrt{169-x^2} }{x^2-169}\times 2}[/tex]

When x = 12, we get;

[tex]\displaystyle \frac{d\theta}{dt} =\frac{\sqrt{169-12^2} }{12^2-169}\times 2 = -\frac{2}{5} = -0.4[/tex]

The rate of change of the angle, θ, with time at the instant when x = 12 is -0.4 rad/s

Learn more about rate of change here:

https://brainly.com/question/24686935


Related Questions

A rectangular pool is 6 meters wide and 8 meters long. If you swim diagonally across the pool, how many meters would you be swimming?

Answers

If you swim diagonally across the rectangular pool, the distance you swim is 10 meters.

Given the following data:

Width of rectangle = 6 metersLength of rectangle = 8 meters

To determine the distance you swim in meters, we would apply Pythagorean's theorem since the width is along the x-axis while the length is along the y-axis.

Note: The diagonal side of the rectangular pool represents the hypotenuse.

Mathematically, Pythagorean's theorem is given by the formula:

[tex]Hypotenuse^2 = Opposite^2 + Adjacent^2[/tex]

Substituting the given parameters into the formula, we have;

[tex]Hypotenuse^2 = 6^2 + 8^2\\\\Hypotenuse^2 = 36+64\\\\Hypotenuse^2 = 100\\\\Hypotenuse = \sqrt{100}[/tex]

Hypotenuse = 10 meters.

Read more here: https://brainly.com/question/18890335

Yoni has a ribbon that measures 5/3 yards. She wants to cut it into 3 equal pieces. What is the length of each piece of ribbon? 5\8 yards 5/6 yards 5/9 yards 5/3 yards

Answers

Answer:

5/9 yards

Step-by-step explanation:

[tex] \frac{5}{3} \div \frac{3}{1} \\ = \frac{5}{3} \times \frac{1}{3} \\ = \frac{5}{9} [/tex]

I need help with this please​

Answers

0.25 but half but 26:26 Its same but half of half ....

whats -2 - 19t if t=-1​

Answers

Answer:

17

Step-by-step explanation:

-2 - 19 x -1

-2 + 19(because two negatives make a positive)

17

Answer:

17 is the answer.

Step-by-step explanation:

Given:

t = -1

Let's substitute.

=> -2 - 19t

=> -2 - 19(-1)

=> -2 - (-19)

=> -2 + 19

=> 17

Therefore, 17 is the answer.

Hoped this helped.

Select the graph of the function f(x) = 4+ 1/x+6

Answers

Answer:

F(x) = 4+ 1/x + 6 = 10x + 1

                                    x

how many seconds are there in 3 minute By the process ​

Answers

Answer:

Step-by-step explanation:

You can easily convert 3 minutes into seconds using each unit definition:

Minutes

minute = 60 s = 60 s

Seconds

1 s

= 1 sec / 60 = 0.01667 min

With this information, you can calculate the quantity of seconds 3 minutes is equal to.

In 3 min there are 180 s.

Which is the same to say that 3 minutes is 180 seconds.

Evaluate each expression

Answers

Answer:

4 * 4 ÷ 4 = 4

8 ÷ (2*2) = 2

Step-by-step explanation:

[tex]4 * 4 \div4\\\rule{150}{0.5}\\\text{Use PEMDAS}\\\\4 * 4 \div4\\\\4 * 1\\\\\boxed{4}[/tex]

==============================

[tex]8 \div (2*2)\\\rule{150}{0.5}\\\text{Use PEMDAS}\\\\8 \div (2*2)\\\\8 \div 4\\\\\boxed{2}[/tex]

I hope this helps.

Graph the following inequality and then select the correct graph below x + 2 > 1

Answers

Answer:

The graph is attached below.

Step-by-step explanation:

First, we want to isolate the "x" term from the equation. We do this by subtracting "2" from both sides.

This gives us x is greater than -1. So, we can graph:

How to find the area of a missing square

Answers

Check the picture below.

btw, when Pythagoras said the square of this equals that and so on, he really meant the square or square area.

find the discriminant of -2x^2+8=x^2-28

Answers

Answer:

If I'm not wrong I think the answer should be (-28)

The gas tank in dads car holds 5 gallons. The gas tank in moms truck holds 50% more than that. How much gas does the truck's tank hold.

Answers

Answer:

7.5 gallons

Step-by-step explanation:

the 50% of 5 gallons is 2.5 then add up 5 gallons so the answer is 7.5 gallons of gas

(a) $21,000.00 is to be divided in the ratio 5:7:9 respectively for three siblings Antony, Terry
and Jack. Calculate how much money each sibling will get.

Answers

Answer:

See below for answer

Step-by-step explanation:

Set up the equation 5x+7x+9x=2100 and solve for x:

5x+7x+9x=2100

21x=2100

x=100

Now multiply the proportion by 100:

5:7:9 * 100 = 500:700:900

This means that Antony will get $500, Terry will get $700, and Jack will get $900.

squared root of -100 =

Answers

10 i I hope this help

Step-by-step explanation:

Please this is a wrong question. If you mean square root of 100 then it's 10. As for -100, it's an error.

Work out the area of the shaded shape.

Answers

Answer:

Step-by-step explanation:

A = 8(14) - 9(8 - 4) = 76 m²

whats 4000+60=
and whats 60+4000=

Answers

Answer:

4060

Step-by-step explanation:

Answer:4060

Step-by-step explanation:

2/5 x 7/9 = ( fractions )

Answers

Answer:

32/45 is your required answer

Answer:

your answer will be 14/45

Step-by-step explanation:

2/5 × 7/9

= 2 × 7

  5 × 9

= 14/45

heleppppppppppppp
plssssssssssssssss

Answers

Answer:

21

Step-by-step explanation:

Answer:

(3,3)

Step-by-step explanation:

Point B is the only point that inside the rectangle alone. Point A is not found in any shape and points C and D are inside the oval. coordinates are labeled (x,y). The coordinates of point B are (3,3)

I understand if this a little difficult to understand and i sincerely apologize for that..

please help ill mark brainliestO​

Answers

Answer:

56

Step-by-step explanation:

find the perimeter of the triangle A(4,-2) B(9,-2) C(9,10)

Answers

Answer:

  30 units

Step-by-step explanation:

A graph can help you see the lengths of the sides. This is a right triangle, so the length of the hypotenuse is found using the Pythagorean theorem:

  5² +12² = b² = 169

  b = √169 = 13

The perimeter is 5+12+13 = 30 units.

Match the verbal phrase on the left with the corresponding equation on the right. Write the letter of the answer on the space provided1.c increased by 5 is 5 2.4 more than a number is 12 3. The product of 4 and n is 12 4. The difference of 27 and k is 15 5.8 less than 3 times x is 10 6. 3 times x increased by 8 is 20 7. a number minus 8 is 3 8. three times a number is 9 9. twice a number plus 1 is 11 10.6 less than a number is 5a. 27-k=15 b. n + 4 = 12 d. 3x+8 = 20 e. k-8=3 f. 3x-8=10 g. 2x + 1 = 11 h. c + 5 = 15 i. 4n = 12 c. c-6=15 j. 3n = 9​

Answers

Answer:

See below

Step-by-step explanation:

1. c increased by 5 is 5                       ⇒ h. c + 5 = 5 2. 4 more than a number is 12           ⇒ b. n + 4 = 12 3. The product of 4 and n is 12          ⇒ i. 4n = 12 4. The difference of 27 and k is 15    ⇒ a. 27 - k = 155. 8 less than 3 times x is 10              ⇒ f. 3x - 8 = 10 6. 3 times x increased by 8 is 20      ⇒ d. 3x + 8 = 20 7. A number minus 8 is 3                   ⇒ e. k - 8 = 3 8. Three times a number is 9            ⇒ j. 3n = 9​9. Twice a number plus 1 is 11           ⇒ g. 2x + 1 = 11 10. 6 less than a number is 5            ⇒ c. c - 6 = 15

Which of the following is an equilateral triangle based on the given figure?

Answers

Check the picture below.

Answer:

ΔABE

Step-by-step explanation:

In ΔBCD,

Two sides are equal, i.e,

BC = CD

therefore, it is a Isoceles Triangle.

In ΔBDE,

No sides are equal,

therefore, it is Scalene Triangle.

In ΔABE,

AB = BE = AE

Therefore, it is equilateral triangle.

Hope it helps you!!

Elizabeth earned $150 a week tutoring . If he saved $75, what percent of the money he earned did he save ?

Answers

Answer:

50%

Step-by-step explanation:

75/150 = x/100

x = 50

Answer:

50%

explanation

half of 150 is 75(75x2)

in 2011 i sold 105276 tickets.
This is 7% less then the number of tickets i sold in 2018.

How many tickets i sell in 2018?

And

Show a check of your answer.

Answers

Answer:

sorry I don't know the answer of this

What will a 68% do to a 72.99%?

Answers

Answer: If you are wondering about your grades, it becomes 70.495. Therefore, your grade becomes a 70.

It will be lowered vy like one or two percent

i think

Jay works as a waiter at a restaurant.
He works 12 hours each weekend. Jay makes $5.50 per
hour and he gets to keep 60% of his tips.
If Jay wants to earn $150 before taxes, how much tip
money should he get during the weekend?
PLEASE HURRY

Answers

Answer:

67.33.

Step-by-step explanation:

To figure out the tip, you need to find 20% of $52.60.

0.2×52.6=10.52

You should leave $10.52 for the waiter if you want to leave him exactly 20%.

To figure the tax, you need to find 8% of $52.60.

0.08×52.6=4.208

Next, add them up:

52.6+10.52+4.208=67.328

The total bill, including tax and tip, will be $67.33.

Consider the functions f(x) = 10^x and g(x)= f(x+4)
How will the graph of the function g differ from the graph of f ?

A) the graph of the function g is the graph of function f shifted 4 units down
B) the graph of the function g is the graph of function f shifted 4 units to the right
C) the graph of the function g is the graph of function f shifted 4 units to the left
D) the graph of the function g is the graph of function f shifted 4 units up

Answers

D because u move it 4 to the right then it’s shifts the f

Consider the equation of a circle x^{2} -2x + y^{2} - 4y - 4 = 0 if the line 2x - y + a = 0 is its diameter. then find the value of a?

Answers

Answer:

Step-by-step explanation:

Find the centre first by reoriganisation it into the form (x - cx)^2 + (y -cy)^2 = r^2

x^2 + y^2 + 6x -6y +5 = 0

(x + 3)^2 - 9 + (y - 3)^2 - 9 + 5 = 0

(x + 3)^2 + (y - 3)^2 = 13

The radius does not matter the centre is ( -3, +3)

The diameter must pass through the center so substituting into the equation for the line

2x-y+a = 0

-6 -3 + a = 0 so a = 9

The value of 'a' is 0 and this can be determined by using the standard form of the equation of a circle.

Given :

Equation of a Circle --   [tex]x^2-2x+y^2-4y-4=0[/tex]

Equation of a Line -- 2x - y + a = 0

The following steps can be used in order to determine the value of 'a':

Step 1 - First make the equation of a circle in standard form.

[tex]x^2-2x+y^2-4y-4=0[/tex]

[tex](x-1)^2-1+(y-2)^2-4-4=0[/tex]

[tex](x-1)^2+(y-2)^2 = 3^2[/tex]

Step 2 - From the above step, it can be concluded that the center of the circle is (1,2).

Step 3 - If (1,2) is the center of the circle then it also satisfies the equation of diameter (2x - y + a = 0).

2x - y + a = 0

2(1) - 2 + a = 0

a = 0

For more information, refer to the link given below:

https://brainly.com/question/23528207

Hello hello there help

Answers

Answer:

Step-by-step explanation:

A translation 1 unit left and 2 units down :)

Answer:
1 unit to the left and 2 units down.

evaluate the expression 5 /6 + -3 /5

Answers

Step-by-step explanation:

[tex] \frac{7}{30} [/tex]

[tex] \frac{5}{6} + ( - \frac{3}{5} ) \\ lcm = 30 \\ \frac{25 + ( - 18)}{30} = \frac{7}{30} [/tex]

A farm lets you pick 3 pints of raspberries for $12.00

Answers

do you want me to find the answer or something because ur just doing something and not saying what to do with it

Other Questions
What is the absolute value? What symbol represents absolute value? please explain and i will give brainly Regan cycles 78 miles in 6 hours.His average speed for the first 30 miles is 15 mph.Work out Regan's average speed for the last 48 miles. Someone plz help me :( Put the correct number(s) by Soldiers; Spies; Nurses; Economics.Also, I will give Brainliest to the person that's correct. There are 70 students in the school band. 40% of them are sixth graders, 20% are seventh graders, and the rest are eighth graders.1. How many band members are sixth graders? band members2. How many band members are seventh graders? band members3. What percentage of the band members are eighth graders? When was Mark Twain born? who is playing chance on young and the restless right now Which choice is similar to the figure shown? The diagram shows the velocity-time graph for a car travelling in a straight line along a road. Calculate the acceleration between t = 2.0 s and t = 5.0 s. Whats the difference between an event and in event handler a. How will a forensic nurse process the evidence of the bite mark? A car is 15 feet long. A truck is 80% longer than the car. How long is the truck?Enter numerical answer only. (just the number)also thank you to everyone that has been helping me out when i have quetions.also be as fast as you can cause this quiz is do in 30 min cause i am staying after school. what is cosec32/sec58= The population in a major metropolitan city is given by the formulaP(t)=5.le.0111where t is measured in years since 2000 and P(t) is measured in millions.What does the model predict the population is in the year 2015?Interpret your result with a complete sentence. Just help me on 6 and 7 please write a story with the following title: A bus journey I will never forget What is the difference between a laparoscopic and open appendectomy? Which of these do not affect fluid friction?The surface of an objectThe viscosity (thickness) of fluid an object is inThe shape of an objectThe weight of an object In the accompanying diagram, overline BA perp overline BD and overline BC perp overline BE Which statement is true?