Given sin theta=1/3 and 0 < theta< π/2; find tan 2 theta.

Answer:

[tex]\displaystyle \frac{dy}{dx} = \frac{-cos(x) - ysec(xy)tan(xy)}{-sin(y) + xsec(xy)tan(xy)}[/tex]

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Algebra I

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Trig Differentiation

Derivative Rule [Chain Rule]:                                                                                       [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Implicit Differentiation

Step-by-step explanation:

Step 1: Define

Identify

sin(x) + cos(y) + sec(xy) = 251

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Implicit Differentiation

Book: College Calculus 10e

Answer:

He bought about 176 ounces or 22 cups, or 5.2 liters.

Step-by-step explanation:

1.) 4 * 28 = 112

2.) 112 + 64 = 176 (answer in ounces)

3.) 8 ounces in a cup

4.) 176 ÷ 8 = 22 (answer in cups)

5.) About 4.227 cups in a liter

6.) 22 ÷ 4.227 = 5.204636858

7.) Round to the nearest tenth = 5.2 (answer in liters)

9514 1404 393

Answer:

  $351

Step-by-step explanation:

Use the simple interest formula for this.

  I = Prt

where P is the invested amount at annual rate r for t years.

Using your values, we find the interest to be ...

  I = $300·0.13·9 = $351

The account will earn #351 in interest over 9 years.

Step-by-step explanation:

which class are you

just to confirm

Answer:

Mean=2.53

median=2

mode=2

range=3

Step-by-step explanation:

1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4

MEAN

Add up all data values to get the sum

Count the number of values in your data set

Divide the sum by the count

38/15=2.53

MEDIAN

Arrange data values from lowest to the highest value

The median is the data value in the middle of the set

If there are 2 data values in the middle the median is the mean of those 2 values.

MODE

Mode is the value or values in the data set that occur most frequently.

RANGE

18-15=3

Answer:

yeah what you need help with

Answer:

option B

Step-by-step explanation:

Answer:

18.5 - - - - NO

24.3 ____ NO

21.6 __ YES

26.5 ___No

23.3 ___ YES

Step-by-step explanation:

Estimate = 22.5 gallons

Error margin = 4%

Hence ;

4% of 22.5 = 0.9

Actual usage :

(22.5 - 0.9) = 21.6

(22.5 + 0.9) = 23.4

Actual usage is within (21.6 ; 23.4)

Hence,

18.5 - - - - NO

24.3 ____ NO

21.6 __ YES

26.5 ___No

23.3 ___ YES

Answer:

360 cubic inches (remember your units!)

Step-by-step explanation:

the formula for volume of a rectangular prism is length times width times height times depth so you have to do 8 times 5 times 9 witch is 360 cubic inches

Answer:

a. (-4,8)

Step-by-step explanation:

the two lines intersect at this point

Answer:

1.B,C,D

2.A,D,E

I don't really know how to explain it to you but thats your answer :D

Answer:  a is 21 b is 45 and c is yes more people are going above because the median is above the speed limit

Step-by-step explanation:

Answer:

Tad ran 6 miles while Elaine ran 4 miles.

Step-by-step explanation:

Since Tad runs one-half mile for every one-third mile that Elaine runs, to determine, if together they run a total of 10 miles, how far does Tad run, the following calculation must be performed:

0.5 x 2 = 1

0.333 x 2 = 0.666

10 / 1.666 = X

6 = X

6 x 1 = 6

6 x 0.666 = 4

Therefore, Tad ran 6 miles while Elaine ran 4 miles.

Answer:

Step-by-step explanation: hope u like that cus i sike that C?

Answer:

B looks like a 180 degree angle cause its js a straight line and isnt curved or bent. Brainliest plz?

Step-by-step explanation:

Answer:

Is the annual dividend 1 dollar per share? Because if so, that means you would get 500 dollars yearly, and then divide that by 4 to get quarterly, making the answer 125 dollars in the quarterly check.

The amount that you receive on a quarterly dividend check will be $125.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

Barnes and Noble had a $1.00 annual dividend in 2008. If you owned 500 shares of Barnes and Noble. Then the cost of the 500 shares will be

⇒ 500 x $1

⇒ $500

Then the amount that you receive on a quarterly dividend check will be

⇒ $500 / 4

⇒ $125

The amount that you receive on a quarterly dividend check will be $125.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

Answer:

Hi again:

77 square millimetres

Step-by-step explanation:

Have a good day :)

Answer:

56 mm²

Step-by-step explanation:

12 - 4 = 8

8 · 7 = 56

56 ÷ 2 = 28

28 mm²

28 mm² + 28 mm²

56 mm²

Answer:

A train ticket costs $42

Step-by-step explanation:

5x + 30 = 240 (6 * 5 = 30, cost of lunch times 5 members of family)

5x = 240 - 30

5x = 210

x = 42

A train ticket costs $42.

Answer:

Step-by-step explanation:

[tex] \frac{4f^{2} }{3} \div \frac{1}{4f} [/tex]

[tex] \frac{4 {f}^{2}}{3} (4f)[/tex]

[tex]4 \frac{4 {f}^{2} }{3} f[/tex]

[tex] \frac{16 {f}^{2} }{3} f[/tex]

[tex] \frac{16 {f}^{3} }{3} [/tex]

Answer:

75o

Step-by-step explanation:

2x+5 = 155 (parallel lines)

x=(155-5)/2=75 deg

LETS GOOOOOOOOOOOOOOO

Answer:

girly

Step-by-step explanation:

I'd tell u to go with c I could be wrong tho but that's my guess and tell me if I got it right okay?

Step-by-step explanation:

the answer is n²

n plus n is 2n

and we have 2n as option b.. pls the answer is 2n

Answer:

[tex]-2 -\sqrt{3}[/tex]

Step-by-step explanation:

First consider numerator

[tex]sin \frac{\frac{7\pi}{6}}{2} = sin \frac{7\pi}{12}= sin (\frac{\pi}{4} + \frac{\pi}{3})[/tex]

Using the formula : sin (A + B) = sin A cos B + cos A sin B

[tex]sin \frac{\pi}{4} = \frac{\sqrt{2} }{2}, \ cos \frac{\pi}{4} = \frac{\sqrt{2} }{2}\\\\sin \frac{\pi}{3} = \frac{\sqrt{2} }{2}, \ cos \frac{\pi}{3} = \frac{1}{2}[/tex]

[tex]sin(\frac{\pi}{4} + \frac{\pi}{3}) = sin \frac{\pi}{4} \cdot cos \frac{\pi}{3} + cos \frac{\pi}{4} \cdot sin \frac{\pi}{3}[/tex]

                [tex]=\frac{\sqrt{2} }{2} \cdot \frac{1}{2} + \frac{\sqrt{2} }{2} \cdot \frac{\sqrt{3} }{2} \\\\= \frac{\sqrt{2} }{4} + \frac{\sqrt{6} }{4}\\\\=\frac{\sqrt{2} +\sqrt{6} }{4}[/tex]

Second consider denominator

[tex]cos \frac{\frac{7\pi}{6}}{2} = cos \frac{7\pi}{12}= cos (\frac{\pi}{4} + \frac{\pi}{3})[/tex]

Using the formula : cos (A + B) = cos A cos B - sin A sin B

[tex]sin \frac{\pi}{4} = \frac{\sqrt{2} }{2}, \ cos \frac{\pi}{4} = \frac{\sqrt{2} }{2}\\\\sin \frac{\pi}{3} = \frac{\sqrt{2} }{2}, \ cos \frac{\pi}{3} = \frac{1}{2}[/tex]

[tex]cos(\frac{\pi}{4} + \frac{\pi}{3}) = cos \frac{\pi}{4} \cdot cos \frac{\pi}{3} -sin \frac{\pi}{4} \cdot sin \frac{\pi}{3}[/tex]

[tex]=\frac{\sqrt{2} }{2} \cdot \frac{1}{2} - \frac{\sqrt{2} }{2} \cdot \frac{\sqrt{3} }{2}\\\\=\frac{\sqrt{2}}{4} - \frac{\sqrt{6}}{4}\\\\= \frac{\sqrt{2} -\sqrt{6} }{4}[/tex]

Therefore,

           [tex]tan \frac{7\pi}{12} = \frac{sin \frac{7\pi}{12}}{cos\frac{7\pi}{12}}[/tex]

                     [tex]= \frac{\frac{\sqrt{2} +\sqrt{6} }{4}} {\frac{\sqrt{2} -\sqrt{6} }{4} }\\\\=\frac{\sqrt{2} +\sqrt{6} }{4} \times \frac{4 }{\sqrt{2} -\sqrt{6}}\\\\=\frac{\sqrt{2} +\sqrt{6} }{\sqrt{2} -\sqrt{6}}[/tex]

Either we can stop here or Rationalize the denominator:

[tex]\frac{\sqrt{2} +\sqrt{6} }{\sqrt{2} -\sqrt{6}} \times \frac{\sqrt{2} +\sqrt{6} }{\sqrt{2} +\sqrt{6}} = \frac{(\sqrt{2} +\sqrt{6})^{2} }{(\sqrt{2})^2 -(\sqrt{6})^2} = \frac{2 + 6 +2\sqrt{12} }{2-6} = \frac{8+2\sqrt{12} }{-4} = \frac{8+ 4\sqrt{3} }{-4} = -2-\sqrt{3}[/tex]

Answer:

Mean: 2.125

median: 2

range: 4

Answer:

x=5

Step-by-step explanation:

(2)^x/2 = 16

Multiply both sides by 2

(2)^x/2 *2 = 16*2

2^x = 32

Rewrite 32 as a power of 2

2^x = 2^5

x=5

Answer:

x=5

Step-by-step explanation:

(2)^x/2 = 16

Multiply both sides by 2

(2)^x/2 *2 = 16*2

2^x = 32

Rewrite 32 as a power of 2

2^x = 2^5

x=5

Answer:

14.0625 = [tex]\frac{225}{16}[/tex]

6.41666666666... = [tex]\frac{77}{12}[/tex]

Hope that this helps!

Answer:

f has no critical points.

Step-by-step explanation:

We are given:

[tex]f(x)=\cos(x)+2x[/tex]

A function has critical points whenever its derivative equals 0 or is undefined.

Differentiate the function:

[tex]f'(x)=-\sin(x)+2[/tex]

Since this will never be undefined, solve for its zeros:

[tex]0=-\sin(x)+2[/tex]

Hence:

[tex]\displaystyle \sin(x)=2[/tex]

Recall that the value of sine is always between -1 and 1.

Thus, no real solutions exist.

Therefore, f has no critical points.