A 170 ft string attached to a kite makes a 40⁰ angle with the ground. What is the height of the kite to the nearest tenth? 130.2 ft 33 ft 142.6 ft 109.3 ft

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:

[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:

AB= 5.582

Step-by-step explanation:

Centeral angle /360° = AB length/2 pi r

[tex] \frac{80}{360} = \frac{ab}{4} \\ ab = 5.582[/tex]

Answer:

5.6

Step-by-step explanation:

the length of arc AB =

80/360 × 2× 3.14×4

= 2/9 × 3.14 × 8

= 5.58 => 5.6

Step-by-step explanation:

which class are you

just to confirm

Answer:

according to me the ans is 3.

Answer:

The answer to the problem is 15.

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:

8

Step-by-step explanation:

6g = 48

/6 /6

divide 6 by both sides

g = 8

hope this helped!

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:

x = 4.4

Step-by-step explanation:

Flat cost = $57.5/month

Cost of 1GB = $4

But Aubrey wants to keep her bill at $75.1/month.

Let 'x' be the number of GBs she can use while staying within her budget.

So, the equation will be → 4x + 57.5 = 75.1

Now, solve the equation :-

[tex]=> 4x + 57.5 - 57.5 = 75.1 - 57.5[/tex]

[tex]=> 4x = 17.6[/tex]

[tex]=> \frac{4x}{4} = \frac{17.6}{4}[/tex]

[tex]=> x = 4.4[/tex]

Answer:

Mean: 2.125

median: 2

range: 4

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:

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:

yeah what you need help with

Answer:

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

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

Hope that this helps!

Answer:

number 3 sir

Step-by-step explanation:

Step-by-step explanation:

x = 7 cos 210 = 7×(-½√3) = -3.5√3

y = 7 sin 210 = 7×(-½) = -3.5

point C (-3.5√3 , -3.5)

Answer:

48°

Step-by-step explanation:

The angle CRS looks like a "L" shape, meaning that both lines are perpindicular to each other, resulting in a right angle (which is 90°)

90° + 42° = 132°

180° - 132° = 48°

Answer:

<RCS = 48 degrees

Step-by-step explanation:

I'm pretty sure that is a right triangle

180-90-42=48

LETS GOOOOOOOOOOOOOOO

Answer:

96

Step-by-step explanation:

Total of 4 test at 90

90 * 4 = 360

Current total

88 * 3 = 264

Score needed

360 - 264 = 96

Answer:

96

Step-by-step explanation:

this is how i solved it:

88 x 3 = 264 ( the sum of the three test score )

now i just gotta look for a number to add to 264 that will give me 90 (the wanted mean score) if i divide the sum by 4 (the four test scores).

so the equation would be:

(264 + x) / 4 = 90

264 + x = 360

x= 96

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.

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:

180 D

Step-by-step explanation: