how do reference angles work and how do you find them?

Differentiation of trigonometric functions has wide-ranging applications in many fields, including physics, engineering, finance, and signal processing. It is used to calculate rates of change, solve optimization problems, model signals, analyze experimental errors, and more.

The applications of differentiation of trigonometric functions are wide-ranging and can be found in many fields, including science, engineering, and finance. Some specific applications of differentiation of trigonometric functions include:

1. Calculating rates of change: In physics, the rates of change of trigonometric functions (such as the velocity and acceleration of a moving object) can be calculated using differentiation.

2. Optimization problems: In engineering and other fields, optimization problems involving trigonometric functions (such as finding the maximum or minimum value of a function) can be solved using differentiation.

3. Signal processing: In electrical engineering and telecommunications, trigonometric functions are used to model signals and their derivatives are used to calculate signal properties such as frequency and amplitude.

4. Financial mathematics: In finance, trigonometric functions can be used to model interest rates and other financial phenomena, and differentiation can be used to calculate financial derivatives such as options.

5. Error analysis: In scientific research, differentiation can be used to analyze experimental errors and estimate uncertainties in measurements.

These are just a few examples of the many applications of differentiation of trigonometric functions. The use of trigonometric functions and their derivatives is widespread and plays a critical role in many fields of study.

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Answer:

\(\huge\boxed{\sf x = 85}\)

Step-by-step explanation:

0.2x - 6 = 11

0.2x = 11 + 6

0.2x = 17

x = 17/0.2

\(\rule[225]{225}{2}\)

Given:-

\( \: \)

Solution:-

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \purple {━━━━━━━━━━━━━━━━━━━━━━━━━━━━}\)

hope it helps!

Answer:

6 * 1/9

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

6/9 = 0.66666666666666666666666666666667

6 * 1/9 = 0.66666666666666666666666666666667

Answer:

To find 4% of 975, we can use the percent equation:

x = (4/100) * 975

Simplifying this expression, we get:

x = 0.04 * 975

Multiplying 0.04 and 975, we get:

x = 39

Therefore, 4% of 975 is 39.

It's important to know that the sum of two opposite numbers is zero because opposite numbers have the same absolute value but opposite sign, for example, 2 and -2 are opposite numbers.

The correct number line must have its final position on zero.

Notice that the number line A shows -5 as the initial number and then goes back 5 units to zero.

Answer:

C

Step-by-step explanation:

Difference means subtract, and the only one that has a subtraction included is C

Answer:

85x(500-0.10x)

Step-by-step explanation:

Answer:

a. A testable prediction about the relationship between variables

Step-by-step explanation:

A hypothesis is the FIRST step in conducting research or experimenting. In other terms, a scientific guess based on limited knowledge. Contrary to our hypothesis, conclusion comes last in researching and states the summary of the information gathered.

The reason why it isn't letter D is because a hypothesis's provability can only be determined once you have your conclusion, which is after you have conducted a research or experiment.

The letters B and C are too unrelated to what an hypothesis is.

- 8th grade student :)) (also buried under her own mountain of assignments and activities)

The weight percent of the structure that is crystalline in a polypropylene that has a density of 0.904 g/cm³ is 53.8%.

Polypropylene is a semi-crystalline thermoplastic material with a specific gravity of 0.946 g/cm³ when crystalline and 0.855 g/cm³ when amorphous.

The weight percent of the structure that is crystalline in a polypropylene that has a density of 0.904 g/cm³ is 56.3%.

Therefore, the given density of polypropylene lies in between the crystalline and amorphous densities. So, to calculate the weight percent of the structure that is crystalline in a polypropylene that has a density of 0.904 g/cm³, we use the formula below:

Weight percent crystallinity = [(density of the sample - amorphous density)/(crystalline density - amorphous density)] × 100Substituting the given values in the formula above, we get:

Weight percent crystallinity = [(0.904 g/cm³ - 0.855 g/cm³)/(0.946 g/cm³ - 0.855 g/cm³)] × 100

= (0.049 g/cm³/0.091 g/cm³) × 100

= 0.538 × 100

= 53.8%

Therefore, the weight percent of the structure that is crystalline in a polypropylene that has a density of 0.904 g/cm³ is 53.8%.'

Thus, the answer is 53.8%.

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The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, & The mass-normalised mode shapes can be  normalising the mode shape vectors f1, f2, and f3.

Part (a)

In Equation Q2, the spectral matrix, undamped natural frequencies, damping ratios, and fundamental frequency need to be calculated.

The mass matrix is given by [85.16400 083.3770 0046.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].

The stiffness matrix is given by [0.16400 00.3770 000.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].

The damping matrix is given by [0 0 0; 0 0 0; 0 0 0].The undamped natural frequencies, damping ratios, and fundamental frequency for the system in Equation Q2 can be calculated from the spectral matrix.

The characteristic equation can be written as det(K-mω^2M)=0.where K is the stiffness matrix, M is the mass matrix, ω is the angular frequency, and m is the mass-normalised mode shape.

The roots of this equation are the undamped natural frequencies, and the damping ratios can be calculated from the undamped natural frequencies and mode shapes.

The mass-normalised mode shapes can be calculated by normalising the mode shape vectors f1, f2, and f3.

Part (b)

The mass-normalised mode shapes can be calculated using the mode shape vectors f1, f2, and f3.Part (c)The response of the system for the first physical coordinate y1 can be calculated using the mode superposition method. The initial modal displacements and velocities are given in terms of the modal coordinates.

The response is then calculated using the equation y(t)= Σ ai φi(t), where ai are the modal amplitudes, and φi(t) are the modal shapes given by the mode shape vectors f1, f2, and f3.

The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, where Y is the vector of physical coordinates. The modal amplitudes can be calculated from the initial modal displacements and velocities.

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The equation that satisfies the data in the table is,

y = -4x - 4 [Option D]

Definition of an Equation:

An equation is defined as a mathematical assertion in which you use mathematical symbols to demonstrate the equality of two amounts. A combination of expressions with variables and constants on either side of the equality sign make up an equation.

The (x, y) coordinates from the given table are,

(-1,0), (0, -4), (1, -8)

Now, these points must satisfy the required equation.

Considering the first point (-1, 0), if we substitute these values of x and y coordinates in y=4x-4, the equality is no longer maintained.

Similarly, (-1,0) does not satisfy the second and third equations, that are, y = -x + 4 and y = x + 4, respectively, either.

Taking the fourth equation, y = -4x - 4

Putting x = -1 in this equation, we get,

y = -4(-1) - 4

y = 4 - 4

y = 0

Likewise, this equation satisfies the rest of the data in the table too.

Therefore, y = -4x - 4 is the required equation.

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The expression for the length of the sail is x = 7( tan 50° ).

According to the given question.

The sail of a boat is in the shape of a right triangle.

And, the sail of a boat is a right triangle with an acute angle at the tip equal to 50 degrees and the side of the sail which is the hypotenuse to the right triangle is 7 meters long.

Now, the side that measures 7 meters would be the adjacent because its right next to the angle and its not the hypotenuse because its not the largest side

And, the side which we do not know the length to will be the opposite side because it is opposite from where the angle is.  

So, we have the the measure of the adjacent side and the angle of the tip. And we have to find the expression for the length of the sail.

Let the length of the sail be x meters.

Now, in the given right angled triangle

We can say that

tan A = Opposite side/Adjacent side

⇒ tan 50° = x/7

⇒ x = 7( tan 50° )

Hence, the expression for the length of the sail is x = 7( tan 50° ).

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The friend has to save for 5 and 2/3 of a month to in order to make up the remaining 85 to get the 125 headphone.

An inequality that consists of two or more parts is called a compound inequality. Either "or" or "and" may be used in these components. A number between 5 and 10 could be used as x in an inequality, for instance, if it states that "x is larger than 5 and less than 10". Any time one of the two inequalities is true when the two inequalities are united by the word or, the compound inequality is solved. The two separate solutions have been combined to form the final answer. Inequalities that are separated by "and" or "or" form a compound inequality. The intersection of the inequality graphs is shown by the graph of a compound inequality with a "and."

Cost of the headphone 125.

What the friend have: 40.

What need to save: 125-40 = 85

Let x = amount to be saved per month

Months to save up the 85 is 15

The equation would be 15 x = 85

Therefore x = 85/15

Which is 5 2/3 months.

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The marching band is holding a fundraiser. One of the solutions to the scenario is 46 T-shirts and 82 yearbooks = $2822. The correct option is B.

An occasion for raising money for a cause, charity, or non-profit group is known as a fundraising event (also known as a fundraiser).

The T-shirts sell $15 and the yearbook for $26.

The band needs to raise $2800

Write a model that shows the number of T-shirts and yearbooks that must be sold.

Then graph the model and determine three combinations of T-shirts and sweatshirts that satisfy the model.

Let x = no. of $15 t-shirt

Let y = no. of $26 yearbook

The equation

15x + 26y = 2800

Therefore, the correct option is B, 46 t-shirts and 82 yearbooks.

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Thus, the company must consider fixed monthly payments of amount $497.92 into the account to reach $97,000 in 13 years.

To find the monthly payment needed to reach $97,000 in 13 years, we can use the sinking fund formula:

FV = PMT * [(1 + i)^n - 1] / i

where:
FV = future value ($97,000)
PMT = monthly payment (unknown)
i = monthly interest rate (3.2% compounded monthly, which is 0.032 / 12 = 0.002667)
n = number of months (13 years * 12 months/year = 156 months)

Rearrange the formula to solve for PMT:

PMT = FV * i / [(1 + i)^n - 1]

PMT = 97,000 * 0.002667 / [(1 + 0.002667)^156 - 1]

PMT ≈ 497.92

So, the company should make fixed monthly payments of approximately $497.92 into the account to reach $97,000 in 13 years.

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The rate of change for the equation y - x = 10 is 1.

To find the rate of change for the equation y - x = 10, we need to determine how y changes with respect to x.

We can rewrite the equation as y = x + 10 by adding x to both sides.

Now, we can observe that the coefficient of x is 1. This means that for every unit increase in x, y will increase by 1. Therefore, the rate of change for this equation is 1.

In other words, as x increases by 1 unit, y will increase by 1 unit as well.

As a result, 1 represents the rate of change for the equation y - x = 10.

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Answer:

120 degrees

Step-by-step explanation:

vertical angle of isoceles = 180 - 2(base angles) = 180 - 2(30) = 120

Answer:

isosceles triangle means both angle or sides equal so in this way

unknown angle + 30 + 30 = 180°

unknown angle+60=180

so unknown angle=120°

which is vertical angle

There of  288 different kinds of  lunch combination .

What is combination ?

The Munchery Restaurant advertises that you can have a different lunch combination every day of the year.

types of soups  =  12

types of sandwich = 4

types of bread = 4

find the number of combinations we multiply all the possible types we have

Number of combinations = 12 × 6 ×  4  =  288

There of  288 different kinds of  lunch combination .

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Answer:

A subject and a predicate

Step-by-step explanation:

Have a good day :)

If firm issues​ commercial paper with $1000000 face-value and pays EAR of​ 7.4%, then amount the firm will receive is $981500.

To calculate the amount the firm receives from issuing the three-month commercial paper, we need to determine the total interest earned over the three-month period.

The Effective Annual Rate (EAR) of 7.4% indicates the annualized interest rate. Since the commercial paper has 3-month term, we adjust the EAR to account for the shorter period.

To find the quarterly interest rate, we divide the EAR by the number of compounding periods in a year. In this case, since it is a 3-month period, there are 4-compounding periods in a year (quarterly compounding).

Quarterly interest rate = (EAR)/(number of compounding periods)

= 7.4%/4

= 1.85%,

Now, we calculate interest earned on "face-value" of $1,000,000 over 3-months,

Interest earned = (face value) × (quarterly interest rate)

= $1,000,000 × 1.85% = $18,500,

So, amount firm receives from issuing 3-month commercial paper is the face value minus the interest earned:

Amount received = (face value) - (interest earned)

= $1,000,000 - $18,500

= $981,500.

Therefore, the amount that firms receives is $981500.

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Therefore, the Inventory account is debited for $5,000, and Cash account is credited for $3,000 and the accounts payable account is credited $2,000.

Transaction: The transaction in the given scenario is the purchase of $5,000 worth of books.Explanation: In accounting, every transaction includes two aspects; debit and credit. In the given scenario, the purchase of books worth $5,000 will have the following debits and credits.Account(s) debited and for how much: The inventory account is debited for $5,000.Account(s) credited and for how much: The cash account is credited for $3,000, and the remaining $2,000 is credited to the accounts payable account. Why: The inventory account is debited as it is an increase in the inventory. The cash account is credited as the payment is made in cash, and the remaining $2,000 is credited to the accounts payable account as it is a liability account. The accounts payable will be settled in the coming month

Therefore, the Inventory account is debited for $5,000, and Cash account is credited for $3,000 and the accounts payable account is credited $2,000.

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The equation of the locus of the point P so that the area of triangle PAB is 8.5 square units will be 5 k + h = 34.

Let coordinate of P be (h, t)

We are given the coordinates of A and B as:

A = (2,3) and B = (−3,4)

Now, we also know that Area of triangle PAB is:

A = 1 / 2 (h ( 3 − 4 ) + 2 ( 4 − k ) − 3 ( k − 3 ) )

± 8.5 = 1 / 2 ( h ( - 1 ) + 2 ( 4 - k ) - 3 ( k - 3 ) )

± 17 = ( - h + 8 - 2 k - 3 k + 9 )

± 17 = ( 17 - 5 k - h )

When + 17 is there:

5 k + h = 0

When - 17 is there:

5 k + h = 34

So, locus of the point P will be 5 k + h = 34.

Therefore, the equation of the locus of the point P so that the area of triangle PAB is 8.5 square units will be 5 k + h = 34.

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Your question was incomplete. Please refer the content below:

A(2,3) and B(−3,4) be two given points. Find the equation of the locus of P so that the area of triangle PAB is 8.5 square units.

Answer:

I'm sorry but I don't know how to do function notation. I'm so sorry that I couldn't help you with this.

Plugging in 5.5 for the March temperature yields April 16th as the estimated bloom date.

An equation is a mathematical statement that two expressions are equal. It is written in the form of an expression, with an equal sign (=) between two expressions that have the same value. Equations are used to solve for unknown values, to determine relationships between different variables, or to describe a mathematical process.

Using the equation that was fit to the data, the date in April when Tess' flowers will bloom if the average temperature in March is 5.5° is April 16th. This is based on the equation: April bloom date = -24.47 + 0.75 (March temperature). Plugging in 5.5 for the March temperature yields April 16th as the estimated bloom date.

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Answer:

-a^5x^3

Step-by-step explanation:

hope this helps! :)

Let's separate this out and multiply the coefficients first, then the variables.

2 1/3 = 7/3

7/3 * -3/7 = -1

(a^2)(x)(a^3)(x^2)

When we multiply terms with exponents, we ADD the exponents.

(a^5)(x^3)

Answer: (-1)(a^5)(x^3)

Coefficient: -1

Hope this helps!

The resultant of the vertical vector of 3 units combined with the horizontal vector of 4 units has a magnitude of 5 units.

To find the resultant of a vertical vector of 3 units combined with a horizontal vector of 4 units, we can use the Pythagorean theorem.

The magnitude of the resultant vector can be calculated as the square root of the sum of the squares of the individual vector components.

Using the given values, the vertical vector has a magnitude of 3 units and the horizontal vector has a magnitude of 4 units.

Using the Pythagorean theorem, we can find the magnitude of the resultant vector:

Resultant magnitude = √(3^2 + 4^2)

= √(9 + 16)

= √25

= 5

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Answer:

419.999999994 =420

Step-by-step explanation:

Its all in the equations lol

Answer:

- 2/6 to - 1/3

Step-by-step explanation: