Why is verifying trig identities so hard?

Answers

Answer 1

Verifying trig identities can be difficult because they involve manipulating complex equations with multiple trigonometric functions that have various associated angles and coefficients.

For example, the Pythagorean Identity states that sin2θ + cos2θ = 1, which must be verified by using the identity sin2θ = 2sinθcosθ and substituting it into the equation. This results in a complex equation: 2sinθcosθ + cos2θ = 1, which must then be simplified and rearranged in order to show that it is true for all values of θ. Furthermore, trig identities can involve multiple steps that involve multiple functions and angles, which can make verifying them even more difficult.

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Related Questions

How many quart in a cubic feet ?

Answers

The volume of a cubic foot is equal to 29.9220779 US liquid quarts. This conversion factor is based on the definitions of the cubic foot.

So the volume of a cubic foot is equal to 29.9220779 US liquid quarts. This conversion factor is based on the definitions of the cubic foot as a unit of volume equal to a cube with sides that are one foot in length and the quart as a unit of volume in the US customary system.

The quantity of cubic feet can be multiplied by 29.9220779 to get the conversion to quarts. For instance, if you have a container with a 2 cubic foot volume, the quantity of quarts in that container would be:2 cubic feet multiplied by the US liquid quart density of 29.9220779 gives 59.8441558 US quarts. The volume of a cubic foot is equal to 29.9220779 US liquid quarts. This conversion factor is based on the definitions of the cubic foot as a unit of volume equal to a cube with sides that are one foot in length and the quart as a unit of volume in the US customary system.

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Which graph has a slope of 4/5?

Answers

Answer:

B

Step-by-step explanation:

Rise over run should be 4 rise and 5 to the side run

Answer:

Step-by-step explanation:

The last one (placed below)

Just take two random points (x1,y1) and (x2,y2) from the graph and calculate the slope according to the expression:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

The graph placed below, passes through the points (5,4) and (0,0). So if we replace these coordinates within the formula:

[tex]m=\frac{5-0}{4-0}=\frac{5}{4}[/tex]

Please help!!!!!Triangle ABC is similar to triangle FGH. Given the following angle measures, find the
missing angle measures.

Answers

The measures of angles in similar triangles are ∠ F = 22°, ∠ G = 75° and ∠ H = 83°

What are similar triangles?

Similar triangles have the same corresponding angle measures and proportional side lengths.

Given that, Triangle ABC is similar to triangle FGH, we need to find the measures of the angles,

The sum of interior angles of a triangle = 180°

Considering Δ ABC,

∠ A + ∠ B + ∠ C = 180°

∠ C = 180°-(22°+75°)

∠ C = 83°

Since, we know that the similar triangles have congruent corresponding angles,

Therefore,

∠ A = ∠ F, ∠ B = ∠  G and ∠ C = ∠ H

Therefore, the measures of angles in Δ FGH are ∠ F = 22°, ∠ G = 75° and ∠ H = 83°

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I don’t understand the questions

Answers

The solutions to the expressions using laws of exponents are;

17) y^(19/28)

18) 1/a^(5/9)

How to use Laws of Exponents?

The product rule of exponents states that "To multiply two expressions with the same base, add the exponents while keeping the base the same". Thus;

y² × y³ = y²⁺³

= y⁵

17) y^(3/7) × y^(1/4)

Applying product rule of exponents gives;

y^(³/₇ + ¹/₄)

= y^(19/28)

18) The negative exponent rule states that: To convert any negative exponent into positive exponent, the reciprocal should be taken." Thus;

x⁻³ = 1/x³

Thus;

a^(-5/9) = 1/a^(5/9)

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Ernest has 16 math problems to do for homework. He has already finished p of them. Write an expression that shows how many math problems Ernest has left.

Answers

The mathematical expression that shows the number of math problem left for Ernest is 16-p

What is linear expressions?

Linear expressions are expression that it's highest power in of it's variable is 1. Linear expression can have more than one variables.

Some of the examples of linear equations are 2x – 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x – y + z = 3.

Ernest has 16 math problem , he has solved p out of it.

To actually know the remaining math problem left, we subtract the number he has done from the number of original problem

This means the number r of problem left = 16-p

therefore the expression is 16-p

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The table shows the total amount of fuel used based
on the number miles flown by a plane.

Find the amount of used fuel per mile (m) and the Initial amount of fuel used (b).

Answers

The amount of fuel used per mile (m) = unit rate = 5.2 gallons per mile.

Initial amount (b) = 0 gallon.

How to Find the Unit Rate and Initial Amount of a Proportional Relationship?

A proportional relationship can be represented as an equation of the form y = mx, where x and y are variables and m is the constant of proportionality, also known as the unit rate

Unit rate (m) = amount of fuel used per mile = 156/30 or 312/60 = 5.2 gallons per mile.

Initial amount (b) = starting value or y-intercept = 0 gallon.

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9,372,282 rounded to 1,000

Answers

Answer: 9,372,000
- Hope this Helps

Answer: You would round down so 9,372,000

Step-by-step explanation: Since you are rounding to the nearest 1,000 it would be Answer: 9,372,000

Please give me branliest

In excerise 13-16 find the measures of the numbered angles in rhombus DEFG image it’s only one question image below

Answers

The measures of the numbered angles in rhombus DEFG are m ∠ 1 = m ∠ 2 = m ∠ 4 = 27°, m ∠ 3 = 90° and m ∠ 5 = m ∠ 6 = 63°

What is a rhombus?

A flat shape with 4 straight sides that are all equal length. Also opposite sides are parallel and opposite angles are equal. It is a type of parallelogram.

Given is a rhombus DEFG, we need to find the measures of the numbered angles,

We know that, diagonals of a rhombus bisect each other at right angle, and also bisects the vertex angles,

Also, the opposite angles are equal,

Therefore,

m ∠ 1 = m ∠ 2 = m ∠ 4 = 27°

m ∠ 3 = 90°

m ∠ 5 = m ∠ 6 = 90° - m ∠ 1

m ∠ 5 = m ∠ 6 = 90° - 27° = 63°

m ∠ 5 = m ∠ 6 = 63°

Hence, the measures of the numbered angles in rhombus DEFG are m ∠ 1 = m ∠ 2 = m ∠ 4 = 27°, m ∠ 3 = 90° and m ∠ 5 = m ∠ 6 = 63°

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A candle maker is ordering wax. Each small candle uses 12 ounces of wax. Each large candle uses 18 ounces of wax. The candle maker wants to make 42 small candles and 38 large candles.

Which answer is the most reasonable estimate of the total amount of wax needed?

Answers

Answer:

1188

Step-by-step explanation:

12x42 + 18x38  = 1188

35:60 in its simple form

Answers

Answer:7/12

Step-by-step explanation:

Answer:

7/12

Step-by-step explanation:

Inga divided two identical rectangles into equal parts. She colored one part of each rectangles

Answers

Divisions of the rectangle will be equal apart from the color Inga assign.

What is a rectangle?

A rectangle is a two-dimensional shape that has four sides and four right angles. The opposite sides are parallel and equal in length. The area of a rectangle can be calculated by multiplying the length of the rectangle by its width.

Here,
Since the rectangles are identical, they would have the same area and thus, the same divided parts. Therefore, the areas of the colored parts would also be equal.

Thus, divisions of the rectangle will be equal apart from the color Inga assign.

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Directions: Using the withholding tax tables for federal and state taxes on Figure 2.2, Figure 2.3, and Figure 2.4 of your textbook, complete the following phrases.

For a single person, 0 allowances, who made $295 last week

State withholding tax: $
Federal withholding tax: $

Answers

The amount of State withholding tax is, $20.65 and the amount of Federal withholding tax is, $17.7.

What is the percentage?

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Assuming the State withholding tax to be 7% and the Federal withholding tax to be 6%.

Given, A  person made $295 last week.

Therefore, The amount of Federal withholding tax is,

= $(6/100)×295.

= $17.7.

And, The amount of State withholding tax is,

= (7/100)×295.

= $20.65

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What are the measures of the angles? Please help 55 points.

Answers

Answer: 5

Step-by-step explanation:

Opposite angles of parallelograms are always equal, thus resulting in the equation, 20 + 2x = 6x simplified to 20 = 4x, so x is equal to 5. Hope this helps!

Answer:

The answer is a) 5

Step-by-step explanation:

what does (0 -1)(1 -3) equal in y=a(b)^x form

Answers

The exponential equation that coordinate points formed is y = -(3)^x

Determining exponential function from coordinate points

Given the coordinate points (0 -1) and (1 -3), we need to determine the equivalent in the form y=a(b)^x

The equivalent simultaneous equation is:

-1 = ab^0 .......... 1

-3 = ab^1 ............ 2

From equation 1;

-1 = a(1)

a = -1

Substitute a = -1 into equation 2

-3 = (-1)b
b = 3

The required exponential equation is y = -1(3)^x

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Mr. Yu applies 12 ounce of fertilizer to every 58 square meter of his lawn.

How many ounces of fertilizer does Mr. Yu use per square meter for his lawn?

Enter your answer in the box as a fraction in simplest form.

ounces per square meter

Answers

Answer: 0.20689655

Step-by-step explanation: because you take 12 divided by 58

Here is an equation: x + 3y = 6.
Use the whole numbers 0-6 without repeating to create two (x, y) coordinate pairs that are solutions and one that is not.

Answers

The two solutions of the linear equation are:

(0, 2)

(3, 1)

And a coordinate pair that is not a solution is:

(0, 5)

How to find the coordinate pairs?

Here we have the linear equation:

x + 3y = 6

And we want to find two ordered pairs that are solutions.

To find them,wecan evaluate in two values of x and then find the correspondent values of y.

if x = 0

0 + 3y = 6

y = 6/3 = 2

if x = 3

3 + 3y = 6

3y = 6 - 3

3y = 3

y = 3/3 = 1

So the two solutions are (0, 2) and (3, 1)

And a point that is not a solution can be one with the same x-value than one of the above ones but a different y-value, like (0, 5)

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Linda bought 6 pounds of rice for 4$ How many dollars did she pay per pound of rice

Answers

Answer: 24

Step-by-step explanation: 6*4=24

4+4+4+4+4+4=24

Answer:

she paid $1.50 / 1lb

Step-by-step explanation:

6lbs divided by $4 = 1.50 or $1.50 / 1lb

According to the midpoint method, the price elasticity of demand for apples between point X and point Y is approximately (0.02/0.1/0.2/5) , which suggests that the demand for apples is (elastic/inelastic) between points X and Y.

Answers

If the price elasticity of demand is equal to 0.02/0.1, then the demand for apples is inelastic and if the price elasticity of demand is equal to 0.2/5, then the demand for apples is elastic.

The price elasticity of demand is calculated using the midpoint method with formula:

Price Elasticity of Demand = (Percent Change in Quantity Demanded) / (Percent Change in Price)

The value of the price elasticity of demand tells us whether the demand for a product is elastic (sensitive to price changes), inelastic (insensitive to price changes), or unitary elastic (neither elastic nor inelastic). A value of price elasticity of demand greater than 1 indicates that the demand for the product is elastic, meaning that a small change in price leads to a large change in the quantity demanded. A value of price elasticity of demand less than 1 indicates that the demand for the product is inelastic, meaning that a small change in price leads to a small change in the quantity demanded.

If the price elasticity of demand is equal to 0.02/0.1, then the demand for apples is inelastic between points X and Y, meaning that a small change in price leads to a small change in the quantity demanded. If the price elasticity of demand is equal to 0.2/5, then the demand for apples is elastic between points X and Y, meaning that a small change in price leads to a large change in the quantity demanded.

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Does someone mind helping me with this problem? Thank you!

Answers

Answer:3y +=7  

=>3y-7-x

 =>y=(7-x)/3                               Step-by-step explanation:Solve for 'y' means, solve the equation to get the value of y and in terms of ,x means value of y not necessarily in pure constant form,but in the form of x.

please answer the question below!

Answers

The values of x in f(x)=2x g(x)=2^x is x=2 and x=0.77.

What is the solution for an equation?

The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.

We are given that;

f(x) 2x and g(x)=2^x

Now,

To graph the functions on the same coordinate plane, we can plot some points and connect them with a line:

f(x) = 2x

(0, 0), (1, 2), (2, 4), (3, 6), ...

g(x) = 2^x

(0, 1), (1, 2), (2, 4), (3, 8), ...

To find the solutions to the equation f(x) = g(x), we need to set the two expressions equal to each other and solve for x:

2x = 2^x

x=2, 0.77

Therefore, the answer of the given equation will be x=2, 0.77

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a process in which a number is changed, such as by adding, subtracting, dividing or multiplying is called___

Answers

The process in which a number is changed, such as by adding, subtracting, dividing or multiplying is called mathematical operation.

A mathematical operation is a process that changes a number in some way. The most common mathematical operations are:

Addition is adding two or more numbers together to find their sum.

Subtraction is finding the difference between two numbers by subtracting one from the other.

Multiplication is finding the product of two or more numbers by multiplying them together.

Division is finding the quotient of two numbers by dividing one by the other.

In addition to these basic operations, there are also other mathematical operations such as modulo, exponentiation, and square roots.

These operations are used to perform various mathematical calculations and are fundamental to many areas of mathematics, including algebra, calculus, and geometry. They are also used in many real-world applications, such as in finance, engineering, and science.

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give example discrete variable

Answers

Discrete variables are a subset of variables that have a limited range of values. A variable that counts how many kids a family has, for instance, can only be a whole number, such as 0, 1, 2, etc.

Discrete variables, like integers or categories, are a form of variable that can only take specified, distinct values. For instance, a discrete variable is the number of siblings a person has because it can only be 0, 1, 2, 3, etc.Discrete variables are a subset of variables that have a limited range of values. A continuous variable, on the other hand, can accept any value within a range.Whole numbers like 0, 1, 2, 3, and so forth are frequently used as discrete variables. The number of kids in a household, the number of products in a shopping cart, or the number of individuals in a room are all examples of discrete variables.

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how to convert torr to mmhg

Answers

Torr and mmHg are two units of pressure that are often used interchangeably. In fact, 1 mmHg is equal to 1 torr, which means that they are equivalent units of measurement.

To convert torr to mmHg, you can simply multiply the pressure value in torr by 1, since 1 torr is equivalent to 1 mmHg. For example, if you have a pressure of 760 torr, you can convert it to mmHg as follows:

760 torr x 1 mmHg/torr = 760 mmHg

Therefore, 760 torr is equivalent to 760 mmHg. Alternatively, you can also convert mmHg to torr by dividing the pressure value in mmHg by 1. For example, if you have a pressure of 760 mmHg, you can convert it to torr as follows:

760 mmHg ÷ 1 mmHg/torr = 760 torr

Therefore, 760 mmHg is equivalent to 760 torr.

Torr and mmHg are two units of pressure that are often used interchangeably. In fact, 1 mmHg is equal to 1 torr, which means that they are equivalent units of measurement.

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PLEASE HELP I REALLY NEED IT! Write an equation for the nth term of the geometric sequence 5,15,45,135,405,…
Then find a8

Answers

Answer:

              An equation to represent the given geometric sequence would be [tex]a(x)=5*3^{x-1}[/tex], and a(8) of the geometric sequence will be 10,935.

Step-by-step explanation:

              In order to write an equation for a geometric sequence, first we must analyze the sequence to find its starting value and its constant ratio. The starting value is simply the first term in the sequence, which is 5. As for the constant ratio, it is the rate of change that the equation uses. In this sequence, the constant ratio is 3. Now, we can write out an equation for this geometric sequence.

              We know the first term of the sequence is 5, and the common ratio is 3, so we can write out a function for the geometric sequence, which will be [tex]a(n)=5*3^{n-1}[/tex]. NOTE that the exponential power is n - 1, and not n. This is because the first term of the sequence is 5, and not the "0th" term, therefore we must subtract 1 from n (the term number) to have the right sequence.

              Lastly, we can use the equation [tex]a(n)=5*3^{n-1}[/tex] to find the 8th term of the sequence by replacing n with 8. So [tex]a(x)=5*3^{n-1}[/tex] would become [tex]a(8)=5*3^{8-1}[/tex], and you will get [tex]a(8)=5*3^{8-1}[/tex] ⇒ [tex]a(8)=5*3^{7}[/tex] ⇒ [tex]a(8)=5*2187[/tex] ⇒ [tex]a(8)=10,935[/tex]. Therefore, the equation for the nth term of the geometric sequence would be [tex]a(n)=5*3^{n-1}[/tex], and the 8th term of the sequence is 10,935.

Have a great day! Feel free to let me know if you have any more questions :)

I need some help thank you :)
Write an algebraic expression to represent the following situation: "Greg has nickels and pennies in his pocket. The number of pennies is 7 less than twice the number of nickels. Let N represent the number the nickels. Write an expression for the number of pennies."

Answers

An expression that is used to represent the number of pennies is; 2n - 7

How to solve Algebra word problems?

Algebraic word problems are defined as questions that require translating sentences to equations, then solving those equations. The equations we need to write will only involve basic arithmetic operations.

Now, we are told that;

Number of pennies  is 7 less than twice the number of nickels.

Thus. if n represents the number of nickels, then we can say that;

Number of Pennies = 2n - 7

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Find the solution of the system of equations
3x+7y=-17
-3x+9y=-15

Answers

Answer: The solution of the system of equations is (x, y) = (-1, -2).

Step-by-step explanation:

We can solve this system of equations by using either elimination or substitution method. Here, we'll use elimination:

Adding the two equations, we get:

(3x + 7y) + (-3x + 9y) = -17 - 15

Simplifying the left side and right side:

16y = -32

Dividing both sides by 16:

y = -2

Now we can substitute y = -2 into either of the original equations and solve for x. Let's use the first equation:

3x + 7(-2) = -17

Simplifying:

3x - 14 = -17

Adding 14 to both sides:

3x = -3

Dividing both sides by 3:

x = -1

How do you find the horizontal and vertical asymptote of a curve?

Answers

Answer: search it up

Step-by-step explanation:

Which values of x make the following statement true? Choose all correct
answers.
x-9.5 = a negative number
X = 9
X = -9.5
x = -9
x = 10
X = -10
x = 10.5

Answers

The values of x make the statement true are x = 9 X = -9.5 x = -9 and x = -10

Which values of x make the statement true?

From the question, we have the following parameters that can be used in our computation:

x-9.5 = a negative number

Using the above as a guide, we have the following:

x - 9.5 < 0

Make x the subject

x < 9.5

This means that the values of x are less than 9.5

From the options, we have:

x = 9 X = -9.5 x = -9 and x = -10

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URGENT ANSWER PLS

The explicit formula below describes a linear function, where n
is a positive integer.

f(n)=3n−8
Which recursive formula describes the same function?

A
a1=3an=an−1−8

B
a1=−5an=an−1+3

C
a1=3an=an−1−5

D
a1=−8an=an−1+3

Answers

Answer:

[tex]Option\ B[/tex]

Step-by-step explanation:

[tex]The\ explicit\ formula\ given:\\f(n)=3n-8\\Since\ n\ can\ be\ any\ positive\ real\ number\,\\The\ formula\ describes\ an\ AP\ whose\ d=3.\\Also,\ Substituting\ n=1:\\f(n)=3*1-8\\f(n)=-5\\Hence, a_1=-5[/tex]

[tex]However,\\We\ also\ know\ that,\\d=a_n-a_{n-1}\\Hence,\\a_n-a_{n-1}=3\\Or,\\a_n=a_{n-1}+3\\These\ conditions\ are\ appropriately\ specified\ on\ Option\ B.[/tex]

Can someone help me with this please

Answers

The sides of the rectangle are

1. (x - 1)2. (x + 6)3. (x - 5)4. (x + 1)

the codes are CFID

How to find the unknow part of the rectangle

The unknown part of the rectangle is solved using division of polynomial and the check is completed by multiplication of the polynomial involved

checking for the correct answers

1. 2(x + 5)(x - 1) = (2x + 10)(x - 1)

2x² - 2x + 10x - 10

2x² + 8x - 10

2. 3(x - 1)(x + 6) = (3x - 3)(x + 6)

3x² + 18x - 3x - 18

3x² + 15x - 18

3. 2(x + 1)(x - 5) = (2x + 2)(x  -5)

2x² - 10x + 2x - 10

2x² - 8x - 10

4. 5(x - 1)(x + 1) = (5x -5)(x + 1)

5x² + 5x - 5x - 5

5x² - 5

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in a criminal case, the state must prove its case by a preponderance of the evidence.true or false what do you think about education? Is education importabt? What is a famous quote from John Steinbeck? Please help!!!! Factor What is the definition "monarchy"?A. Rule by one personB. Rule by elected representativesC. Rule by the many, or the peopleD. Rule by a god or gods, either directly or indirectly Who was the original singer of Lynyrd Skynyrd? Classify each scenario based on whether it will lead to upward or downward pressure on the equilibrium price of the good marked in bold. Upward pressure on price Downward pressure on price Answer Bank The Nile River floods this year adding an exceptional amount of silt to the soil, resulting in increased crops of cotton. An outbreak of mad cow disease causes Americans to abstain from eating beef. An impending nuclear holocaust causes people to stock up on twonkies, a popular snack cake provided by many companies. Extreme weather in New York, where the Super Bowl is scheduled to be played, makes people disinterested in purchasing Super Bowl tickets. which one of the following terms is best used to refer to "a city and its suburbs"? urbanized (or urban) areaMetropolitan areamegalopolisurban place fill in the blank. a(n)___solution makes all of the computing hardware resources available, and the customers, in turn, are responsible for installing and managing the systems, which they can normally do, for the most part, over the internet. Implement a program that reads in a text file, counts how many times each word occurs in the file and outputs the words (and counts) in the increasing order of occurrence, i.e. the counts need to be output in sorted order rare words first. Word is any sequence of alphanumeric characters. Whitespace and punctuation marks are to be discarded. That is, the punctuation marks should not be counted either as a part of the word or as a separate word. You are free to make your program case sensitive (Hello and hello are counted as separate words) or case insensitive. File name is supplied on command line. You are to use the following classes.Using vectors is not allowed. You may use standard sorting algorithms or implement insertion sort form scratch. For the second class (WordList), implement a copy constructor (implementing deep copy), destructor and an overloaded assignment (either classical or copy-and-swap). Make sure your class works correctly with the following code. For your constructors, use member initialization lists where possible, use default values for function parameters where appropriate. Enhance class interface if necessary.demo code:class WordOccurrence {public:WordOccurrence(const string& word="", int num=0);bool matchWord(const string &); // returns true if word matches storedvoid increment(); // increments number of occurrencesstring getWord() const; int getNum() const;private:string word_;int num_;};class WordList{public:// add copy constructor, destructor, overloaded assignment// implement comparison as friendfriend bool equal(const WordList&, const WordList&);void addWord(const string &);void print();private:WordOccurrence *wordArray_; // a dynamically allocated array of WordOccurrences// may or may not be sortedint size_;}; What is the answer to this equation: [tex]4\cdot\frac{(6^2\cdot10+\sqrt{-600+5000\cdot3})}{4!}-\log_{10}{((\frac{1}{100})^{-\frac{1}{2}}\cdot10^{10})}[/tex] What is the area of a triangle that has a base of 4 1/2 inches and a height of 3 inches The sum of two numbers is 46 and the difference is 12. What are the numbers?Larger Number :Smaller Number : What is the area of the parallelogram? What was Shirley Chisholm most famous quote? What is the famous quote of John Donne? Between 1800 and 1910, the percentage of the U.S. population living in cities of 100,000 residents or larger went from ____ percent to roughly ___ percent.a. 15; 20b. 10; 20c. 5; 20d. 0; 20 I) Design a concerto grosso using today's instrumentation or any of the earlier types of instruments. Choose 3 soloists. Define your tutti section (in other instruments). Soloists: (1) (2) (3) Tutti: ____________________________________________________________ Which of your solo instruments will play the spectacular solo cadenza right before the tutti plays one more final ritornello? _________________ Which of the following administrative agencies is not an independent agency? use exhibit 1-2 multiple choice:a. the equal employment opportunity commissionb. the national transportation safety boardc. the nuclear regulatory commissiond. the small business administratione. the federal trade commission In which list can all particles be accelerated by an electric field?1) Alpha, beta, and neutrons.2) Alpha, protons, and neutrons.3) Alpha, beta, and protons.4) Beta, protons, and neutrons