Students were asked to prove the identity (cot x)(cos x) = csc x − sin x. Two students' work is given.Did either student verify the identity properly? Explain why or why not.

Students Were Asked To Prove The Identity (cot X)(cos X) = Csc X Sin X. Two Students' Work Is Given.Did

Answers

Answer 1

Answer:

Yes, both students A and B verified the identity properly.

Because in the final step, the expressions on both sides of the equation were equal ( RHS = LHS) and the correct trig identities were utilized in the course of the solution.

Explanation:

Given the below identity;

\(\mleft(\cot x\mright)\mleft(\cos x\mright)=cscx-\sin x\)

Let's analyze the steps Student A used in proving the above identity;

Step 1:

\(\frac{\cos x}{\sin x}\cdot\cos x=\csc x-\sin x\)

Recall;

\(\begin{gathered} \tan x=\frac{\sin x}{\cos x}\text{ and cot x }=\frac{1}{\tan x} \\ \therefore\text{cot x }=\frac{1}{\frac{\sin x}{\cos x}}=1\div\frac{\sin x}{\cos x}=1\cdot\frac{\cos x}{\sin x}=\frac{\cos x}{\sin x} \end{gathered}\)

Step 2:

\(\frac{\cos^2x}{\sin x}=\csc x-\sin x\)

Step 3:

\(\frac{1-\sin ^2x}{\sin x}=\csc x-\sin x\)

The below trig identity was applied here;

\(\begin{gathered} \cos ^2x+\sin ^2x=1 \\ \therefore\cos ^2x=1-\sin ^2x \end{gathered}\)

Step 4:

\(\frac{1}{\sin x}-\frac{\sin ^2x}{\sin x}=\csc x-\sin x\)

Step 5:

\(\csc x-\sin x=\csc x-\sin x\)

Note that;

\(\begin{gathered} \frac{1}{\sin x}=\csc x \\ \text{and} \\ \frac{\sin^2x}{\sin x}=\sin x \end{gathered}\)

We can see from the above that Student A verified the identity properly because in the final step, the expressions on both sides of the equation were equal ( RHS = LHS) and the correct trig identities were utilized.

Let's analyze the steps of Student V;

Step 1:

Recall that;

\(\csc x=\frac{1}{\sin x}\)

So Step 1 is given as;

\(\cot x\cos x=\frac{1}{\sin x}-\sin x\)

Step 2:

Note that;

\(\frac{\sin^2x}{\sin x}=\sin x\)

So Step 2 is given as;

\(\cot x\cos x=\frac{1}{\sin x}-\frac{\sin^2x}{\sin x}\)

Step 3:

Using sin x which is the LCM to multiply through, we'll have;

\(\cot x\cos x=\frac{1-\sin^2x}{\sin x}\)

Step 4:

Recall the below trig identity;

\(\begin{gathered} \cos ^2x+\sin ^2x=1 \\ \therefore\cos ^2x=1-\sin ^2x \end{gathered}\)

Applying the above identity, we'll have;

\(\cot x\cos x=\frac{\cos^2x}{\sin x}\)

Step 5:

Note that;

\(\cos ^2x=\cos x\cdot\cos x\)

So we'll have;

\(\cot x\cos x=\frac{\cos x}{\sin x}\cdot\cos x\)

Step 6;

Recall that;

\(\begin{gathered} \tan x=\frac{\sin x}{\cos x} \\ \text{and} \\ \cot x=\frac{1}{\tan x}=\frac{1}{\frac{\sin x}{\cos x}}=1\div\frac{\sin x}{\cos x}=1\cdot\frac{\cos x}{\sin x}=\frac{\cos x}{\sin x} \\ \therefore\cot x=\frac{\cos x}{\sin x} \end{gathered}\)

So we'll have;

\(\cot x\cos x=\cot x\cos x\)

We can see from the above that Student B verified the identity properly because in the final step, the expressions on both sides of the equation were equal ( RHS = LHS) and the correct trig identities were utilized.


Related Questions

PLEASE HELP! urgent! Write the equation of a line in a slope-intercept form and standard form

PLEASE HELP! urgent! Write the equation of a line in a slope-intercept form and standard form

Answers

Answer:

\(y = \frac{3}{4}x -3\) --- Slope intercept

\(4y - 3x =- 12\) --- Standard form

Step-by-step explanation:

Given

The attached linear graph

Required

The equation

Select any two points on the line

\((x_1,y_1) = (0,-3)\)

\((x_2,y_2) = (4,0)\)

Next, calculate the slope (m)

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

So, we have:

\(m = \frac{0 --3}{4 - 0}\)

\(m = \frac{3}{4}\)

The slope intercept is then calculated using:

\(y = m(x - x_1) + y_1\)

So, we have:

\(y = \frac{3}{4}(x - 0) -3\)

\(y = \frac{3}{4}(x) -3\)

\(y = \frac{3}{4}x -3\)

Multiply through bu 4

\(4y = 3x - 12\)

Subtract 3x from both sides

\(4y - 3x =- 12\) --- Standard form

Create and expression that is equivalent to 3x+2x+x using the fewest terms

Answers

Answer:

6x

Step-by-step explanation:

add the terms to make one term

PLEASE WHOEVER DOES IT GETS BRAINLIEST

PLEASE WHOEVER DOES IT GETS BRAINLIEST

Answers

Answer:

first one on top to the left

Step-by-step explanation:

it’s the third one i believe

Need help on this guys, help pls.

Need help on this guys, help pls.

Answers

Answer:

1,740 261

20+3

Final answer 23

Step-by-step explanation:

Sorry If I am wrong.

Find the graph of Y equals negative X squared plus 5X -6 by making a table of a few values and plotting the points

Find the graph of Y equals negative X squared plus 5X -6 by making a table of a few values and plotting

Answers

Given the function:

\(y=-x^2+5x-6\)

Let's find the graph of the function by making a table of few values and plotting the points.

Let's find 3 different points by inputting random values for x and solve for y.

• When x = 0:

Substitute 0 for x and solve for y

\(\begin{gathered} y=-0^2+5(0)-6 \\ y=0+0-6 \\ y=-6 \\ \\ \text{ Here, we have the point:} \\ (0,\text{ -6\rparen} \end{gathered}\)

• When x = 2:

Substitute 2 for x and solve for y

\(\begin{gathered} y=-(2)^2+5(2)-6 \\ y=-4+10-6 \\ y=0 \\ \\ Here,\text{ we have the point:} \\ (2,\text{ 0\rparen} \end{gathered}\)

• When x = 3:

Substitute 3 for x and solve for y

\(\begin{gathered} y=-(3)^2+5(3)-6 \\ y=-9+15-6 \\ y=0 \\ \\ \text{ Here, we have the point:} \\ (3,\text{ 0\rparen} \end{gathered}\)

• When x = 1:

\(\begin{gathered} y=-(1)^2+5(1)-6 \\ y=-1+5-6 \\ y=-2 \\ \\ We\text{ have the point:} \\ (1,\text{ -2\rparen} \end{gathered}\)

Therefore, we have the table of values representing the function:

Now, let's plot the points to find the graph:

(0, -6), (1, -2), (2, 0), (3, 0)

We have the graph below:

Find the graph of Y equals negative X squared plus 5X -6 by making a table of a few values and plotting
Find the graph of Y equals negative X squared plus 5X -6 by making a table of a few values and plotting
Find the graph of Y equals negative X squared plus 5X -6 by making a table of a few values and plotting

Solve the triangle. Round to the nearest tenth.
Find c aswell

Solve the triangle. Round to the nearest tenth.Find c aswell

Answers

Answer:

Set your calculator to Degree mode.

a² = 17² + 20² - 2(20)(17)cos(89°)

a² = 677.13236

a = 26.0 in.

sin(89°)/26.02177 = (sin B)/17

sin B = 17sin(89°)/26.02177

B = 40.8°

C = 50.2°

a triangular prism (like a box of toblerone) of mass m, whose two ends are equilateral triangles parallel to the xy plane with side 2a, is centered on the origin with its axis along the z axis. find its moment of inertia for rotation about the z axis. without doing any integrals write down and explain its two products of inertia for rotation about the z axis.

Answers

The moment of inertia for rotation about the z axis is  \(I & =\frac{a^2 M}{3}\).

A triangular prism of mass m, whose two ends are equilateral triangles.

Two ends are equal.

The xy plane with side 2a, is centered on the origin with its axis along the z axis.

Find the moment of inertia for rotation the z-axis.

It is divide into 4 triangles with side 'a' k one side is 3cm.

\($$\begin{aligned}& I_{\text {BiG }}=16 I_{\text {small }} . \\& I_{\text {BIG }}=4 I_{\text {small }}+P_{A T}\end{aligned}$$\)

It is fact that the big triangle is made up from four small triangles. connected with parallel axis theorem.

Now, we have to find the distance from the center of mas of small outer triangles to the origin. so, that it is PAT.

\($$\therefore z=2 \sqrt{x^2-\frac{a}{2} ^2}$$\)

\($$\begin{aligned}& =2 \sqrt{\left(\frac{a}{\sqrt{3}}\right)^2-\frac{a^2}{4}} \\& =2 \sqrt{\frac{a^2}{3}-\frac{a^2}{4}} \\I_{\text {Big }} & =\frac{\sqrt{3}}{3} a \cdot \\& \left.=4 I_{\text {small }}+3 m \frac{\sqrt{3}}{3} a\right)^2 \\I_{\text {Big }} & =4 I_{\text {small }}+\frac{3 m}{4} \frac{1}{3} a^2 \\& =\frac{a^2}{4}\end{aligned}$$\)

⇒ Now, by using the \($I_{\text {Big }}=I$\)

⇒\(I & =4\left(\frac{\sqrt{2}}{16}\right)+\frac{a^2 M}{4} \\\)

⇒\(4 I & =I+a^2 m\)

⇒\(4 I-I & =a^2 m \\\)

⇒\(3 I & =a^2 M . \\\)

⇒\(I \quad & =\frac{a^2 M}{3}\)

Therefore, the moment of inertia is \(I & =\frac{a^2 M}{3}\).

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If each quadrilateral below is a rectangle, find the missing measures.

Please helpppp

Answers

The measures of the angles are JKN = 27 degrees and JNK = 126

How to determine the measures of the angles

The complete question is added as an attachment

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

The rectangle

On the rectangle, we have

JKN = NJK

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

JKN = 27 degrees

Next, we use the sum of angles in a triangle theorem

The sum of angles in a triangle is 180

Mathematically, this is represented as

J + N + K = 180

So, we have the following representation

JNK = 180 - 27 * 2

Evaluate

JNK = 126

Hence, the measure of the angle JNK is 126 degrees

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If each quadrilateral below is a rectangle, find the missing measures.Please helpppp

PLEASE HELP ASAP
The diagrams show a polygon and the image of the polygon after a transformation.
Use the diagrams to determine which statements are true. Select all statements that are true.

PLEASE HELP ASAP The diagrams show a polygon and the image of the polygon after a transformation.Use

Answers

The correct statements regarding the transformations are given as follows:

Parallel lines will always be parallel after a reflection.Lines that are not parallel will never be parallel after a translation.

What are transformations on the graph of a function?

Examples of transformations are given as follows:

A translation is defined as lateral or vertical movements.A reflection is either over one of the axis on the graph or over a line.A rotation is over a degree measure, either clockwise or counterclockwise.For a dilation, the coordinates of the vertices of the original figure are multiplied by the scale factor, which can either enlarge or reduce the figure.

Parallel lines are lines that have the same slope, that is, lines that do not intercept, and the transformations do not change whether the lines are parallel or not.

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A rectangular garden is 8 ft longer than it is wide. Its area is 425 ft2. What are its dimensions?

Answers

Answer:

17 ft.

Step-by-step explanation:

Because 17x25=425

And 25-8=17

What’s the value of x in both a & b?

Whats the value of x in both a & b?

Answers

Answer:

a) 7

b) 2 2/7

Step-by-step explanation:

A) 2/7=2/x

x=7

B) 2/7=x/8

cross multiply

16=7x

x=16/7, or 2 2/7, or 2.2857

what is the remainder for the synthetic division problem? (image attached)​

what is the remainder for the synthetic division problem? (image attached)

Answers

Answer:

D

Step-by-step explanation:

3 | 1   5   - 8   6

   ↓   3    24   48

   ----------------------

    1   8   16    54 ← Remainder

determine the general solution of cos2X -7cosX -3=0​

Answers

Answer:

x=2pi/3 +2pi n, 4pi/3 +2pi n for all integar of n.

Step-by-step explanation:

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 23.5 for a sample of size 775 and standard deviation 12.2. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 95% confidence level). Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

Answers

The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:

\(22.6 < \mu < 24.4\)

How to obtain the confidence interval?

The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:

\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)

Looking at the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.96.

The lower bound of the interval is then given as follows:

\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)

The upper bound of the interval is then given as follows:

\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)

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help me please im stuck​

help me please im stuck

Answers

i’m pretty sure it’s b
I think it’s” b”because that makes more sense

Look at Jerrys monthly budget below. What percentage of Jerrys net income is spent on transportation?

Net Monthly Income: 2,970.00

Housing: $750.00
Utilities: $120.00
Food: $450.00
Transportation: $650.00
Savings: $300.00
Other Expenses: $500.00

Total Monthly Expenses: 2,970.00

A. 28%
B. 25.3%
C. 86.7%
D. 21.9%

Answers

Answer:

D. 21.9%

Step-by-step explanation:

(650÷2970)x100= 21.88% rounded off 21.9%

joe paid 14.00 for a broard game. THis is 70% of the orginal price. What was the orginal price?

Answers

Answer:

20.00

Step-by-step explanation:

14 is 70% of X

70/100 × X = 14

X = 14 × 100/70

X = 20.00

What is the inverse of the following conditional? If Tracy is not going to Quinn's candy shop then she is not going to buy sour straws.

Answers

In order to find the inverse of this conditional, we need to negate both the first and second statement.

So we have:

First statement: "Tracy is not going to Quinn's candy shop"

Second statement: "she is not going to buy sour straws"

Negating these, we have:

First statement: "Tracy is going to Quinn's candy shop"

Second statement: "she is going to buy sour straws"

So the inverse will be:

"If Tracy is going to Quinn's candy shop then she is going to buy sour straws.​"

Explain a time in your life you underwent metamorphosis

Answers

Answer: Maybe when you Grew from a Baby to a toddler because that would be you growing over time

Step-by-step explanation:

I Hope This Helps!

The average diameter of a tree is measured over time. The equation y=3/5x, where x is the time in years and y is the diameter in inches, models the relationship. What is the predicted diameter, in inches, of the three after 12 years?

Answers

Your answer is b so there you go have a great day!!!!

Please help me I will mark brainliest! The ratio of the number of boys to the number of girls in a school is 3:4. One-third of the boys and three-eighths of the girls wear spectacles, If there are 612 pupils who do not wear spectacles, a)find the total number of the pupils in the school, and b) how many more girls than boys are there in the school

Answers

Answer:

a) 952

b) 136

Step-by-step explanation:

Ratio of b:g = 3:4, based on this we have:

Number of boys = 3xNumber of girls = 4xTotal number of pupils = 3x+4x = 7x

Number of spectacle wearers:

1/3*3x + 3/8*4x = x + 3/2x = 2.5x

Number of those not wearing spectacles:

7x - 2.5x= 4.5x

And this number equals to 612, then we can find the value of x:

4.5 x = 612x= 612/4.5x= 136

a) Total number of pupils:

7x = 7*136 = 952

b) The difference in the number of boys and girls:

4x-3x= x = 136

Answer:

total number of students: 952

number of girls more than boys :136 more girls

Step-by-step explanation:

1/3 of boys +3/8 girls= spectacles

612 people do not wear spectacles

3:4= boys: girls

total number of students

3+4=7

boys + girls = total ratio

7= total ratio

1/3×3=1 3/8×4=3/2

1+3/2=5/2

7-5/2=9/2 9/2=612 students

If 9/2=612 Then 7=?

7= 7÷ 9/2×612

=952 people

Girls more than boys

if 7= 952

3= 3/7 × 952=408 boys

if 7 = 952

4= 4/7 ×952=544girls

Girls - boys

544- 408 = 136 girls

18) What is the slope of the line that contains points (–6, –6) and (–3, 1)?

Answers

The slope of the line is 7/9

How to determine the slope of the line

It is important to note that the equation of a line is represented as;

y = mx + c

Where;

y is a point on the linem is the slope of the linex is a point on the x - axisc is the intercept of the y-axis

The formula for calculating the slope of a line is expressed as;

Slope, m = y₂ - y₁/x₂ - x₁

Now, let's substitute the values into the formula from the points given we have;

Slope, m =1 -(-6)/ -3 - (-6)

expand the bracket

Slope, m = 1 + 6/ 3 + 6

add the values

Slope, m = 7/9

Hence, the value is 7/9

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Kallie works at a pet store. Part of her job is to add the correct amount of water conditioner to each fish tank the list below provides information about the number of fish tanks and the amount of water conditioner she uses.
1: there are 12 fish tanks that need water conditioner
2: Each fish tank is filled with 20 quarts of water
3: for every 10 gallon of water, Kallie uses 1 teaspoon of water conditioner
What is the total number of teaspoons of water conditioner kallie will use for all the water in 12 fish tanks?

Answers

Therefore, Kallie will need to use a total of 6 teaspoons of water conditioner for all the water in 12 fish tanks.

What is equation?

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign, with the expression on the left being equal to the expression on the right. Equations are used to represent various relationships and situations in mathematics and other fields, and are solved to find the values of variables that make the equation true.

Here,

First, we need to determine the total amount of water in all 12 fish tanks. Since each fish tank is filled with 20 quarts of water, the total amount of water in all 12 fish tanks is:

12 fish tanks * 20 quarts per fish tank = 240 quarts of water

To convert quarts to gallons, we divide by 4 (since there are 4 quarts in a gallon):

240 quarts / 4 quarts per gallon = 60 gallons of water

Now, we can use the given conversion factor to determine how many teaspoons of water conditioner are needed for 60 gallons of water. Since for every 10 gallons of water, Kallie uses 1 teaspoon of water conditioner, for 60 gallons of water, she will use:

60 gallons / 10 gallons per teaspoon = 6 teaspoons of water conditioner

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Suppose an account pays 6% interest that is compounded annually. At the beginning of each year, $2,000 is deposited into the account (starting with $2,000 for the first year).

Answers

Using the future value formula, it is found that the value of the account after the tenth deposit is of $26,361.59.

What is the future value formula?

The future value formula is given by:

\(V(n) = P\left[\frac{(1 + r)^n - 1}{r}\right]\)

In which:

P is the payment.n is the number of payments.r is the interest rate.

For this problem, the parameters are given as follows:

P = 2000, r = 0.06, n = 10.

Hence the value of the account will be of:

\(V(10) = 2000\left[\frac{(1 + 0.06)^{10} - 1}{0.06}\right]\)

V(10) = $26,361.59.

What is the missing information?

The complete problem is:

"Suppose that there is an account that pays 6% interest that is compounded annually. At the beginning of each year, $2,000 is deposited into the account (starting with $2,000 for the first year).

What will be the value of the account after the tenth deposit if no withdrawals or additional deposits are made?"

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115 degrees (5x-10degrees) what does x equal show your work

Answers

Answer: 21

Step-by-step explanation:

115-10=105

105/5=21

Match the vocabulary word with the correct definition. 1. axis of rotation a line around which a two-dimensional shape is rotated or revolved to create a three-dimensional shape 2. cross section the two-dimensional shape that results from cutting a three-dimensional shape with a plane 3. solid of revolution the three-dimensional shape that is produced when a two-dimensional shape is rotated or revolved around a line

Answers

Answer:

See step by step explanation

Step-by-step explanation:

Matching the vocabulary word with the correct definition, we get;

1. Axis of Rotation: a line around which a two-dimensional shape is rotated or revolved to create a three-dimensional shape.

It is a straight line through a rigid body when all its part are in rotation.

2. Cross section: the two-dimensional shape that results from cutting a three-dimensional shape with a plane. It is a internal view of an object that is made by cutting through it.

3. Solid of Revolution: the three-dimensional shape that is produced when a two-dimensional shape is rotated or revolved around a line. In mathematics, it is a solid shape that is obtained by revolving a curve around an axis.

Un cuerpo de 30 kg de masa se encuentra a una altura de 5 metros en relación al suelo, siendo g= 9,8 m/s2, calcula la energía potencial del cuerpo ​

Answers

Answer:

bro speak english

SPEAK ENGLISH

Sorry bro I don’t understand Spanish

Help plssssss I really need the answer asap! I’d really appreciate it

Help plssssss I really need the answer asap! Id really appreciate it

Answers

I think it’s 6.70820393 but it could be wrong
I am almost positive it is 6.70820393

Find the slope of each line passing through the given points using the slope formula.
(-3, -10) and (-1, -1) URGENT Please answer

Answers

Slope (m)= y\x= 9/2 = 4.5

your equation for the line is

y=4.5x+3.5

Just number 9 with work

Just number 9 with work

Answers

The answer of the given question based on rational parent function , to identify a correct transformation of the function, The correct answer choice is (c) Left 5.

What is Function?

A function is  mathematical relationship that assigns  unique output value for each input value. It describes relationship between two variables, where  output value is dependent on input value. A function can be represented by  equation, a graph, or  table. In its simplest form,  function takes  input value, performs a specified operation on that value, and produces  corresponding output value.

Functions are used to model real-world phenomena, to solve problems, and to analyze and understand complex systems. They are  fundamental concept in mathematics and are used in  wide variety of fields, like science, engineering, economics, and finance.

The given equation is y = 12/(x + 5), which represents the rational parent function. To identify a correct transformation of the function, we can consider the effect of each transformation on the parent function.

a) Vertical reflection: This transformation would change the sign of the function, resulting in y = -12/(x + 5). This is not the given equation, so it is not a correct transformation.

b) Vertical stretch by 12: This transformation would multiply the function by 12, resulting in y = 12(12/(x + 5)) = 144/(x + 5). This is not the given equation, so it is not a correct transformation.

c) Left 5: This transformation would shift the function to the left by 5 units, resulting in y = 12/(x + 10). This is a correct transformation of the function, as it represents a horizontal shift of 5 units to the left.

d) Down 5: This transformation would shift the function down by 5 units, resulting in y = 12/(x + 5) - 5. This is not the given equation, so it is not a correct transformation.

Therefore, the correct transformation of the rational parent function as described by the given equation is a horizontal shift of 5 units to the left. The answer choice is (c) Left 5.

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The correct transformation of the function on rational parent function as described by the given equation. The correct answer choice is (c) Left 5.

What is Function?

A function is  mathematical relationship that assigns  unique output value for each input value. It describes relationship between two variables, where  output value is dependent on input value. A function can be represented by  equation, a graph, or  table. In its simplest form,  function takes  input value, performs a specified operation on that value, and produces  corresponding output value.

The given equation is y = 12/(x + 5), which represents the rational parent function. To identify a correct transformation of the function, we can consider the effect of each transformation on the parent function.

a) Vertical reflection: This transformation would change the sign of the function, resulting in y = -12/(x + 5). This is not the given equation, so it is not a correct transformation.

b) Vertical stretch by 12: This transformation would multiply the function by 12, resulting in y = 12(12/(x + 5)) = 144/(x + 5). This is not the given equation, so it is not a correct transformation.

c) Left 5: This transformation would shift the function to the left by 5 units, resulting in y = 12/(x + 10). This is a correct transformation of the function, as it represents a horizontal shift of 5 units to the left.

d) Down 5: This transformation would shift the function down by 5 units, resulting in y = 12/(x + 5) - 5. This is not the given equation, so it is not a correct transformation.

Therefore, the correct transformation of the rational parent function as described by the given equation is a horizontal shift of 5 units to the left. The answer choice is (c) Left 5.

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Other Questions
Find the y-intercept for the parabola defined by this equation: y = 2x + x 1 Separate the values with a comma. Enter the correct answer. What is the area of this plane figure? 45 square centimeters 50 square centimeters 65 square centimeters 90 square centimeters 59 divided by 4=? Also, please don't use a fraction just keep it simple like 68R7.R/r=remainder Suppose we have a rod of length n inches and we also have an array of prices P, where P[i] denotes the selling price ($) of a piece that is i inches long. In class, we introduced an algorithm that uses dynamic programming to find a way of cutting the rod into pieces that maximizes the revenue (See CLRS Ch15.1 for reference). Suppose now we have to pay a cost of $1 per cut. The profit can be defined as revenue minus the total cost of cutting. Suggest an algorithm to find a way to cut the rod that maximizes our profit. State a expression for the run time of your algorithm. each object in a discretionary access control system has an access control list associated with it. T/F A recipe for Potato Soup is listed below:3 1/2 cups of peeled and diced potatoes1/3 cup finely chopped onion3 1/4 cup water2 cups of milk1/2 teaspoon salt5 tablespoons of butter1/3 cup diced celery3/4 cup of diced ham2 tablespoons of chicken bouillon granules1 tablespoon ground black pepper5 tablespoons of all purpose flour.You accidently use 5 cups of potatoes. Approximately how many cups of water will you need for 5 cups of potatoes? There are N provinces (1 2... N. King Bob wants to create his kingdom. For this, he needs to capture some provinces. Two provinces can be connected by water, land, or by both. A pair of provinces are connected by land and B pairs of provinces are connected by water. Since bob's navy is very weak, he does not want any of his captured provinces to be connected by water, moreover, Bob has a strong army, so he wants to capture every province that is connected to his kingdom by landMore formally, the following conditions must be satisfied:For each captured province every province connected to it by land should also be captured.No two provinces captured should be connected by water directly or byany other provinces.Any two captured provinces should be connected directly or through other captured provincesTaskOutput the maximum number of provinces that Bob can capture satisfying the given conditions. If bob can't capture any province then output 0ExampleAssumptionsT=1N-5A=2B-1land 1. 21 (2, 3 1.21water-13ApproachProvince 1 is connected to province 2 by land, province fis connected toprovince 3 by water, and province 2 is connected to 3 by land.Following provinces can be captured (4) (5) Group of provinces [1 2 3] can't be captured because fand 3 areconnected by water. Therefore the minimum number of provinces that can be captured is1.Function descriptionComplete the function solved provided in the editor. This function takes thefollowing five parameters and returns the required answer.N Represents the number of provincesA Represents the number of provinces connected by landB Represents the number of provinces connected by waterland[A](2) land[[0] and land[1] represent that these provinces areconnected by land water B2) water[i][0] and water[i][1] represent that these provinces areconnected by waterInput formatNote: This is the input format that you must use to provide custom input (available above the Compile and Test button).The first line contains 7, the number of test cases. 7 also specifies thenumber of times you have to run the solve function on a different set ofInputs:For each test case:The first line contains N, the number of provinces.The second line contains A, the number of pairs of provincesconnected by land.The third line contains B, the number of pairs of provinces connected by water.The next A lines contain two space separated integers Le. twoprovinces connected by land,The next 8 lines contain two space-separated integers le. twoprovinces connected by waterOutput formatFor each test case in a new line, print the answer.Constraints11 N 1050A+BN1 What is the slope of a line perpendicular to the line is question is 3x-3y=54? fully reduce your answer. (its not 1) A solution of hydrochloric acid of unknown concentration was titrated with 0.16 M NaOH. If a 350-mL sample of the HCl solution required exactly 17 mL of the NaOH solution to reach the equivalence point, what was the pH of the HCl solution? What is the value of x in the equation 3(2x-1)=21 a.3 b.11/3 c.4 d.25/2 a boy of mass 43.2 kg runs and jumps onto a stationary skateboard. The boy lands on the skateboard with a horizontal velocity of 4.10 m/s. The skateboard has a mass of 2.50 kg.Using ideas about conservation of momentum,calculate the combined velocity of the boy and skateboard just after the boy lands on it.(Pls explain. I've got my physics exams very soon) 8) rent, electricity, and executive salaries that do not vary with production or sales level are referred to as costs. a) fixed b) variable c) break-even d) target e) promotional A chemical equation is shown below.KNO3 KNO2 + O2What are the coefficients that should be added to balance this equation? Use complete sentences to explain your answer.Explain how this chemical reaction demonstrates the conservation of mass. (8 points) Claim #1: William Shakespeare is considered one of the greatestplaywrights of all time.Claim #2: William Shakespeare was a fraud who many believe didn'teven write his own plays.Which piece of evidence best supports claim #2?O A. Shakespeare invented many words that are still used today.O B. Shakespeare's plays touch on themes that are still relevant totoday's audiences.O c. Most of Shakespeare's plays are still performed around the worldtoday.D. Shakespeare was thought to be illiterate and unable to write evena simple sentence. Problem: Within a population of butterflies, the color brown (B) is dominant over the color white (b). 40% of the butterflies are white. Given this information, choose the correct answers that will properly identify the values for dominant and recessive alleles and genotypes of the population. What is the value for the dominate allele of the example above? Question 1 options:0.040.600.880%Question 2Within a population of butterflies, the color brown (B) is dominant over the color white (b). 40% of the butterflies are white. Given this information, choose the correct answers that will properly identify the values for dominant and recessive alleles and genotypes of the population.What is the value for the recessive allele of the above example? Question 2 options:0.600.80.4080%Question 3 Within a population of butterflies, the color brown (B) is dominant over the color white (b). 40% of the butterflies are white. Given this information, choose the correct answers that will properly identify the values for dominant and recessive alleles and genotypes of the population. Using the H-W equation; if the 2pq value of the butterflies was 0.48, what does this indicate?Question 3 options:Heterozygous individuals Homozygous individualsDominant alleles onlyMore information is needed Question 4 Within a population of butterflies, the color brown (B) is dominant over the color white (b). 40% of the butterflies are white. Given this information, choose the correct answers that will properly identify the values for dominant and recessive alleles and genotypes of the population. Using your H-W equation, calculate the following. The value of q is 0.28; what is the value of p2?Question 4 options:0.520.320.720.08Question 5 Within a population of butterflies, the color brown (B) is dominant over the color white (b). 40% of the butterflies are white. Given this information, choose the correct answers that will properly identify the values for dominant and recessive alleles and genotypes of the population. What does the above information tell us about the answer of p = 0.72? Question 5 options:Homozygous recessive individuals are more commonHeterozygous individuals are more commonBoth the dominant and recessive alleles are equally dispersed in this populationHomozygous dominant individuals are more common Question 6 Heterozygous individuals will display the dominant trait but carry the recessive allele that can be passed to future offspring.Question 6 options: True False The data indicate the following approximate percentages:14.4% of this group were male and worked in education25.2% of this group were female and worked in business 34.5% of this group were male54.7% of this group worked in education.5 ptsQuestion 1Based on the scenario above, complete the following table.Employment By Number (Frequency Table)EmploymentBy GenderBusinessEducationTotalMale2,997,714Female6,010,3429.768,670Total6,756,04214.914,000 Is over drainage suitable for cultivation of citrus? Why? Pls need help fast a client asks why three medications are prescribed to treat his tuberculosis. the nurse informs the client of which reasons? hi guys,in autumn the tree....their leaves. lose or are losing?which one is correct? 2Select the correct answer from each drop-down menu.Statement 1: A number is prime if and only if it only has two unique factors.Statement 2: A number has more than two unique factors if and only if it is not prime.Statement 2 is true v The contrapositive of a biconditional statement isResetnever truealways truesometimes true