Use the Root Test to determine whether the series convergent or divergent. [infinity] n2 + 2 7n2 + 5 n n = 1 Identify an. Evaluate the following limit. lim n → [infinity] n |an| Since lim n → [infinity] n |an| ? 1, ---Select--- .

Answers

Answer 1

By using the Root Test on the series "∑n" , we found that the series is Divergent and diverges to infinity .

The Root Test states that, if the limit of nth root of the absolute value of the nth term of a series is less than 1, then the series converges. and

If the limit is greater than or equal to 1, the test is inconclusive.

In the series ∑n , the nth term of the series is "n" ,

So, the nth root of the absolute value of nth term is the nth root of |n|, which is = n^(1/n).

we see that as n approaches infinity, the nth root : n^(1/n) approaches 1, So,  the limit of the nth root of the absolute value of the nth term is equal to 1. Which means that the Root Test is inconclusive for this series.

Therefore , the series ∑n diverges, it is a known series called as Harmonic series, which diverges to infinity.

The given question is incomplete , the complete question is

Use the Root Test to determine whether the series convergent or divergent.  ∑n , where n is from 1 to infinity .

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Related Questions

Can anyone help me with this please, I need written out work not just an answer please

Answers

Answer:

hhyýuhhhí7 and Pakistan were colonized together so the britains could no win the fight with india therefore

Step-by-step explanation:

because at that time india and Pakistan were colonized together so the britains could no win the fight with india therefore Britain's plan to intimidate

Answer:

See below

Step-by-step explanation:

I am assuming you need help only for the bottom questions as the top is VERY simple (the top of the cross is literally multiplication of the numbers and the bottom of the cross is addition). This questions needed to be worth more points, with that being said

1. [tex]4y^3 - 2y + 3y^2 - 5y - y^2[/tex]

Combine like terms

[tex]4y^3 - 2y^2 - 7y[/tex]

2. [tex](2x^2 - x + 1) - (x+1)[/tex]

Remove numbers from brackets by distribution property (just imagine a one on the outside of the bracket)

[tex]2x^2 - x + 1 -x - 1\\2x^2 - 2x\\2x(x - 1)[/tex]

3. [tex]-2p^3(-2p^4 + 5p^2 - p)[/tex]

This is just distribution property, multiple the outside by inside (you add the exponents when you multiply)

   [tex]4p^7 - 10p^5 + 2p^4[/tex]

4. [tex](3y-6)(2y+3)[/tex]

You multiply each term on the inside of one bracket with the ones on the inside of the other bracket

[tex]6y^2 + 6y -12y -18\\6y^2 - 6y - 18\\6(y^2 - y -3)[/tex]

5. [tex](x+6)(x-6)[/tex]

Same as above but honestly its much quicker if you know the b term in ax^2 + bx + c = 0 always equals 0 in this case

[tex]x^2 -6x + 6x -36\\x^2 - 36[/tex]

[WILL GIVE BRAINLIEST!]
Angle α is in quadrant III and angle β is in quadrant IV. If sin α = –5/6 and cos β = 1/2, find cos(α + β).

Answers

Answer:

Step-by-step explanation:

The expansion for cos(x+y) is cosx*cosy - sinx*siny. We have sin x and cos y, now we need cosx and siny.

Angle x is in QIII and has a sin ratio of -5/6. Since the hypotenuse will never be negative and sin is opposite over hypotenuse, the side across from the reference angle, aka the height of the triangle, is -5 and the hypotenuse is 6. Using Pythagorean's Theorem we can find the third side:

[tex]6^2=(-5)^2+x^2[/tex] and

[tex]36=25+x^2[/tex] and

[tex]36-25=x^2[/tex] so

x = √11.

We do the same for the other angle y. We have the cos of angle y is 1/2 and since the cos ratio is adjacent over hypotenuse, the side next to the reference angle is 1 and the hypotenuse is 2 and we will find the third side using Pythagorean's Theorem:

[tex]2^2=1^2+y^2[/tex] and

[tex]4=1+y^2[/tex] and

[tex]3=y^2[/tex] so

y = √3.

We already know sinx = -5/6, now we know that cosx = -√11/6.

We already know cosy = 1/2, now we know that siny = -√3/2.

Now we can fill in the expansion for cos(x+y):

[tex](-\frac{\sqrt{11} }{6})(\frac{1}{2})-(-\frac{5}{6})(-\frac{\sqrt{3} }{2})[/tex] Multiplying straight across the top and bottom we get

[tex]-\frac{\sqrt{11} }{12}-\frac{5\sqrt{3} }{12}[/tex] which simplifies to

[tex]\frac{-\sqrt{11}-5\sqrt{3} }{12}[/tex]

And you're done!

if ₱60,000.00 was deposited in a bank and became ₱61,625.00 at the end of 150 days, find the interest rate using exact and ordinary days.

Answers

Days exactly: The rate of interest is 4.17%. The interest rate of  amount is 4.21% on regular days.

I = P x R x T/365, where I is the interest, P is the principal, R is the rate, and T is the duration, can be used to determine the interest rate using exact days.

I = 61625 - 60000 = 625, P = 60000, R =?, and T = 150 are the numbers used in this calculation. The formula for 625 reads as follows: 625 = 60000 x R x 150/365. By multiplying both sides by 365/150, we may find R. As a result, R = 625 x 365/90000 = 4.17%.

I = P x R x T/360, where I is the interest, P is the principal, and R is the rate of return, can be used to get the interest rate using regular days.T stands for time, and R represents the rate. I = 61625 - 60000 = 625, P = 60000, R =?, and T = 150 are the numbers used in this calculation. The formula for 625 reads as follows:

625 = 60000 x R x 150/360. By dividing both sides by 360/150, we may find R. As a result, R = 625 x 360/90000 = 4.21%.

I = P x R x T/365, which means that R = I x 365/P x T = 625 x 365/60000 x 150 = 4.17%. Exact days

I = P x R x T/360 on typical days, which means that R = I x 360/P x T is 625 x 360/60000 x 150, or 4.21%.

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I need help PLEASE PEOPLE!!

Answers

Answer:     3

Step-by-step explanation:

22.5% of 40= 9 which is the amount for cats

30% of 40= 12 which is the amount for dogs.

12-9=3

The answer is 3 trust me

Find the amount in a continuously compounded account for the following condition.
Principal, $4000; Annual interest rate, 5.7%; time, 2 years
The balance after 2 years is $

(Round the final answer to the nearest cent as needed. Round all intermediate values to five decimal places as needed.)

Answers

The balance after 2 years would be $4482.25

What exactly is compound interest?

Compound interest is when you earn interest on both your savings and your interest earnings.

The formula for finding the amount in a continuously compounded account is: A = P * e^(rt), where A is the final amount, P is the principal, r is the annual interest rate as a decimal, t is the time in years, and e is the mathematical constant approximately equal to 2.718.

Using this formula, we have:

            [tex]A = $4000 * e^(0.057 * 2) = $4000 * e^0.114\\\\A = $4000 * 1.12061367\\\\A = $4482.25[/tex]

So the balance after 2 years would be $4482.25

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In Exercises 27-34, determine the values ofr and s for wlhich the given system of linear equations has (a) no solutions, (b) exactly one solution, and (c) infinitely many solutions.
27.
x₁ + rx₂ = 5
3x₁ + 6x₂ = s
28.
-x₁ + 4x₂ = s
2x₁ + rx₂ = 6

Answers

(a) No solutions when r ≠ 6 and s ≠ 5. (b) Exactly one solution when r = 6 and s = 5. (c) Infinitely many solutions when r = 6 and s is arbitrary.

For the system of equations to have (a) no solutions, both r and s must have values that do not satisfy the equations. For example, if r ≠ 6 and s ≠ 5, then the equations cannot both be true. For the system to have (b) exactly one solution, both r and s must have values that satisfy the equations. For example, if r = 6 and s = 5, then the equations are both true and have one unique solution. For the system to have (c) infinitely many solutions, one of the variables must have a value that satisfies the equations, while the other variable may take on any value. For example, if r = 6 and s is arbitrary, then the equations are both true and have infinitely many solutions.

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table 6 gives the regression statistics from estimating the model Δln (Salest) = b0 + b1Δln (Salest −1) + εt. table 6 Change in the natural log of Sales for Cisco Systems Quarterly Observations, 3Q:1991–4Q:2000 regression Statistics R-squared Standard error Observations Durbin–watson intercept Δln (Salest −1) Coefficient 0.0661 0.4698 0.2899 0.0408 38 1.5707 Standard error 0.0175 0.1225 t-Statistic 3.7840 3.8339 a. Describe the salient features of the quarterly sales series. b. Describe the procedures we should use to determine whether the ar(1) specification is correct. C. assuming the model is correctly specified, what is the long-run change in the log of sales toward which the series will tend to converge

Answers

As per the regression equation, the value of intercept coefficient is 1.5707

Regression is a statistical technique used to determine the relationship between an independent variable and a dependent variable.

In this case, the regression statistics provided in table 6 show the results of estimating the model

=> Δln (Sales t) = b0 + b1Δln (Sales t −1) + εt,

where Δln (Sales t) is the change in the natural log of sales for Cisco Systems quarterly observations from 3Q:1991 to 4Q:2000.

The R-squared value of 0.0661 indicates that only about 6.61% of the variation in the change in the log of sales can be explained by the change in the log of sales from the previous quarter.

The standard error of 0.4698 indicates the average deviation between the actual and predicted change in the log of sales.

If the results show that the specification is correct, then the long-run change in the log of sales toward which the series will tend to converge can be determined by the intercept coefficient, which in this case is 1.5707.

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Which ordered pairs represent points on the graph of this equation? Select all that apply.
2y=4–5x

Answers

The graph of the equation is attached, and the coordinates are (0, 2), (2, -3), (1, -0.5), and (-2, 7).

What is the cartesian plane?

When two parallel lines intersect, a two-dimensional coordinate plane called the cartesian plane is created. The horizontal line is the X-axis, while the vertical line is the Y-axis. If the sign of x is positive, the coordinate point (x, y) in the Cartesian plane indicates that the point is on the right of the origin; otherwise, it indicates that the position is on the left of the origin.

Given equation, 2y = 4 - 5x

let's find the coordinates for the graph,

when x = 0

2y = 4

y = 2

(0, 2)

when x = 2

2y = 4 - 5*2

2y = -6

y = -6/3

y = -3

(2, -3)

when x = 1

2y = 4 - 5

2y = -1

y = -0.5

(1, -0.5)

when x = -2

2y = 4 - 5(-2)

2y = 14

y = 7

(-2, 7)

coordinates for the graph are (0, 2), (2, -3), (1, -0.5), (-2, 7).

Hence graph lies in coordinates (0, 2), (2, -3), (1, -0.5), (-2, 7).

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elena is a college freshman taking an introductory statistics course. her professor has assigned the class the task of organizing data on the relationship between level of income and happiness. what will elena use to summarize her data in a single score?

Answers

Elena will likely use a measure of central tendency, such as the mean or median, to summarize her data in a single score.A measure of central tendency is a statistical value that summarizes a set of data.

It is accomplished by assigning a representative score, usually the most common value in a dataset. Elena's statistics course assignment requires her to utilise either the mean or the median to summarise the link between money and happiness.

The mean is computed by summing all of the values in a dataset and dividing by the total number of values. When a set of data is ordered numerically, the median is the midway value. Both of these metrics generate a single score that reflects the full dataset, making it easier to comprehend and make inferences from it.

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What conjectures can you make about a point on the perpendicular bisectors of a segment and a point of a bisector of an angle ?

Answers

The conjectures which you can make about a point on the perpendicular bisectors of a segment and a point of a bisector of an angle include the following below:

If a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.If a point lies on the bisector of an angle, then it is equidistant from the two sides of the angle.

What is a Bisector?

Th line that divides something into two equal parts and it is usually applied to the line segments and angles.

The following relationships between them is that if there is a point which lies on the perpendicular bisector of a segment, then it is most likely to be equidistant from the endpoints of the segment when scrutinized thereby making it the correct choice.

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a regular hexagon with 6 sides is inscribed in a circle with a radius of 11 millimeters. what is the area of the figure?

Answers

The area of the figure ( a regular hexagon ) is 314.37 square millimeters     .

A regular hexagon which is inscribed in a circle consist of 6 equilateral triangle. All angle is equal.

So side length of the regular hexagon will be same with the radius of circle.

From the question we have following information :

1. Regular hexagon inscribed in a circle

2. Radius of circle is 11 millimeters.

To find the area of the hexagon we can use following formula

A = (3√3) / 2 * [tex]r^{2}[/tex]

Substituting r = 11mm into the equation for the area of the hexagon,

A = (3√3) / 2 * [tex]11^{2}[/tex] = (3√3) / 2 * 121 = 314.367 square millimeters

So the area of the figure is approximately 314.37 square millimeters (rounded to two decimal places).

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Hudson is blocking off several rooms in a hotel for guests coming to his wedding. The
hotel can reserve small rooms that can hold 3 people, and large rooms that can hold 4
people. Hudson reserved twice as many large rooms as small rooms, which altogether
can accommodate 66 guests. Write a system of equations that could be used to
determine the number of small rooms reserved and the number of large rooms
reserved. Define the variables that you use to write the system.

Check picture for full question.

Answers

Answer:

The picture won't show. are there answer options?

Step-by-step explanation:

Small room (S) - hold 3 people

Large room (L)- hold 4 people

Hudson reserved twice as many large rooms = 2x Large room #

2L + S = 66

So,

Let S = Small room

Let L = Large room

I hope this can make things slightly easier for you. I tried to make it more visible for you. Please comment if you need more help.

solve each equation for x e^2− 4x = 8

Answers

subtract e^2/4 from both sides of the equation to get x = (e^2 - 8)/4. This is the final answer of the equation.

e^2 - 4x = 8

4x = e^2 - 8

x = (e^2 - 8)/4

To solve for x in this equation, the first step is to subtract 8 from both sides of the equation. The next step is to divide both sides of the equation by 3.This results in the equation:  x = 4.Once 8 is subtracted from both sides, the equation becomes e^2 - 4x = 0. Then, divide both sides of the equation by 4, which gives 4x = e^2/4. Finally, subtract e^2/4 from both sides of the equation to get x = (e^2 - 8)/4. This is the final answer of the equation.

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Special quadrilateral

Answers

The following are the respective measures of angles and lengths of the rectangle ABCD:

m∠1 = 49°, m∠2 = 41°, m∠3 = 41°, m∠ADC = 90°, AB = 6.9, BD = 10, and CE = 5.

How to calculate the angles and lengths for the rectangle.

Considering the triangle AEB, angles A and B are base angles of a the isosceles triangle AEB so;

2(m∠ABE) + 98 = 180° {sum of interior angles of a triangle}

m∠ABE = (180 - 98)/2

m∠ABE = 41°

m∠1 = 90° - 41° {complementary angles of a rectangle}

m∠1 = 49°

angles m∠2 and m∠BAC are alternate angles and are equal so;

m∠2 = 41°

m∠ADC is one of the four interior angles of a rectangle so m∠ADC = 90°

Considering the right triangle ∆ABD and the tangent of angle B = 41°, we can solve for the length of AB as follows:

tan 41° = 6/AB {opposite/adjacent}

AB = 6/tan41° {cross multiplication}

AB = 6.9022.

m∠3 and m∠ABD are alternate angles so;

m∠3 = 41°

lines AC and BD are diagonals of the rectangle and they bisect each other, since EB = 5 then;

BD = 2 × 5 = 10

CE = 5

Therefore, the following are the respective measures of angles and lengths of the rectangle ABCD:

m∠1 = 49°, m∠2 = 41°, m∠3 = 41°, m∠ADC = 90°, AB = 6.9, BD = 10, and CE = 5.

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PLS ANSWER!!! Question down below! Limited time!

Answers

Answer:

Step-by-step explanation:

Please help me solve for the rest of them

Answers

The angles in the given triangle are ∠2=65°,∠5=100°,∠6=100°,

∠7=35°,∠8=145°,∠9=115°.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle is less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now,

Given ∠4=115°,∠1=35°

∠2+∠4=180  ( supplementary angles)

∠2=180-115=65°

∠1+∠2+∠3=180 (sum of angles of a triangle=180°)

∠3=180-65-35=80°

∠3+∠5=180

∠5=180-80=100°

∠5=∠6=100°  (opposite angles)

∠1=∠7=35° (opposite angles)

∠7+∠8=180 (supplementary angles)

∠8=180-35=145°

∠4=∠9=115°  (opposite angles)

Hence,

           The angles in the given triangle are ∠2=65°,∠5=100°,∠6=100°,

∠7=35°,∠8=145°,∠9=115°.

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In a large city, taxicabs charge $1.00 for the first mile and $0.30 for each additional mile. Frank has only $3.50. What is the maximum
distance he can travel (not including a tip for the cabbie)?

Answers

The maximum distance Frank can travel would be 10 miles.

What is maximum distance?

For maximum distance that is maximum range of a projectile, the angle of projectile should be 45°.

From given question,

taxicabs charge for first mile = $1.00

for each additional mile = $0.30

The cost for the first mile is $1, and for each additional mile it's $0.30, so for 10 miles it would be $1 + 9 * $0.30 = $4.70. Since Frank has only $3.50, he can travel a maximum of 10 miles.

Therefore, The maximum distance Frank can travel would be 10 miles.

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Sebastian bought 3 envelopes with 6 figures each. How many figures did he buy in all?​​

Answers

Answer: Sebastián bought 18 figurines.

Step by step explanation:

Data :

Sebastian bought = 3 envelopesEach envelope has = 6 figurinesTotal figures = ?

We must bear in mind that Javier bought 3 envelopes of 6 figurines each. Calculate the total number of figurines by adding 6 + 6 + 6 therefore:

[tex]\bf \: 6 + 6 + 6 = \boxed{ \bf18}[/tex]

Rpt: Sebastián bought 18 figurines.

The answer is 18 because if you draw 3 circles and draw six dots in them and you count them the answer will be 18

3.5 minutes into meters per second

Answers

Answer:

0.583 [the 3 goes on forever]

Step-by-step explanation:

Kiara measured a swimming pool and made a scale drawing. The scale she used was 13 centimeters : 6 meters. In the drawing, the pool is 26 centimeters wide. What is the width of the actual pool?

Answers

The width of the actual pool is 156 meters.

Given the scale used in the drawing is 13 centimeters : 6 meters, we can use this ratio to convert the width of the pool in the drawing to the actual width of the pool.

width (actual) = (width (drawing) / 13 cm) * 6 meters
width (actual) = (26 cm / 13 cm) * 6 meters = 2 * 6 meters = 12 meters

So the actual width of the pool is 156 meters

three strangers meet at a taxi stand and decide to share a cab to cut down the cost. each has a different destination but all are heading in more-or-less the same direction. bob is traveling 10 miles, sally is traveling 20 miles, and mike is traveling 30 miles. if the taxi costs $2 per mile, how much should each contribute to the total fare? what do you think is the most common answer to this question?

Answers

The most common answer to this question is that people would suggest splitting the fare equally i.e. each person contributes $40.

Each stranger should contribute to the total fare based on the distance traveled, so the fare would be divided as follows -

Bob: 10 miles * $2/mile = $20

Sally: 20 miles * $2/mile = $40

Mike: 30 miles * $2/mile = $60

Total fare: $20 + $40 + $60 = $120

Therefore, each stranger should contribute $120/3 = $40 to the total fare.

The most common answer to this question is that people would suggest splitting the fare equally, i.e. each person contributes $40, regardless of the distance traveled. This is because it is a simpler and fairer solution, as each person benefits from the shared ride and the cost savings, regardless of the distance traveled.

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what is the bank routing number on the check? a sample check. responses 204.67 204.67 856425785 856425785 403 403 2146578212

Answers

The bank routing number on a check is a 9-digit code used to identify a financial institution in a transaction. It is also known as an ABA routing number, an RTN, and a routing transit number.

In order to determine the routing number on a check:

Look at the bottom left corner of the check, where the routing number is printed in magnetic ink.    The first nine digits of the MICR (Magnetic Ink Character Recognition) line, located at the bottom of the check, represent the routing number.The routing number may also be printed on the check in a different location, such as the top or bottom right.    One could also find their bank routing number by searching online or contacting their bank directly.

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how many distinct initial possible pairings are there for a single-elimination ping-pong tour- nament involving n players that result in distinct tournament brackets, for n = 2, 4, 8?

Answers

The number of distinct initial possible pairings for a single-elimination ping-pong tournament with n players that result in distinct tournament brackets is 2^(log2(n) - 1).

What is logarithm ?

The logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

In a single-elimination ping-pong tournament, each player plays one match in each round until a champion is determined. For n players, there are log2(n) rounds in the tournament, and in each round half the players are eliminated.

For n = 2, there is only 1 player left after the first round, so there is only 1 distinct pairing and 1 distinct tournament bracket.

For n = 4, there are 2 players left after the first round, and they play in the final. There are 2 possible pairings for the first round, which result in 2 distinct tournament brackets.

For n = 8, there are 4 players left after the first round, and there are 4 possible pairings for the first round. These pairings result in 4 distinct tournament brackets.

So the number of distinct initial possible pairings for a single-elimination ping-pong tournament with n players that result in distinct tournament brackets is 2^(log2(n) - 1).

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PLEASE HELP MEEE!!! WILL GIVE BRAINLIEST!!!

Answers

I am pretty sure the answer would be (2,3)

I NEED HELP ASAP!!
How many boxes would Alan have to sell to earn exactly $700?

Answers

Answer: Alan would have to sell exactly 180 boxes.

Step-by-step explanation:

Hey can you please help me what is 2 1/5 x 1 1/4 as a simplest form?

Answers

Answer: 2 3/4.

Step-by-step explanation: To multiply the mixed numbers, we need to first make them into improper fractions. To make 2 1/5 into an improper fraction, we multiply the whole number 2 by the denominator, 5, and add that to the numerator 1, giving us 11/5. We do the same for 1 1/4, giving us 5/4. 5/4 x 11/5 equals 55/20. 55/20 simplifies to 2 3/4.

Please help ASAP the question is in the picture

Answers

The data represent a quadratic function.

What is a quadratic equation?

A quadratic equation is a second-order polynomial equation with a single variable such as x, where ax²+bx+c=0. with a ≠ 0 . Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. Real or complicated solutions are both possible.

To calculate the second difference,

select 3 consecutive y-values, and then subtract the first y-value from the second and the second y-value form the third. Then find the difference of these two resulting values . If all second differences are equal, the data represent a quadratic function.

1) -7,-5, -1

second y value  - first y-value = 2

third   y value  -   second y value = 4

difference of these two resulting values  = 2

2) -5,-1,5

second y value  - first y-value = 4

third   y value  -   second y value = 6

difference of these two resulting values  = 2

The data represent a quadratic function.

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Simplify the following using trigonometric identities:
( 1 + sin (x) ) ( sec (x) - tan (x) )

Answers

Answer:

[tex](1+\sin(x))(\sec(x)-\tan(x))=\cos(x)[/tex]

Step-by-step explanation:

We are going to use the Pythagorean trigonometric identity:

[tex]\sin^2(x)+\cos^2(x)=1[/tex]

and the following relationships between trigonometric functions:

[tex]\sec(x)=\frac{1}{\cos(x)}\\\tan(x)=\frac{sin(x)}{cos(x)}[/tex]

We can transform the expression as follows:

[tex](1+\sin(x))(\sec(x)-\tan(x))=(1+\sin(x))(\frac{1}{\cos(x)}-\frac{\sin(x)}{\cos(x)})=(1+\sin(x))\frac{1-\sin(x)}{\cos(x)}=\frac{(1+\sin(x))(1-\sin(x))}{\cos(x)}[/tex]

Using the formula for the difference of two squares, we can write

[tex](1+\sin(x))(1-\sin(x))[/tex]

as

[tex]1-\sin^2(x)[/tex]

which, according to the Pythagorean trigonometric identity, is equal to

[tex]\cos^2(x)[/tex]

Now we can simplify the original expression to

[tex]\frac{\cos^2(x)}{\cos(x)}=\cos(x)[/tex]

Helppp due tomorrow!!

Answers

Answer:

Length = 7.83, Width = 3.83

Step-by-step explanation:

Assign variables. Let x represent the width

Area (L x W) = 30 m²

(4 + x)(x) = 30

4x + x² = 30

x² + 4x - 30 = 0

Apply Quadratic Formula

[tex]\frac{-4 + \sqrt{4^2 - 4(1)(-30)}}{(2)(1)}[/tex]

Solve

x = -2 ± √34

x = 3. 83... or x = -7.83 (reject this one)

Width = 3.83

Length = x + 4 = 7.83

Show that DF is parallel to AB in that DF equals 1/2 of AB

Answers

The segments DF and AB are parallel, as they have the same slope.

How to obtain the slope of a segment?

A segment is composed by two endpoints, and then the slope is calculated as the change in y divided by the change in x of these points.

The endpoints of segment AB are given as follows:

A(-5,2) and B(1,-2).

Hence the slope is of:

m = (-2 - 2)/(1 - (-5)) = -4/6 = -2/3.

The endpoints of segment DF are given as follows:

D(-4,-2) and F(-1,-4).

Hence the slope is of:

m = (-4 - (-2))/(-1 - (-4)) = -2/3.

As the segments have the same slope, they are parallel.

More can be learned about parallel segments at https://brainly.com/question/24243384

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