If a and b are positive numbers, find the maximum value of f(x) = x^a(2 − x)^b on the interval 0 ≤ x ≤ 2.

Answers

Answer 1

Answer:

The maximum value of f(x) occurs at:

[tex]\displaystyle x = \frac{2a}{a+b}[/tex]

And is given by:

[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

We are given the function:

[tex]\displaystyle f(x) = x^a (2-x)^b \text{ where } a, b >0[/tex]

And we want to find the maximum value of f(x) on the interval [0, 2].

First, let's evaluate the endpoints of the interval:

[tex]\displaystyle f(0) = (0)^a(2-(0))^b = 0[/tex]

And:

[tex]\displaystyle f(2) = (2)^a(2-(2))^b = 0[/tex]

Recall that extrema occurs at a function's critical points. The critical points of a function at the points where its derivative is either zero or undefined. Thus, find the derivative of the function:

[tex]\displaystyle f'(x) = \frac{d}{dx} \left[ x^a\left(2-x\right)^b\right][/tex]

By the Product Rule:

[tex]\displaystyle \begin{aligned} f'(x) &= \frac{d}{dx}\left[x^a\right] (2-x)^b + x^a\frac{d}{dx}\left[(2-x)^b\right]\\ \\ &=\left(ax^{a-1}\right)\left(2-x\right)^b + x^a\left(b(2-x)^{b-1}\cdot -1\right) \\ \\ &= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right] \end{aligned}[/tex]

Set the derivative equal to zero and solve for x:

[tex]\displaystyle 0= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right][/tex]

By the Zero Product Property:

[tex]\displaystyle x^a (2-x)^b = 0\text{ or } \frac{a}{x} - \frac{b}{2-x} = 0[/tex]

The solutions to the first equation are x = 0 and x = 2.

First, for the second equation, note that it is undefined when x = 0 and x = 2.

To solve for x, we can multiply both sides by the denominators.

[tex]\displaystyle\left( \frac{a}{x} - \frac{b}{2-x} \right)\left((x(2-x)\right) = 0(x(2-x))[/tex]

Simplify:

[tex]\displaystyle a(2-x) - b(x) = 0[/tex]

And solve for x:

[tex]\displaystyle \begin{aligned} 2a-ax-bx &= 0 \\ 2a &= ax+bx \\ 2a&= x(a+b) \\ \frac{2a}{a+b} &= x \end{aligned}[/tex]

So, our critical points are:

[tex]\displaystyle x = 0 , 2 , \text{ and } \frac{2a}{a+b}[/tex]

We already know that f(0) = f(2) = 0.

For the third point, we can see that:

[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(2- \frac{2a}{a+b}\right)^b[/tex]

This can be simplified to:

[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]

Since a and b > 0, both factors must be positive. Thus, f(2a / (a + b)) > 0. So, this must be the maximum value.

To confirm that this is indeed a maximum, we can select values to test. Let a = 2 and b = 3. Then:

[tex]\displaystyle f'(x) = x^2(2-x)^3\left(\frac{2}{x} - \frac{3}{2-x}\right)[/tex]

The critical point will be at:

[tex]\displaystyle x= \frac{2(2)}{(2)+(3)} = \frac{4}{5}=0.8[/tex]

Testing x = 0.5 and x = 1 yields that:

[tex]\displaystyle f'(0.5) >0\text{ and } f'(1) <0[/tex]

Since the derivative is positive and then negative, we can conclude that the point is indeed a maximum.

Therefore, the maximum value of f(x) occurs at:

[tex]\displaystyle x = \frac{2a}{a+b}[/tex]

And is given by:

[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]


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NAME THE SONG AND THE SINGER 50 POINTS!!!!!

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Answer:

give heaven some hell by Hardy

Step-by-step explanation:

The value of the digit 2 in 425.3 is *

Answers

Answer:

20 which is twenty

Step-by-step explanation:

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Joe lost his part-time job, which reduced the net family income by 20%. His wife Janice decided to work overtime to compensate for the lost income. Other things being equal, by what percentage must her net salary increase in order to arrive at the same net family income as they had before Joe lost his job?​

Answers

The percentage by which Janice's net salary must be increased in order to arrive at the same net family income as they had before Joe lost his job is 25%.

What are Percentages?

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Let the salary of Joe be represented by x, while the salary of Janice is represented by y.

Since the sum of the salary of Joe and Janice is the net income of the family. Therefore, the net salary when Joe had a job will be,

x + y₁ = 100%

Now, it is known that Joe lost his job, which reduced the net family income by 20%.  Therefore, the net salary now will be only 80% which will be equal to the salary of Janice. Thus, we can write,

y₁ = 80%

Further, Janice decided to work overtime to compensate for the lost income. Therefore, we can write,

y₂ = 100%

Furthermore, the percentage change in salary of Janice can be written as,

Percentage Change = [(100% - 80%)/80% ] × 100%

                                  = 20/80  × 100%

                                  = 25%

Hence, the percentage by which Janice's net salary must be increased in order to arrive at the same net family income as they had before Joe lost his job is 25%.

Learn more about Percentages:

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Explain the step by step process of finding a function for a hyperbola given the center (1,4), vertices (-7,4) and (9,4), and a point on the hyperbola at (-11, -6). Make sure to include the location of the foci.

NO LINKS!! ​

Answers

Answer:

(x -1)²/64 -(y -4)²/80 = 1foci (-11, 4) and (13, 4)

Step-by-step explanation:

The standard form of a hyperbola whose transverse axis is horizontal is ...

  (x -h)²/a² -(y -k)²/b² = 1 . . . . center (h, k); transverse axis 2a; conjugate axis 2b

The distance between the two vertices is given as (9 -(-7)) = 16 = 2a, so the value of a is 8 and we have the partial equation ...

  (x -1)²/8² -(y -4)²/b² = 1

Filling in the given point value gives us an equation for b².

  (-11 -1)²/8² -(-6 -4)²/b² = 1

  9/4 -100/b² = 1

  5/4 = 100/b²

  b² = 80

So, the equation is ...

  (x -1)²/64 +(y -4)²/80 = 1

__

The distance between the foci is 2c, where c² = a² +b².

  c² = 64 +80 = 144 = 12²

  c = 12, so the foci are at ...

  (x, y) = (1 ±12, 4) . . . . . . . 12 units either side of the center

The foci are (-11, 4) and (13, 4).

_____

Additional comment

The steps are ...

use the given information to fill in as much of the equation as you can.use any given points or additional information to find the unknown values in the equationdetermine any additional information asked for (foci, asymptotes, ...)

The relevant relations are ...

  2a = length of transverse axis (distance between vertices)

  2b = length of conjugate axis (distance between co-vertices)

  ±b/a = slope of asymptotes, which are lines through the center

  2c = distance between foci, where c² = a² +b²

The equation is (x -h)²/a² -(y -k)²/b² = 1 for a hyperbola that opens horizontally with center (h, k). Swapping variables x and y will give a hyperbola that opens vertically. If the figure opens vertically, the asymptotes will have slope ±a/b.

The distances from a point to the foci have a constant difference of 2a.

A recipe calls for 3/4 of a cup of flour to make 5/8 of a pound of bread
dough. How many cups of flour are needed to make 1 pound of dough?
Show your work and write your answer in simplest form.

Answers

Answer:

[tex]\huge\boxed{\sf 1 \ pound \ of \ dough = 1\frac{1}{5} \ cup \ of \ flour}[/tex]

Step-by-step explanation:

[tex]\displaystyle \underline{Given \ that:}\\\\\frac{5}{8} \ pound \ of \ dough = \frac{3}{4} \ cup\ of \ flour\\\\Multiply \ 8 \ to \ both \ sides\\\\5 \ pounds \ of \ dough = \frac{3}{4} \times 8 \ cup \ of \ flour\\\\5 \ pounds \ of \ dough = 3 \times 2 \ cup \ of \ flour\\\\5 \ pounds \ of \ dough = 6 \ cups \ of \ flour\\\\Divide \ both \ sides \ by \ 5\\\\1 \ pound \ of \ dough = \frac{6}{5} \ cup \ of \ flour\\\\\boxed{1 \ pound \ of \ dough = 1\frac{1}{5} \ cup \ of \ flour}\\\\[/tex]

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807

Every Thursday, Matt and Dave's Video Venture has “roll-the-dice" day. A customer may choose to roll two fair dice and rent a second movie for an
amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a
second movie may be rented for $0.42. If a two and two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a
second movie on roll-the-dice day. The expected value of X is $0.47 and the standard deviation of X is $0.15.
If a customer rolls the dice and rents a second movie every Thursday for 30 consecutive weeks, what is the approximate probability that the total
amount paid for these second movies will exceed $15.00?

I saw other questions for this but why is the standard deviation 0.15*sqrt of 30 and not 0.15*30 because I thought this is a linear transformation

Answers

Using the normal distribution, it is found that there is a 0.1357 = 13.57% probability that the total  amount paid for these second movies will exceed $15.00.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean.  After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.For n instances of a normal variable, the mean is [tex]n\mu[/tex] and the standard error is [tex]s = \sigma\sqrt{n}[/tex]

In this problem:

Mean of $0.47, standard deviation $0.15, hence [tex]\mu = 0.47, \sigma = 0.15[/tex]30 instances, hence [tex]n\mu = 30(0.47) = 14.1, s = 0.15\sqrt{30} = 0.8216[/tex]

The probability is 1 subtracted by the p-value of Z when X = 15, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Considering the n instances:

[tex]Z = \frac{X - n\mu}{s}[/tex]

[tex]Z = \frac{15 - 14.1}{0.8216}[/tex]

[tex]Z = 1.1[/tex]

[tex]Z = 1.1[/tex] has a p-value of 0.8643.

1 - 0.8643 = 0.1357.

0.1357 = 13.57% probability that the total  amount paid for these second movies will exceed $15.00.

A similar problem is given at https://brainly.com/question/25769446

Can someone help me with both questions I will mark u brilliant

Answers

1. First, he will be climbing 10,000 feet from where he is right now. 10,000 / 1,000 = 10.

-3.6 x 10 = 36 degree decrease.

25 - 36 = -11

At 12,000 feet, the temperature will be -11.

2.  First, we need to do 8.80 x 7 = 61.6

61.6 / 4 = 15.4

61.6 - 15.4 = 46.2

He has $26.20 left.

Hope this helps!

Need help fast worth 20 points
Select the correct answer.
Which set of absolute values is compared correctly
OA. 1-10] < |-5| < |17| < 151
OB. 1-5| > |-10| > |-12| > |17||
OC. |10| > |-15] > [-5| > 12||
OD. |-101 < [12] < |-15| < |17||

Answers

Answer:

i think its b.

Step-by-step explanation:

correct me if im wrong. and it was worth 10 points instead of 20.

What is the possible degree of a polynomial if it has a root of -3 with multiplicity of 2 and, a root of 4 with a multiplicity of 1?

Answers

Answer:

3rd degree

Step-by-step explanation:

factors are

a(x + 3)(x + 3)(x - 4)

polynomial is

a(x² + 6x + 9)(x - 4)

a(x³ + 2x² - 15x - 36)

where (a) could be any real number

The Office of Student Services at a large western state university maintains information on the study habits of its full-time students. Their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. The hours studied follows the normal distribution with a population standard deviation of seven hours. Suppose we select a random sample of 125 current students. What is the probability that the mean of this sample is between 19.25 hours and 21.0 hours

Answers

There is a probability of 77% that the mean of this sample is between 19.25 hours and 21.0 hours

Z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} } \\\\where\ x=raw\ score,\mu=mean,\sigma=standard\ deviation,n=sample\ size[/tex]

Given that μ = 20, σ = 7, n = 125.

For x = 19.25:

[tex]z=\frac{19.25-20}{7/\sqrt{125} } =-1.20\\\\\\For\ x=21:\\\\z=\frac{21-20}{7/\sqrt{125} } =0.62[/tex]

From the normal distribution table, P(-1.20 < z < 0.62) = P(z < 0.62) - P(z < -1.2) = 0.8849 - 0.1151 = 0.7698 = 77%

There is a probability of 77% that the mean of this sample is between 19.25 hours and 21.0 hours

Find out more on z score at: https://brainly.com/question/25638875

Can you identify a parallel or perpendicular equation and type the correct code? Please remember to type in ALL CAPS with no spaces.

Answers

The equation of the line that is parallel to [tex]2\cdot x + 5\cdot y = 10[/tex] is [tex]y = -\frac{2}{5} \cdot x + 3[/tex] and the equation of the line that is perpendicular to [tex]4\cdot x + 3\cdot y =12[/tex] is [tex]y =\frac{3}{4}\cdot x - 1[/tex].

Let be a line whose equation is:

[tex]a\cdot x + b\cdot y = c[/tex] (1)

Whose explicit form is:

[tex]y = -\frac{a}{b} \cdot x +\frac{c}{b}[/tex] (2)

Where:

[tex]x[/tex] - Independent variable.[tex]y[/tex] - Dependent variable.

The slope and x-intercept of the line are [tex]-\frac{a}{b}[/tex] and [tex]\frac{c}{b}[/tex], respectively.

There are two facts:

A line is parallel to other line when the former has the same slope of the latter.A line is perpendicular to other line when the former has a slope described the following form ([tex]m_{\perp} = -\frac{1}{m}[/tex]), where [tex]m[/tex] is the slope of the former.

Then, the equation of the line that is parallel to [tex]2\cdot x + 5\cdot y = 10[/tex] is [tex]y = -\frac{2}{5} \cdot x + 3[/tex] and the equation of the line that is perpendicular to [tex]4\cdot x + 3\cdot y =12[/tex] is [tex]y =\frac{3}{4}\cdot x - 1[/tex].

To learn more on lines, we kindly invite to check this verified question: https://brainly.com/question/2696693


How is the series 9 + 13+ 17+ ... + 149 represented in summation notation?

Answers

Notice that

13 - 9 = 4

17 - 13 = 4

so it's likely that each pair of consecutive terms in the sum differ by 4. This means the last term, 149, is equal to 9 plus some multiple of 4 :

149 = 9 + 4k

140 = 4k

k = 140/4

k = 35

This tells you there are 35 + 1 = 36 terms in the sum (since the first term is 9 plus 0 times 4, and the last term is 9 plus 35 times 4). Among the given options, only the first choice contains the same amount of terms.

Put another way, we have

[tex]\displaystyle 9 + 13 + 17 + \cdots + 149 = \sum_{k=0}^{35} (9 + 4k)[/tex]

but if we make the sum start at k = 1, we need to replace every instance of k with k - 1, and accordingly adjust the upper limit in the sum.

[tex]\displaystyle 9 + 13 + 17 + \cdots + 149 = \sum_{k-1=0}^{35+1} (9 + 4(k-1))[/tex]

[tex]\displaystyle 9 + 13 + 17 + \cdots + 149 = \sum_{k=1}^{36} (5 + 4k)[/tex]

y=1/4x−2y=−2x+3 help solve problem.

Answers

Answer:

  (x, y) = (2 2/9, -1 4/9)

Step-by-step explanation:

Equate the values of y and solve for x.

  1/4x -2 = -2x +3

  (2 1/4)x = 5 . . . . . . . . add 2+2x to both sides

  x = 20/9 = 2 2/9 . . . multiply by 4/9

  y = -2(2 2/9) +3 = -4 4/9 +3 . . . . substitute for x in the second equation

  y = -1 4/9

The solution is x = 2 2/9, y = -1 4/9.

Please help me in this 4th grader question, its a homework and i was sick over the weekend

Answers

Answer:

what is your question ask then I shall answer you

Write 0.511 as a fraction.

Answers

Answer:

511 / 1000

Step-by-step explanation:

0.511 = 511 / 1000

Answer:

511/1000

Step-by-step explanation:

Steps to convert 0.511 into a fraction:  

Write 0.511 as 0.511/1

For each digit following the decimal point, multiply both the numerator and denominator by ten:

0.511/1

          = 0.511 * 1000/ 1 * 1000 = 511/1000

As an aside, the entire number-integral section is: blank.

The decimal component is as follows: 0.511 = 511/1000

The following is the complete breakdown of simple fractions: 511/1000

 

The diagonal of a rectangle big-screen TV screen measures 152cm. The length measures 132cm. What is the height if the screen?​

Answers

Answer:

75.36cm

Step-by-step explanation:

We use the pithagorean theorem: height^2 = 152^2 - 132^2 = 5680;

height = [tex]\sqrt{5680} = 75..36 cm[/tex]

The teen club had a cupcake sale.
They sold 2/3 of their cupcakes in the morning. They sold 1/6 of their cupcakes in the afternoon. They sold 200 cupcakes altogether.
How many cupcakes were left to sell?

Answers

40. Let C be the total number of cupcakes. Then 2/3 x C + 1/6 x C = 200.

Combining , 5/6 x C = 200. So C = 240.

240–200= 40

Approximately what portion of the box is shaded blue?

A.2/3. B.9/10
C.3/5

Answers

the answer should be b 9/10

What is the equation of the line: * parallel to the line y = -¼x + 5 and * passing through the point (2, -1)
y = -¼x - 1/2
y = ¼x + 2
y = -¼x + 4
y = ¼x - 1

Answers

Answer:

last one

Step-by-step explanation:

Stuck on this, need help on this.

Answers

Answer:

Domain: (-∞ , ∞)

Range: y <= 8        [8 , -∞)

Step-by-step explanation:

x = 2

f(x) = 8

x<=2

f(x) <=8

3] What is - 2y + 10 + 2y - 8 simplified?
a) – 4y + 18
C) 18
b) 4y + 2
d) 2
Expressions

Answers

Answer:

d. 2

Step-by-step explanation:

-2y +10+2y-8

10-8. ( -2y+2y = 0)

2

Answer:

d) 2

Step-by-step explanation:

We can first combine like terms

-2y + 2y = 0

Now, our expression is simply 10 - 8, which is 2

So, the answer is

d) 2

Charles wants to buy an anime book that is on sale for $14.99. Her sister kyra wants to buy a novel book for $17.99. Both of them has to pay a 7% tax. Kyra has a coupon for 15% discount. Whats the difference between the amount that each siblings has to pay?

Answers

Answer:

The difference between their total amounts is .34 cents

also it didnt look like i was supposed to count a discount for charles so i didnt :)

Step-by-step explanation:

Charles

14.99 times .07 = 1.04

14.99 + 1.04 = 16.03

Kyra

17.99 times .15 = 2.69

17.99 -2.69 = 15.30

15.30 times .7 = 1.07

15.30 + 1.07 = 16.37

16.37 - 16.03 = .34

At TGI Fridankay's you order a drink for $2.99, an appetizer for $9.99, the cajun chicken pasta for $11.50, and a dessert for $7.99. You had amazing service and know that you are going to tip your waiter 20%! The waiter also gave you a 10% coupon to use. There is also a 7% sales tax on the bill. What is your total bill after the tip, discount, and tax?

Answers

The total bill after the tip, discount, and tax is $37.76.

The total cost of the order is reduced by the coupon and increased by the tax paid and tip.

Total cost of the items bought = cost of the drink + appetizer + Cajun + dessert

$2.99 + $9.99 + $11.50 + $7.99 = $32.47

Value of the tip = 20% x $32.47 = $6.49

Cost of the items after the coupon: (100% - 10%) x $32.47

90% x $32.47

0.9 x $32.47 = $29.22

Cost of the items after the tax: (1.07) x $29.22 = $31.27

Total cost of the items = $31.27 +$6.49 = $37.76

To learn more about taxes, please check: https://brainly.com/question/25311567

Solve for g. Make sure to use scrap paper to show your work.

( 144 + 6 x 8 ) ÷ 3 = g

192
64
48
NO NOT PUT THIS IN A FILE

Answers

Answer:

64

Step-by-step explanation:

P E D M A S

() ² ÷ × + -

6 x 8 = 48

114 + 48 = 192

(192) ÷ 3 = g

192 / 3 = 64

g = 64

Define
Rough calculating​

Answers

Answer:

A rough calculation or guess is approximately correct, but not exact. roughly adverb.

Step-by-step explanation:

A farmer has 220 bushels of apples to sell at roadside stand. She sells an average of 14 3/5 each day. Represent the total change in the number of bushels has for sale after 6 days.The total change in the number of bushels has for sale is ???, please answer as a fraction

Answers

Answer:

Step-by-step explanation:

He has sold (16+1/4) bushels/day x 5 days = (16 x 5) + (1/4 x 5) = 80 + 5/4 = 81 + 1/4 = 81.25

The change in the number of bushels is 140 - 81.25 = 58.75 or 58 and 3/4 bushels

In other words, he has 58.75 (or 18 and 3/4) bushels remaining and has sold 81.25 (or 81 and 1/4) bushels

Please help me prove that RST is congruent to RUT!

Answers

Answer:

See image

Step-by-step explanation:

On line 3, the reason is filled in that "All right angles are congruent" so kind of working backwards, the statement must say that two right angles are congruent. Use the angles in the previous two statements. Line 4 has the statement completely filled in, the reason is bc it is given in the list of given statements beside the diagram. Line 5 says that RT is congruent to itself. That is reflexive property, like a reflection in a mirror. Same ~= same.

You can see from the markings on the image that you have Angle-Side-Angle, which is one of several ways that we can show that triangles are congruent. ASA is what is shown in statements 1-5. See image.

An angle measures 136°. What is the measure of its supplement?

Answers

Answer:

44⁰.

Step-by-step explanation:

Its supplement = 180 - 136

= 44 degrees.

HELP! Due in 5 minutes

Answers

ANSWER:

the first one: 30x+48

The second one: x y^2(10 y + 15)

The third one: 30 x y - 5 x^2

Hope this helped!

sorry if im wrong. :)

GOOD LUCK!! <3

Write the equation to the line parallel to y= 3x – 5 that goes through the point (-2, -7) using any form.

Thank you!

Answers

Answer:

y = 3x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x - 5 ← is in slope- intercept form

with slope m = 3

Parallel lines have equal slopes , then

y = 3x + c ← is the partial equation

To find c substitute (- 2, - 7 ) into the partial equation

- 7 = - 6 + c ⇒ c = - 7 + 6 = - 1

y = 3x - 1 ← equation of parallel line

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Read the lines from Canto V of The r*pe of the Lock and answer the question. Some thought it mounted to the Lunar sphere, Since all things lost on earth are treasur'd there. There Hero's wits are kept in pond'rous vases, And beau's in snuff-boxes and tweezer-cases. There broken vows and death-bed alms are found, And lovers' hearts with ends of riband bound, The courtier's promises, and sick man's pray'rs, The smiles of harlots, and the tears of heirs, Cages for gnats, and chains to yoke a flea, Dry'd butterflies, and tomes of casustry. These lines offer a possible explanation for where the lost lock has gone, but they also offer Pope another chance to satirize behaviors. What are his satirical targets in this passage? What do the targeted behaviors, and the people who behave in these ways, have in common? In a written response at least 200 words, answer these questions using details from the text. Include in your response an explanation of whether Pope's satire in this section is Horatian or Juvenalian. Please help me with this question please just help me with what is this is or synthesis singlereplacement combustion decomposition double replacement You are going to a private apple orchard to pick apples. There is a one-time entry feethat everyone pays, and you also pay a certain amount per pound of apples you pick. Itcosts $42 to buy 5 pounds of apples, and it costs $54 to buy 7 pounds of apples.Based on this information, what is the one-time entry fee? what does the expression 3(20+15) represent? The equation A = 1/2bh (one halve) gives the area A of a triangle, where b is the lengthof the base and h is the height. Solve this equation for h. Identify the factors (new resources, increased productivity, education, technology, slave economy, territorial expansion) that increase economic growth.Describe how the Aztec nation created wealth from the nations surrounding them. At the end of seafloor spreading, where does the molten rock solidify? What is the surface temperature of Sirius B in Kelvins? Nolan was given a box of assorted chocolates for his birthday. Each night, Nolan treated himself to 3 chocolates. After 8 nights, there were 6 chocolates remaining in the box. nivel 1, captulo 5 7 Nutrition is the science of food which studies all of the following excepta) Digestion of food(b) Absorption of food(c) Menu at your birthday(d) Nutrients present in food 3(y+5)=15 someone please help me with this question my assignment is already late find the equation of a circle (3,2) (1,4) In the triangle, x = 3. Find y.A) y = 6B) y = 7y= V3D) y= 3.72 Evaluate the equation.3w = 96 A. w = 288 B. w = 32 C. w = -32 D. w = -288 What are the 20 national park of Nepal? Fifty-five percent of the members of the junior varsity swim team wear glasses. Of the team memebers who do not wear glasses, 30 percent of them are in the 10th grade. To the nearest whole percent, what is the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade?. Julio is putting a rectangular pool in his backyard. The length ofthe pool is 7 feet more than the width. The perimeter of the poolis 54 feet. What is the length of the pool?23.5471710 Stacie is writing about Wonder by R. J. Palacio.I started to follow her, but Julian cut right in front of me, which actually made me stumble backward."Oops, sorry about that!" said Julian.But I could tell from the way he looked at me that he wasn't really sorry at all.Which best shows that Stacie has made a personal connection to understand Augusts character?Once, after I hurt my brothers feelings, my parents told me to apologize. I was not really sorry at the time, but I had to apologize anyway. I know how August feels.Pushing people is a really mean thing to do. Julian was especially mean to push August, because August already has many physical challenges. I feel very sad for August.My older sister sometimes bothers me at home. She usually says she is sorry, but I know that she does not really mean it. I understand how frustrated August might feel.If I were a principal at the school, I would make a rule that no one could cut in line or shove people. This would help people like August, so he would not be pushed around.PLZ HURRY IN TIMED TEST Please help me with this question