Determine the number of terms, n, given the geometric series 1 3 9 27 ... and sn=3280.

Answers

Answer 1

The number of terms, 'n' is 8

How to determine the number of terms

Let's determine the common ratio;

common ratio, r = 3/1 = 3

The formula for sum of geometric series with 'r' greater than 1 is given as;  Sn = a( r^n - 1) / (r - 1)

n is unknown

Sn = 3280

Substitute the value

3280 = 1 ( 3^n - 1) / 3- 1

3280 = 3^n -1 /2

Cross multiply

3280 × 2 = 3^n - 1

6560 + 1 = 3^n

6561 = 3^n

This could be represented as;

3^8 = 3^n

like coefficient cancels out

n = 8

Thus, the number of terms, 'n' is 8

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Related Questions

25 Points + BRANIEST. PLEASE HELP

Answers

Answer:

sorry I don't know please forgive because I can't copy the question

Diameter 2
Find the area of the shape

Answers

Answer:

pi or 1 pi

Step-by-step explanation:

Area = 1/4 * pi * r^2 (because it is 1/4 of a full circle)

1/4 * pi * 2^2 (the radius is 2 because it is given in the picture)

1/4 * pi * 4 = 1 pi

area = pi

hope this helps! <3

1)Find the L.C.Mof the following set of numbers by prime factorization method:
a)6 and 9
b)16 and 24
c)24,48 and 64

2)Find L.C.M of the following set of numbers by division method:
a)6 and 15
b)25,30 and 75

Note: Answer must have proper explanation ​

Answers

Answer:

a) 18

b) 48

c) 192

a) 30

b) 150

Step-by-step explanation:

Answer:

1

a ) 18

b ) 48

c ) 144

2

a ) 30

b ) 150..

[tex]...[/tex]

Find the product or type impossible[5 -2 4] [2 7 -3]

Answers

Answer:

Step-by-step explanation:

You can only multiply matrices if the number of columns in the matrix on the left is the same exact number as the number of rows in the matrix to the right of that other matrix.

The matrix on the left, |5 -2  4| has the dimensions

                                      1 x 3 (1 row, 3 columns)

The matrix to its right, |2  7  -3| has the dimensions

                                      1 x 3 (1 row, 3 columns).

Putting those dimensions next to each other in that order:

                  1 x 3     1 x 3

The bold print 3 and 1 have to be the same number (both 3's or both 1's) in order for the multiplication to work. This doesn't work; it's impossible.

Answer: -16

Step-by-step explanation:

i was on a unit exam typing in random numbers since i didn't know it and -16 is the right answer.

What values of c and d make the equation true? rootindex 3 startroot 162 x superscript c baseline y superscript 5 baseline endroot = 3 x squared y (rootindex 3 startroot 6 y superscript d baseline endroot)

Answers

Values of c and d make the equation true are c=6, d=2

Equations

We must find the values of c and d that make the below equation be true

                                [tex]\sqrt[3]{162x^{c}y^{5} } = 3x^{2} y^{3} \sqrt[3]{6y^{d} }[/tex]

cubing on both sides -

                               [tex](\sqrt[3]{162x^{c}y^{5} })^{3} = (3x^{2} y^{3} \sqrt[3]{6y^{d} })^{3}[/tex]

The left side just simplifies the cubic root with the cube:

                                 [tex]{162x^{c}y^{5} } = (3x^{2} y^{3} \sqrt[3]{6y^{d} })^{3}[/tex]

On the right side, we'll simplify the cubic root where possible and power what's outside of the root:

                                  [tex]{162x^{c}y^{5} } = 27x^{6} y^{3} ({6y^{d})[/tex]

Simplifying

                                     [tex]{x^{c}y^{5} } = x^{6} y^{3} ({y^{d})[/tex]

                                     [tex]{x^{c}y^{5} } = x^{6} y^{3+d}[/tex]

On equating,

                                   c = 6

                                   d = 2

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If two fair dice are rolled, what is the probability that the total showing is either even or less than five?

Answers

The Probability that the total showing is either even or less than five = 5/6

What is Probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where, broadly speaking, 0 represents the event's impossibility and 1 implies certainty.

According to the given data:

The example space for rolling two dice is:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

36 events total.

Events that have a sum that is even or less than Five .

Total instances when the aggregate is even or less than Five equals 30.

P(sum is even or less than 5)

= (Total no of favorable event)/(Total no of event)

= 30/36

=5/6

probability that the total showing is either even or less than five = 5/6

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Express your answer in scientific notation. 0.00045-2.5x10^-5​

Answers

Answer:

4.25 × 10^-4

Step-by-step explanation:

0.00045-2.5x10^-5

= (4.5 × 10^-4) - (0.25 × 10¹ × 10^-5)

= (4.5 × 10^-4) - (0.25 × 10^{1-5} )

= (4.5 × 10^-4) - (0.25 × 10^-4)

= (4.5 - 0.25) × 10^-4

= 4.25 × 10^-4

Evaluate the surface integral. s y ds s is the surface z = 2 3 x3/2 y3/2 , 0 ≤ x ≤ 4, 0 ≤ y ≤ 1

Answers

The surface integral of the given surface [tex]z=\frac{2}{3}(x^\frac{3}{2}+y^\frac{3}{2})[/tex] in the intervals 0 ≤ x ≤ 4, 0 ≤ y ≤ 1 is 7.36615.

How to evaluate the surface integral?

To evaluate the surface integral, the formula applied is

[tex]S=\int\limits^b_a\int\limits^d_c {f(x,y)} \ dy\ dx[/tex]

⇒ S = [tex]\int\limits^b_a \int\limits^d_c {\sqrt{1+(\frac{dz}{dx})^2+(\frac{dz}{dy})^2 } } \, dy \, dx[/tex]

Where the differentiation is partial differentiation and f(x, y) = z.

Calculation:

The given function is

f(x, y) = [tex]z=\frac{2}{3}(x^\frac{3}{2}+y^\frac{3}{2})[/tex]

Then, applying the partial differentiation w.r.t x and y respectively,

dz/dx = [tex]\frac{2}{3}(\frac{3}{2})x^{1/2}[/tex] = [tex]x^{1/2}[/tex]

dz/dy = [tex]\frac{2}{3}(\frac{3}{2})y^{1/2}[/tex] = [tex]y^{1/2}[/tex]

Then,

we have surface integral  formula as

S = [tex]\int\limits^b_a \int\limits^d_c {\sqrt{1+(\frac{dz}{dx})^2+(\frac{dz}{dy})^2 } } \, dy \, dx[/tex]

On substituting,

⇒ S = [tex]\int\limits^4_0 {\int\limits^1_0 {\sqrt{1+(x^{1/2})^2+(y^{1/2})^2} \, dy } \, dx[/tex]

⇒ S = [tex]\int\limits^4_0 {\int\limits^1_0 {\sqrt{1+x+y} \, dy } \, dx[/tex]

On integrating w.r.t y

⇒ S = [tex]\int\limits^4_0 {\frac{2}{3}(1+x+y)^{3/2}} \,|_0^1 dx[/tex]

Applying limits,

⇒ S = [tex]\int\limits^4_0 {\frac{2}{3}[(1+x+1)^{3/2}-(1+x+0)^{3/2} } \, dx[/tex]

⇒ S = [tex]\frac{2}{3} \int\limits^4_0 {[(x+2)^{3/2}-(x+1)^{3/2}}] \, dx[/tex]

Again applying the integration w.r.t x

⇒ S = [tex]\frac{2}{3}[\frac{2}{5}(x+2)^{5/2}-\frac{2}{5}(x+1)^{5/2}]|_0^4[/tex]

Applying the limits and simplifying,

⇒ S = [tex]\frac{4}{15}[(4+2)^{5/2}-(4+1)^{5/2}-(0+2)^{5/2}+(0+1)^{5/2}][/tex]

⇒ S = [tex]\frac{4}{15}[1+36\sqrt{6}-25\sqrt{5}-4\sqrt{2}][/tex]

∴ S = 7.36615

Therefore, the surface integral of the given function is 7.36615.

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A laundry detergent company wants to determine if a new formula of detergent, a, cleans better than the original formula, b. researchers randomly assign 500 pieces of similarly soiled clothes to the two detergents, putting 250 pieces in each group. after washing the clothes, independent reviewers determine the cleanliness of the clothes on a scale of 1–10, with 10 being the cleanest. the researchers calculate the proportion of clothes in each group that receive a rating of 7 or higher. for detergent a, 228 pieces of clothing received a 7 or higher. for detergent b, 210 pieces of clothing received a rating of 7 or higher. based on the 90% confidence interval, (0.02, 0.12), is there convincing evidence that the new formula of laundry detergent is better? there is convincing evidence because the interval is entirely above 0. there is not convincing evidence because the sample sizes are too small. there is convincing evidence because the number of clothing items receiving a higher rating is greater for the new formula than for the original formula. there is convincing evidence because the sample proportion of clothes receiving a higher rating is greater for the new formula than the original formula.

Answers

In the hypothesis, based on the 90% confidence interval, (0.02, 0.12), there is convincing evidence that the new formula of laundry detergent is better because the interval is entirely above 0

How to illustrate the information?

Let's define the null hypothesis and alternative hypothesis first.

H0:p1-p2=0

Ha:p1-p2>0

Also, 90% CI is (0.02,0.12), we know that if the 0 of the null hypothesis is not in the confidence interval then we reject the null hypothesis.

In the given scenario 0 is not within the given interval, hence we reject the null hypothesis and accept the claim that new detergent A cleans better.

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i dont know how to do this could someone help

Answers

Answer:

17, 5

Step-by-step explanation:

Let the width be x

width = x

length = x + 12

length x width = x(x + 12)

length x width = x² + 12x

x² + 12x = 85

x² + 12x - 85 = 0

Now it is just a quadratic:

The 2 numbers we need are 17 and -5

(x + 17)(x - 5) = 0

x = -17 or x = 5.

Since width and length cannot be negative, x must equal 5.

Width = 5

length = 17

The answer is 17, 5.

We are given two things :

Length exceeds width by 12 inchesArea = 85 square inches

We can represent the length and width as x + 12 and x respectively.

Now, the formula for the area of a rectangle is :

Area = Length x width

Now, let's substitute the values for length and width in the formula along with the area.

(x + 12)(x) = 85x² + 12x = 85x² + 12x - 85 = 0

We now have a quadratic equation, which can either be solved by splitting the middle term, or by using the quadratic formula. For convenience purposes, we'll go with the first one.

x² + 17x - 5x - 85 = 0x (x + 17) - 5 (x + 17) = 0(x + 17)(x - 5) = 0x = 17, 5

Which type of sediment deposit has an average rate of deposition (per 1000 years) of 1 centimeter (0.4 inch)?

Answers

The sediment deposit that has an average rate of deposition

(per 1000 years) of 1 centimeter is bigenous ooze,pelagic deposit.

Given that average rate of deposition is  per 1000 years of 1 centimeter.

We are required to find the type of sediment deposit that has an average rate of deposition (per 1000 years) of 1 centimeter.

Biogenic ooze, which is also called biogenic sediment, is any pelagic segment that contains more than 30 percent skeletal material. These sediments can be made up of either carbonate ooze or siliceous ooze.

In plagic sediments feldspar is obtained from local volcanic sources, whereas quartz may be introduced from the continents by wind,upsetting simple patterns.A large number of accessory minerals occur in shales.

Hence if the sediment deposit that has an average rate of deposition

(per 1000 years) of 1 centimeter is bigenous ooze,pelagic deposit.

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how many terms are there in the series 7+21+15+19+.....+79?
anybody can answer these .​

Answers

Answer:

7+21+15+19+.....+79

Here 21 be replaced by 11.

Now., common diffrence btw terms , d = 11-7 = 4

first term , a = 7

Last term , l = 79

number of terms = ( a + l ) ÷ d

=( 7 + 79 ) ÷ 4 = 86 ÷ 4 = 21.5 { It cannot be in decimal }

There's some mistake in the terms you provided please check your question again...

Question 5(Multiple Choice Worth 2 points)
(07.01 MC)
What is the range of the function f(x) = x - 3?

Answers

Answer:

  (-∞, ∞)

Step-by-step explanation:

Unless there are restrictions on the domain, the range of any odd-degree polynomial function is "all real numbers."

Linear function

The given function is a linear function, degree 1. This is an odd degree, so the range of the function is "all real numbers."

  -∞ < f(x) < ∞

  (-∞, ∞) . . . . . in interval notation

The table below shows the linear relationship between the number of people at a picnic and the total cost of the picnic.

A two column table with five rows. The first column, Number of People, has the entries, 6, 9, 12, 15. The second column, Total Cost in dollars, has the entries, 52, 58, 64, 70.

Which statements about the function described by the table are true? Check all that apply.

The independent variable is the number of people.
The initial value (initial fee) for the picnic is $40.
The rate of change is $8.67 per person.
As the number of people increases, the total cost of the picnic increases.
If 4 people attended the picnic, the total cost would be $46.

Answers

The true statements are:

The independent variable is the number of people.The rate of change is $8.67 per person.As the number of people increases, the total cost of the picnic increases.

What are the true statements?

The independent variable is the variable that determines the value of the dependent variable. There is a positive relationship between the number of people at the picnic and the total cost. This is because it can be seen as the number of people at the picnic increases, the total cost changes.

Rate of change = total cost / number of people

$52 / 6 = $8.67

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Answer:

A, B, D

Step-by-step explanation:

right on edge

Explanation to :an insurance agent is paid a salary of gh200 and a commission of 3% on all sales over gh2000 per month. if his total income in a particular month was gh530, what was the amount of his sales for that month

Answers

GH 13000 is the amount of his sales for that month.

how to find sales of the month?

total income = salary + commission

total income = GH530 (given)

salary = GH200 (given)

Commission is 3% on the sales above Gh2000 (given)

Let sales be x

total income = salary + commission

530 = 200+3%(x-2000)

530-200=0.03(x-2000)

330/.03=x-2000

11000=x-2000

x= 13000

total sales = GH13000

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Suppose that two fair dice are rolled. find the probability that the number on the first die is a 1 or the number on the second die is a 4

Answers

Answer:

1/36

Step-by-step explanation:

Assuming the dice has 6 sides in total, we can set up a probability for each scenario.

The chances of the dice landing on 1 will be 1/6, since there are 6 total faces. Same goes for the second die and landing on 4.

Now that we have our 2 probabilities, we multiply them to get the final probability. 1/6 x 1/6 = 1/36.

ASAP NOW
below is the question

Answers

The mean of the data set A is 4.58 while the mean of data set B is 5.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

The mean of a set of numbers is the average of that group of number. It is the ratio of the sum of the data to the total number of data.

Mean of data set A = [(3 * 1) + (4 * 3) + (5 * 2) + (6 * 2) + (7 * 3) + (8 * 1)] / (1 + 3 + 2 + 2 + 3 + 1) = 4.58

Mean of data set B = [(4 * 2) + (5 * 2) + (6 * 2)] / ( 2 + 2 + 2) = 5

The mean of the data set A is 4.58 while the mean of data set B is 5.

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Nelly works part-time in a shop to
cover her university expenses.
The table below shows how many
hours she worked each day last week.
Hours worked
Day
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday

5

4
25
Nelly's weekly pay is worked out
as follows: Monday to Friday
• £8 per hour for the first 15 hours
• £10 per hour for any extra hours
Saturday
.
• double the normal rate of £8 per hour
Work out Nelly's total pay for last week?
You must show all your working.

Answers

Using proportions, Nelly's total pay for last week was of £220.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

From Monday to Friday, she worked 17 hours, hence:

For 15 hours, she was paid £8 per hour.For the last 2 hours, she was paid £10 per hour.

On Saturday, she worked 5 hours, and was paid £16 per hour.

Hence her total payment is found as follows:

15 x 8 + 2 x 10 + 5 x 16 = £220.

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Humood's house is (-5,7)
The school is (3,1)
If each unit in the graph is 50m, find the distance from Humood's house to the school.

Answers

The distance from Humood's house to the school is 500m

How to determine the distance from Humood's house to the school?

The given parameters are:

Humood's house is (-5,7)

The school is (3,1)

The distance between both points is calculated using

[tex]d = \sqrt{(x_2- x_1)^2 + (y_2 - y_1)^2[/tex]

Substitute the known values in the above equation

[tex]d = \sqrt{(-5 - 3)^2 + (7 - 1)^2[/tex]

Evaluate

d = 10

Each unit in the graph is 50m.

So, we have

Distance =10 * 50m

Evaluate the product

Distance = 500m

Hence, the distance from Humood's house to the school is 500m

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where should i place the points!! help please

Answers

Try solving the equation and then try plotting the answer. Sry if I didn’t help

PLEASE HELP ME! THE QUESTION IS DOWN BELOW PLEASE PLEASE HELP ME

Answers

The given expression (8h + 2w - 5h + 3w) can fully be simplified as 3h + 5w.

What is an expression?

An expression can be defined as a type of mathematical equation which is used to show the relationship that is existing between two or more variables and numerical quantities (integers).

In this exercise, you're required to fully simplify the given expression in the lowest terms. Thus, we would simplify the given expression completely by collecting like terms and performing the necessary arithmetic operations (addition and subtraction) as follows:

Collecting like terms, we have:

8h - 5h + 3w + 2w

Subtracting and adding the like terms respectively, we have:

3h + 5w.

In conclusion, we can logically deduce that the given expression (8h + 2w - 5h + 3w) can fully be simplified as 3h + 5w.

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Complete Question:

Fully simplify 8h + 2w - 5h + 3w.


Suppose that a household's monthly water bill (in dollars) is a linear function of the amount of water the household uses (in hundreds of cubic feet, HCF). When
graphed, the function gives a line with a slope of 1.45. See the figure below.
If the monthly cost for 22 HCF is $44.50, what is the monthly cost for 16 HCF?
?

Answers

Answer:

I hope that you are doing well, during this weird time; and that this message finds you in a good place.

To get you started on this problem, you will want to think about how to go about graphing this linear function. You want to keep in mind that you want to plot your dependent variable on the y-axis, as it changes with respect to your independent variable (plotted on the x-axis). In this problem, the cost of the water bill depends on the amount of water used, in HCF. So the graph should be plotted with cost on the y-axis, and HCF on the x-axis.

It follows that you are given the coordinates of (16, $48.37) and (22, y2); where y2 represents the cost when using 22 HCF. You are also given the slope of your line (m, in y = mx + b format). You may recall that you can set-up a slope as the change in y over the change in x, or the "rise over the run" [m = (y2-y1) / (x2-x1)]. We can set this problem up, using this equation to solve for y2 (the cost at 22 HCF) algebraically.

So we would set up the problem as 1.65 = (y2-48.37)/(22-16). We then solve by combining like-terms and using inverse operations as follows:  

  1.65 = (y2 - 48.37) / 6

  1.65(6) = y2 - 48.37

  9.9 = y2 - 48.37

  y2 = $58.27

Step-by-step explanation:

Algebra 2 how do you find the frequency?

Answers

The frequency of the periodic function is given by: 0.0796.

What are the period and the frequency of a function?

The period of a function is given by the distance between it's repetitions.The frequency of a function is found dividing one by the period.

From the graph, we have that the period is of 4pi hours, hence the frequency is:

f = 1/4pi = 0.0796.

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When searching for the value 10 in the array [2, 3, 5, 6, 9, 13, 16, 19], a recursive binary search algorithm will return what?

Answers

When searching for the value 10 in the array [2, 3, 5, 6, 9, 13, 16, 19], a recursive binary search algorithm will return false since the element is not found in the array.

About Binary Search Algorithm

The binary search algorithm, applied on arrays are of recursive type. The broad strategy is to look at the middle item on the list. The procedure of the binary search algorithm is either terminated (key found), the left half of the list is searched recursively, or the right half of the list is searched recursively, depending on the value of the middle element.

The function carrying out the binary search algorithm in a code returns true if the desired element is found in the array, else returns false. Since the element 10 is not present in the given array: [2, 3, 5, 6, 9, 13, 16, 19], the binary search algorithm will return false.

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Aakash has a fever. His body temperature during the day was 99.2°F. By evening, his body temperature has increased by 3.4°F.
His body temperature in the evening is
°F.

Answers

Given that, Aakash has a fever, if  his body temperature during the day was 99.2°F and by evening his body temperature has increased by 3.4°F, Aakash's body temperature in the evening is 102.6° Fahrenheit.

What is Aakash body temperature in the evening?

The body temperature is simply a measure of how well a human body can produce and get rid of heat. the normal body temperature is or 37 degrees Celsius or 98.6 degrees Fahrenheit.

Given the data in the question;

Body temperature during the day =  99.2° FahrenheitTemperature Increase = 3.4° Fahrenheit Body temperature in the evening = ?

To get Aakash body temperature in the evening, we simply add the initial body temperature and the the temperature increase.

Temperature in the evening = 99.2° Fahrenheit + 3.4° Fahrenheit

Temperature in the evening = 102.6° Fahrenheit

Given that, Aakash has a fever, if  his body temperature during the day was 99.2°F and by evening his body temperature has increased by 3.4°F, Aakash's body temperature in the evening is 102.6° Fahrenheit.

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Mr. Salazar assigns the same number of homework questions each school day. The ratio table below shows the total number of homework questions assigned after a certain number of school days.
Homework
Number of days
Total number of questions
4
20
8
40
11
55
16
?

After 16 days, how many total homework questions have been assigned?

Answers

After 16 days, the total homework questions that have been assigned would be 80 questions.

How many homework questions would be assigned after 16 days?

Ratio expresses the equivalent relationship between two numbers. It shows the frequency of the number of times that one value is contained within other value(s).

A ratio table can be described as table that shows equivalent values between two numbers.

The first step is to determine the ratio between the number of days and the total number of questions.

Ratio = money saved / money earned

8/10 =  total number of questions / number of days

55 / 11 = 5

Now, multiply the ratio gotten in the previous step by the number of days

Total number of homework questions = number of x ratio

5 x 16 = 80 questions

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Find the absolute maximum and minimum values of f on the set d. f(x, y) = xy2 7, d = {(x, y) | x ≥ 0, y ≥ 0, x2 y2 ≤ 3}

Answers

Assuming you mean [tex]f(x,y) = xy^2[/tex] over the domain

[tex]D = \left\{(x,y) ~:~ x\ge0 \text{ and } y\ge0 \text{ and } x^2 + y^2 \le 3\right\}[/tex]

we first observe that [tex]f(x,y) = 0[/tex] for all [tex](x,y)[/tex] on the coordinate axes.

There are no critical points elsewhere in the interior of [tex]D[/tex], since

[tex]\dfrac{\partial f}{\partial x} = y^2 = 0 \implies y=0[/tex]

[tex]\dfrac{\partial f}{\partial y} = 2xy = 0 \implies x = 0 \text{ or } y = 0[/tex]

Parameterize the circular arc boundary by [tex]x=\sqrt3\cos(t)[/tex] and [tex]y=\sqrt3\sin(t)[/tex], where [tex]0\le t\le\frac\pi2[/tex]. Then

[tex]f(x(t), y(t)) = g(t) = 3\sqrt3 \cos(t) \sin^2(t) = 3\sqrt 3 (\cos(t) - \cos^3(t))[/tex]

Find the critical points of [tex]g[/tex].

[tex]g'(t) = -3\sqrt3 \sin(t) + 9\sqrt3 \cos^2(t) \sin(t) = 0[/tex]

[tex]-3 \sin(t) (1 - 3 \cos^2(t)) = 0[/tex]

[tex]\sin(t) = 0 \text{ or } 1 - 3 \cos^2(t) = 0[/tex]

[tex]\sin(t) = 0 \text{ or } \cos^2(t) = \dfrac13[/tex]

[tex]\sin(t) = 0 \text{ or } \cos(t) = \pm\dfrac1{\sqrt3}[/tex]

In the first case, we get

[tex]t = \sin^{-1}(0) + 2n\pi \text{ or } t = \pi - \sin^{-1}(0) + 2n\pi[/tex]

where [tex]n[/tex] is an integer; the only solution on the boundary of [tex]D[/tex] is [tex]t=0[/tex] corresponding to the point [tex](\sqrt3,0)[/tex].

In the second case, we get

[tex]t = \cos^{-1}\left(\dfrac1{\sqrt3}\right) + 2n\pi \text{ or } t = -\cos^{-1}\left(\dfrac1{\sqrt3}\right) + 2n\pi[/tex]

with only one relevant solution at [tex]t=\cos^{-1}\left(\frac1{\sqrt3}\right)[/tex]  corresponding to [tex](1,\sqrt2)[/tex].

In the third case, we get

[tex]t = \cos^{-1}\left(-\dfrac1{\sqrt3}\right) + 2n\pi \text{ or } t = -\cos^{-1}\left(\dfrac1{\sqrt3}\right) + 2n\pi[/tex]

but there is no [tex]t[/tex] in this family of solutions such that [tex]0\le t\le\frac\pi2[/tex].

So, we find

[tex]\min\left\{xy^2 \mid (x,y) \in D\right\} = 0 \text{ at } (0,0)[/tex]

(but really any point on either axis works)

[tex]\max \left\{xy^2 \mid (x,y) \in D\right\} = 2 \text{ at } (1,\sqrt2)[/tex]

Which graph represents (y-3)^2/25 + (x+1)^2/4 > 1 and y <= square root{x+5}+2

Answers

Answer:

B. the second graph.

Step-by-step explanation:

Literally the photo is on the question.

Second graph represents (y-3)²/25 + (x+1)²/4 > 1 and y <= square root{x+5}+2. Therefore, the correct option is option B.

What is graph?

The study of graphs, that are mathematical constructions used to represent pairwise relationships between things, is known as graph theory in mathematics. In this sense, a network consists of vertices, also known as nodes or points, linked by edges, also known as links or lines.

Undirected graphs, in which edges connect two vertices symmetrically, are distinguished from directed graphs, in which edges connect two vertices asymmetrically. One of the main topics that are investigated in discrete mathematics is graphs. Second graph represents (y-3)²/25 + (x+1)²/4 > 1 and y <= square root{x+5}+2.

Therefore, the correct option is option B.

To know more about graph, here:

https://brainly.com/question/29129702

#SPJ2

Find the surface area of the composite figure.
8 cm
6 cm
7 cm
8 cm
SA =
6 cm
[?] cm²
9 cm
6 cm

Answers

Answer:

382 cm²

Step-by-step explanation:

Front face + Back face:

A = 2(a + b)h/2

A = 2(14 cm + 8 cm)(7 cm)/2

A = 154 cm²

Left face:

A = 7 cm × 6 cm = 42 cm²

Right face:

A = 9 cm × 6 cm = 54 cm²

Bottom face:

A = 14 cm × 6 cm = 84 cm²

Top face:

A = 6 cm × 8 cm = 48 cm²

Total surface area =

= (154 + 42 + 54 + 84 + 40) cm²

= 382 cm²

The diagram shows a cuboid. 4 cm 12 cm x cm the volume of the cube is 120cm² calculate the value of x​

Answers

The answer is 2.5 cm

First, you multiply 4 and 12, and you get 48
Then you take 120 and you divide it by 48.
This leaves you with 2.5
To check you multiply 2.5, 4, and 12

Answer:

The value of x will be 2.5cm.

Step-by-step explanation:

Greetings !

Volume = Length*Width*Height

where,

Volume=120cm³Length=12cmWidth=xHeight=4cm

[tex]v = l \times w \times h \: ...substitute \: values \\ 120cm {}^{3} = 12cm \times w \times 4cm \\ 120cm {}^{3} = 48cm {}^{2} \times w \: ...divide \: both \: \\ sides \:by \: 48cm {}^{2} \\ \frac{120cm {}^{3} }{48cm {}^{2} } = w \\ w = 2.5cm[/tex]

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