Look at the parallelogram ABCD shown below. The table below shows the steps to prove that if the quadrilateral ABCD is a parallelogram, then its opposite sides are congruent. Statement Reasons 1 . AB is parallel to DC and AD is parallel to BC - definition of parallelogram 2 . angle 1 = angle 2, angle 3 = angle 4 - if two parallel lines are cut by a transversal then the corresponding angles are congruent 3 . BD = BD - Reflexive Property 4 . triangles ADB and CBD are congruent - if two sides and the included angle of a triangle are congruent to the corresponding sides and angle of another triangle , then the triangles are congruent by SAS postulate 5 . AB = DC, AD = BC - corresponding parts of congruent triangles are congruent Which statement is true about the table? 1. It is not correct because it provides incorrect sequence of statement 2 and statement 4. 2. It is not correct because it does not provide correct reasons for statement 2 and statement 4. 3. It is accurate because it provides the correct sequence of statements. 4. It is accurate because it provides the correct reasons for the statements.

Answer: 6 / √26

Step-by-step explanation:

Given that f(x, y, z) = xe^y + ye^z + ze^x

so first we compute the gradient vector at (0, 0, 0)

Δf ( x, y, z ) = [ e^y + ze^x,  xe^y + e^z,  ye^z + e^x ]

Δf ( 0, 0, 0 ) = [ e⁰ + 0(e)⁰, 0(e)⁰ + e⁰, 0(e)⁰ + e⁰ ] = [ 1+0 , 0+1, 0+1 ] = [ 1, 1, 1 ]

Now we were also given that  V = < 4, 3, -1 >

so ║v║ = √ ( 4² + 3² + (-1)² )

║v║ = √ ( 16 + 9 + 1 )

║v║ = √ 26

It must be noted that "v"  is not a unit vector but since ║v║ = √ 26, the unit vector in the direction of "V" is ⊆ = ( V / ║v║)

so

⊆ =  ( V / ║v║) = [ 4/√26, 3/√26, -1/√26 ]

therefore by equation   D⊆f ( x, y, z ) = Δf ( x, y, z ) × ⊆

D⊆f ( x, y, z ) = Δf ( 0, 0, 0 ) × ⊆ = [ 1, 1, 1 ] × [ 4/√26, 3/√26, -1/√26 ]

= ( 1×4 + 1×3 -1×1 ) / √26

= (4 + 3 - 1) / √26

= 6 / √26

Answer:

Vertical angles are congruent.

Step-by-step explanation:

Vertical angles are opposite angles formed by intersecting lines, and are always congruent.

Step-by-step explanation:

Let us assume that 1/2+root 3 is rational . So 1/2+root 3 = a/b where a and b are irrationals. since rhs is a rational number root 3 should be also rational .

Answer:

Step-by-step explanation:

Given,

Hypotenuse ( h ) = 158 cm

Perpendicular ( p ) = 83

Base ( b ) = ?

Now, Using Pythagoras theorem:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

[tex] {b}^{2} = {h}^{2} - {p}^{2} [/tex]

Plug the values

[tex] {b}^{2} = {158}^{2} - {83}^{2} [/tex]

Evaluate the power

[tex] {b}^{2} = 24964 - 6889[/tex]

Calculate the difference

[tex] {b}^{2} = 18075[/tex]

[tex]b = \sqrt{18075} [/tex]

Calculate

[tex]b = 134.4 \: cm[/tex]

Hope this helps..

Best regards!!

Answer:

H0: μ=2; Ha: μ>2

Step-by-step explanation:

The null hypothesis is the default hypothesis while the alternative hypothesis is the opposite of the null and is always tested against the null hypothesis.

In this case study, the null hypothesis is that adults were eating, on average, the recommended 2 cups of vegetables a day: H0: μ=2 while the alternative hypothesis is adults were eating, on average, more than the recommended 2 cups of vegetables a day Ha: μ>2.

Answer: 8.5 sq. units.

Step-by-step explanation:

Formula:

Area of triangle : [tex]\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]

Given: Triangle IJK, with vertices I(3,-7), J(7,-4), and K(4,-2)

Then, Area of triangle  IJK = [tex]\dfrac{1}{2}|3(-4-(-2))+7(-2-(-7))+4(-7-(-4))|[/tex]

[tex]\dfrac{1}{2}|3(-2)+7(5)+4(-3)|\\\\=\dfrac{1}{2}|-6+35-12|\\\\=\dfrac{1}{2}(17)\\\\=8.5\text{ sq. units}[/tex]

Hence, the area of this triangle  IJK on a Coordinate Grid = 8.5 sq. units.

Answer:

To verify the Cauchy-Bunyakovsky-Schwarz Inequality, (p,q) must be less than (or equal to) ||p|| • ||q||

(1,1,1) is not equal to (-10,5)

Step-by-step explanation:

a°b° + a^1b^1 + a^2b^2 < 5x (-2x^2 + 1)

Any algebra raised to the power of zero is equal to 1.

a°b° = 1 × 1 = 1

1 + ab + a^2b^2 < -10x^3 + 5x

The vectors:

(1,1,1) < (-10,5)

This verifies the Cauchy-Schwarz Inequality

Triangle Inequality states that for any triangle, the sum of the lengths of two sides must be greater than or equal to the length of the third side.

Answer:  4

Step-by-step explanation:

Simply rotate the graph 1-turn to the left to see where the triangle lands. The x-axis will be the horizontal line and the y-axis will be the vertical line.

The attachment shows the graph rotated 1-turn to the left (90°).

Notice it is in the exact same position as #4.

Answer:

The variance of the data is 15.

σ² = 15

Step-by-step explanation:

The mean is given as

X = 8

х        |    (x - X)    |    (x - X) ²

12       |        4         |    16

9        |        1         |     1    

11        |        3         |    9

5       |        -3        |    9

3       |        -5        |    25

The variance is given by

[tex]\sigma^2 = \frac{1}{n-1} \sum (x - X)^2[/tex]

[tex]\sigma^2 = \frac{1}{5 - 1} (16 + 1 + 9 + 9 +25) \\\\\sigma^2 = \frac{1}{4} ( 16 + 1 + 9 + 9 +25) \\\\\sigma^2 = \frac{1}{4} (60) \\\\\sigma^2 = 15[/tex]

Therefore, the variance of the data is 15.

Answer:

90°

Step-by-step explanation:

Circumcenter of a triangle is obtained by drawing perpendicular bisectors of the sides of a triangle. Hence GE is perpendicular to AC.

Therefore, m∠GEA = 90°

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

            Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

Let's solve your equation step-by-step.

[tex]\frac{1}{3} (x+1)+2x=2[/tex]

Step 1: Simplify both sides of the equation.

[tex]\frac{1}{3} (x+1)+2x=2[/tex]

[tex](\frac{1}{3}) (x) + (\frac{1}{3} ) (1) + 2x = 2[/tex] (Distribute)

[tex]\frac{1}{3} x + \frac{1}{3} + 2x = 2[/tex]

[tex]( \frac{1}{3} x + 2x ) + (\frac{1}{3}) = 2[/tex] (Combine Like Terms)

[tex]\frac {7}{3} x + \frac{1}{3} = 2\\\frac{7}{3} x + \frac{1}{3} = 2[/tex]

Step 2: Subtract 1/3 from both sides.

[tex]\frac{7}{3} x + \frac{1}{3} - \frac{1}{3} = 2 - \frac{1}{3} \\\\\frac{7}{3} x = \frac{5}{3}[/tex]

Step 3: Multiply both sides by 3/7.

[tex]( \frac{3}{7} ) * (\frac{7}{3}x) = ( \frac{3}{7}) * \frac{5}{3} \\\\x = \frac{5}{7}[/tex]

So the answer is : [tex]x = \frac{5}{7}[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Store T sells apples at the lowest rate

Step-by-step explanation:

1st We need to make every statement in order of 1 pound. Then We will easily find the lowest rate of apple.

i) R sell 1.20 $ per pound.

ii) S sell 4 pounds for 5$

i.e S sell 1 pound for 5/4 = 1.25$

iii) T sell 3 pound for 3.48$

i.e T sell 1 pound for 3.48/3 = 1.16$

Analysing the above data I get,

Store T sells apples at the lowest rate

Answer:

The required probability = 0.144

Step-by-step explanation:

Since the probability of making money is 60%, then the probability of losing money will be 100-60% = 40%

Now the probability we want to calculate is the probability of making money in the first two days and losing money on the third day.

That would be;

P(making money) * P(making money) * P(losing money)

Kindly recollect;

P(making money) = 60% = 60/100 = 0.6

P(losing money) = 40% = 40/100 = 0.4

The probability we want to calculate is thus;

0.6 * 0.6 * 0.4 = 0.144

Answer:

y = x+3

Step-by-step explanation:

First step is to find the slope

m = ( y2-y1)/(x2-x1)

   = ( 7-9)/(4 - 6)

   = -2 / -2

  = 1

The we can put is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

y = 1x+b

Putting in one of the points

9 = 1*6+b

Subtracting 6

9-6 = b

3=b

y = 1x+3

y = x+3

Answer:

[tex]\boxed{y=x+3}[/tex]

Step-by-step explanation:

Solve for slope first.

The slope can be found through 2 points.

[tex]slope=\frac{change \: in \: y}{change \: in \: x}[/tex]

[tex]slope=\frac{7-9}{4-6}[/tex]

[tex]slope=\frac{-2}{-2}[/tex]

[tex]slope=1[/tex]

Using slope-intercept form.

[tex]y=mx+b\\m=slope\\b=y \: intercept[/tex]

[tex]y=1x+b[/tex]

Let x = 6 and y = 9.

[tex]9=1(6)+b[/tex]

[tex]9-6=b[/tex]

[tex]3=b[/tex]

[tex]y=1x+3[/tex]

Answer:

11/36

Step-by-step explanation:

Find the probability that neither dice shows a 5 (also means the dice can show any number except 5- where there are 5 possible choices out of 6):

= 5/6 x 5/6

=25/36

If we subtract the probability that neither dice shows a 5, we can obtain the probability that at least 1 dice shows a 5- (either one of them is 5, or both of them is 5)

1- 25/36

=11/36

Answer:

a. uses a related sample - repeated measures

c. uses a related sample (matched subjects)

Step-by-step explanation:

A) You are interested in a potential treatment for compulsive hoarding. You treat a group of 50 compulsive hoarders and compare their scores on the Hoarding Severity scale before and after the treatment. You want to see if the treatment will lead to lower hoarding scores.  

The design described uses a related sample - repeated measures because the scores were compared on the Hoarding Severity scale before and after the treatment.

B) John Caccioppo was interested in possible mechanisms by which loneliness may have deterious effects of health. He compared the sleep quality of a random sample of lonely people to the sleep quality of a random sample of nonlonely people.

The design described uses a related sample (matched subjects)

Answer:

range of the function F(x) is  (-infinity, 3)

Step-by-step explanation:

I do not see the graph function F(x), so will assume that it is a graph of the function F(x) over the complete domain (-inf,inf).

As you can see from the attached graph, the function reaches a maximum at y=+3, and extends all the way to -infinity.

So the range of the function F(x) is  (-infinity, 3)

Answer:

4

Step-by-step explanation:

I suppose this is a trick question.

The answer is equal to the "circular hole" in the numbers. (except 4, which does not contain circular hole).

So by counting the holes,

123456789 = 4

Answer:

4

Step-by-step explanation:

This is a trick/pattern

We have to count the number of holes in each number

1-0

2-0

3-0

4-0

5-0

6-1

7-0

8-2

9- 1

1+2+1 =4

Answer:

C

Step-by-step explanation:

I suppose you have learned that for the sides of a triangle to work, it has to be a + b > c, the 4 is the a, the 8 is the b, the 12 is the c.

So: 4 + 8 > 12; however this is not true, they are equal so the triangle wont be a triangle, it would be lines that never connect.

Answer:

Step-by-step explanation:

The class interval is simply the difference between the lower or upper class boundary or limit  of a class and the lower or upper class boundary or limit of the next class.

In this case for the class

$4 up to $7 18 and

$7 up to $10 36

The lower class boundary of the first class is $4 and the lower class boundary of the second class is $7

Answer:

The length is 5.5 inches

Step-by-step explanation:

The area of a rectangle is

A = lw

66 =  l * 12

Divide each side by 12

66/12 = l

5.5 = l

The length is 5.5 inches

Answer:

5.5 inches

Step-by-step explanation:

Length times width is the area so

12*width =66

same as

66/12=5.5 inches

Ask more questions in the comments if you are still confused.

Answer:

20cm it's is the answers

Step-by-step explanation:

5*4=20

Answer:

Step-by-step explanation:

From the summary of the given data;

After the second dose, 137 of 452 subjects in the experimental group (group 1) experienced drowsiness as a side effect.

Let consider [tex]p_1[/tex] to be the probability of those that experience the drowsiness in group 1

[tex]p_1[/tex] = [tex]\dfrac{137}{452}[/tex]

[tex]p_1[/tex] = 0.3031

After the second dose, 31 of 99 subjects in the control group (group 2) experienced drowsiness as a side effect.

Let consider [tex]p_2[/tex] to be the probability of those that experience the drowsiness in group 1

[tex]p_2[/tex] = [tex]\dfrac{31}{99}[/tex]

[tex]p_2[/tex] = 0.3131

The objective is to be able to determine if the evidence suggest that a lower proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2 at the α=0.05 level of significance.

In order to do that; we have to state the null and alternative hypothesis; carry out our test statistics and make conclusion based on it.

So; the null and the  alternative hypothesis can be computed as:

[tex]H_o :p_1 =p_2[/tex]

[tex]H_a= p_1<p_2[/tex]

The test statistics is computed as follows:

[tex]Z = \dfrac{p_1-p_2}{\sqrt{p_1 *\dfrac{1-p_1}{n_1} +p_2 *\dfrac{1-p_2}{n_2}} }[/tex]

[tex]Z = \dfrac{0.3031-0.3131}{\sqrt{0.3031 *\dfrac{1-0.3031}{452} +0.3131 *\dfrac{1-0.3131}{99}} }[/tex]

[tex]Z = \dfrac{-0.01}{\sqrt{0.3031 *\dfrac{0.6969}{452} +0.3131 *\dfrac{0.6869}{99}} }[/tex]

[tex]Z = \dfrac{-0.01}{\sqrt{0.3031 *0.0015418 +0.3131 *0.0069384} }[/tex]

[tex]Z = \dfrac{-0.01}{\sqrt{4.6731958*10^{-4}+0.00217241304} }[/tex]

[tex]Z = \dfrac{-0.01}{0.051378 }[/tex]

Z = - 0.1946

At the level of significance ∝ = 0.05

From the standard normal table;

the critical value for Z(0.05) = -1.645

Decision Rule: Reject the null hypothesis if Z-value is lesser than the critical value.

Conclusion: We do not reject the null hypothesis because the Z value is greater than the critical value. Therefore, we cannot conclude that a lower proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2

Answer:

the probability that one parachute of the  five parachute is damaged is 0.156

Step-by-step explanation:

From the given information;

Let consider X to be the altitude above the  ground that a parachute opens

Then; we can posit that the probability that the parachute is damaged is:

P(X ≤ 100 )

Given that the population mean μ = 155

the standard deviation σ = 30

Then;

[tex]P(X \leq 100 ) = ( \dfrac{X- \mu}{\sigma} \leq \dfrac{100- \mu}{\sigma})[/tex]

[tex]P(X \leq 100 ) = ( \dfrac{X- 155}{30} \leq \dfrac{100- 155}{30})[/tex]

[tex]P(X \leq 100 ) = (Z \leq \dfrac{- 55}{30})[/tex]

[tex]P(X \leq 100 ) = (Z \leq -1.8333)[/tex]

[tex]P(X \leq 100 ) = \Phi( -1.8333)[/tex]

From standard normal tables

[tex]P(X \leq 100 ) = 0.0334[/tex]

Hence; the probability of the given parachute damaged is 0.0334

Let consider Q to be the dropped parachute

Given that the number of parachute be n= 5

The probability that the parachute opens in each trail be  p = 0.0334

Now; the random variable Q follows the binomial distribution with parameters n= 5 and p = 0.0334

The probability mass function is:

Q [tex]\sim[/tex] B(5, 0.0334)

Similarly; the event that one parachute is damaged is :

Q ≥ 1

P( Q ≥ 1 ) = 1 - P( Q < 1 )

P( Q ≥ 1 ) = 1 - P( Y = 0 )

P( Q ≥ 1 ) = 1 - b(0;5; 0.0334 )

P( Q ≥ 1 ) = [tex]1 -(^5_0)* (0.0334)^0*(1-0.0334)^5[/tex]

P( Q ≥ 1 ) = [tex]1 -( \dfrac{5!}{(5-0)!}) * (0.0334)^0*(1-0.0334)^5[/tex]

P( Q ≥ 1 ) = 1 -  0.8437891838

P( Q ≥ 1 ) = 0.1562108162

P( Q ≥ 1 ) [tex]\approx[/tex] 0.156

Therefore; the probability that one parachute of the  five parachute is damaged is 0.156

Hey there!

If a line is horizontal, the entire line is at the same elevation. On a line, the elevation is the y-value. So, all of the points with the same y-value are on the same horizontal line.

We see that all of these points have different y-values so none of them would be on the same horizontal line.

I hope that this helps! Have a wonderful day!

Answer:

1-{0.2(m-3)+¼}=0

1{0.2m-0.6+¼}=0

1-{(0.8m-2.4+1)/4}=0

1-(0.8m-1.4)/4=0

lcm

(4-0.8m-1.4)/4=0

(2.6-0.8m)/4=0

cross multiply

2.6-0.8m=0

m=2.6/0.8

m=3.25

The solution of the expression are,

⇒ m = 3.25

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Expression is,

⇒ 1 - | 0.2 (m - 3) + 1/4 | = 0

Now, We can simplify as;

⇒ 1 - | 0.2m - 0.6 + 1/4| = 0

⇒ 1 - |0.2m - 0.6 + 0.25| = 0

⇒ 1 - |0.2m - 0.35| = 0

⇒ 1 = 0.2m + 0.35

⇒ 1 - 0.35 = 0.2m

⇒ 0.2m = 0.65

⇒ m = 3.25

Thus, The solution of the expression are,

⇒ m = 3.25

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

Answer:

[tex]\boxed{7.955>7.95}[/tex]

Step-by-step explanation:

7.95 can also be written as 7.950 .

So, we'll compare 7.955 and 7.950.

All the digits in ones, tenths, hundredths place are equal so we'll look at the thousandths place.

5 is in the thousandths place of 7.955 and 0 is in the thousandths place of 7.950. Since 5 is greater than 0 so 7.955 is greater than 7.95. It can also be written as:

7.955 > 7.950

Answer:

Children: $13

Adults: $18

Step-by-step explanation:

Well for both sets we can set up the following system of equations,

[tex]\left \{ {{3a + 4c = 106} \atop {2a + 3c = 75}} \right.[/tex]

So first we need to solve for a in the first equation.

3a + 4c = 106

-4c to both sides

3a = -4c + 106

Divide 3 by both sides

a = -4/3c + 35 1/3

Now we plug in that a for a in 2a + 3c = 75.

2(-4/3c + 35 1/3) + 3c = 75

-8/3c + 70 2/3 + 3c = 75

Combine like terms

1/3c + 70 2/3 = 75

-70 2/3 to both sides

1/3c = 4 1/3

Divide 1/3 to both sides

c = 13

Now we can plug in 13 for c in 3a + 4c = 106,

3a + 4(13) = 106

3a + 52 = 106

-52 to both sides

3a = 54

Divide 3 by both sides.

a = 18

Thus,

an adult ticket is $18 and a children's ticket is $13.

Hope this helps :)

Answer:

Adults pay $18 and children pay $13.5

Step-by-step explanation:

Hello!

You need to calculate the price of the tickets for adults and children for the group trip to New York.

If X represents adult and Y represents children, then you can express the given information as two equations with two unknown values:

Three adults and four children must pay $106. ⇒ 3X + 4Y= $106

Two adults and three children must pay $75. ⇒ 2X + 3Y= $75

I) First step, in one of the equations you have to clear one of the unknown values, I'll clear the value of Y:

3X + 4Y= 106

4Y= 106 - 3X

[tex]Y= \frac{106-3X}{4}[/tex]

II) Second step you have to replace it in the second equation:

2X + 3Y= 75

[tex]2X + 3(\frac{106-3X}{4} )= 75[/tex]

[tex]2X + \frac{3}{4}(106-3X)= 75[/tex]

[tex]2X + (\frac{3}{4}*106 - \frac{3}{4}*3X )= 75[/tex]

[tex]2X + 79.5 -\frac{9}{4}X =75[/tex]

[tex]2X - \frac{9}{4}X= 75 - 79.5[/tex]

[tex]-\frac{1}{4} X= -\frac{9}{2}[/tex]

[tex]X= -\frac{9}{2} * -4= 18[/tex]

The price for adult tickets is $18.

III) Third step, using the calculated value of X, you replace it on the formula obtained in I) yo calculate the price for the children Y:

[tex]Y= \frac{106-3X}{4}= \frac{106-(3*18)}{4} = \frac{27}{2}= 13.5[/tex]

The ticket price for children is $13.5

I hope this helps!

Answer:

B. The set is linearly independent because at least one of the vectors is a multiple of another vector.

Step-by-step explanation:

A set of n vector of length n is linearly independent if the matrix with these vectors as column has none of zero determinant. The set of vectors is dependent if the determinant is zero. In the given question the vectors have no zero determinants therefore it is linearly independent.

The area of the surface above the region R is 4096π square units.

Given that:

The function: [tex]f(x, y) = 64 + x^2 - y^2[/tex]

The region R is the disk with a radius of 8 units [tex]x^2 + y^2 \le 64[/tex].

To find the area of the surface given by z = f(x, y) that lies above the region R, to calculate the double integral over the region R of the function f(x, y) with respect to dA.

The integral for the area is given by:

[tex]Area = \int\int_R f(x, y) dA[/tex]

To evaluate this integral, we need to set up the limits of integration for x and y over the region R, which is the disk cantered at the origin with a radius of 8 units.

Using polar coordinates, we can parameterize the region R as follows:

x = rcos(θ)

y = rsin(θ)

where r goes from 0 to 8, and θ goes from 0 to 2π.

Now, rewrite the integral in polar coordinates:

[tex]Area =\int\int_R f(x, y) dA\\Area = \int_0 ^{2\pi} \int_0^8(64 + r^2cos^2(\theta) - r^2sin^2(\theta)) \times r dr d \theta[/tex]

Now, we can integrate with respect to r first and then with respect to θ:

[tex]Area = \int_0^{2\pi} \int_0^8] (64r + r^3cos^2(\theta) - r^3sin^2(\theta)) dr d \theta[/tex]

Integrate with respect to r:

[tex]Area = \int_0^{2\pi}[(32r^2 + (1/4)r^4cos^2(\theta) - (1/4)r^4sin^2(\theta))]_0^8 d \theta\\Area = \int_0^{2\pi} (2048 + 256cos^2(\theta) - 256sin^2(\theta)) d \theta[/tex]

Now, we can integrate with respect to θ:

[tex]Area = [2048\theta + 128(sin(2\theta) + \theta)]_0 ^{2\pi}[/tex]

Area = 2048(2π) + 128(sin(4π) + 2π) - (2048(0) + 128(sin(0) + 0))

Area = 4096π + 128(0) - 0

Area = 4096π square units

So, the area of the surface above the region R is 4096π square units.

Learn more about Integration here:

https://brainly.com/question/31744185

#SPJ4