The line integral / (4x – 2y) dr + – 2x2 dy, where is the curve r(o) =(-1-2, -212) with Osts 1, is equal to: None of them O 227 6 0115 3 o 112 3 79 3

Answers

Answer 1

The value of the given line integral is 4.

The line integral / (4x – 2y) dr + – 2x2 dy, where the curve r(0) =

(-1,-2, -2), and the point at which it ends is (1,2,1) is equal to: 227.

The line integral / (4x – 2y) dr + – 2x2 dy, where the curve r(0) =

(-1,-2, -2), and the point at which it ends is (1,2,1) is equal to 227.

We need to find the line integral, given that curve r(0) =

(-1, -2, -2) and the point at which it ends is (1, 2, 1). Let us find the path function of the given curve.

r(t) = xi + yj + zk

= (-1)i - 2j - 2k

=> r(0) = (-1, -2, -2)

And the point at which it ends is (1, 2, 1)r(1) = i + 2j + k

= (1, 2, 1)

Let us find the line integral, L.I = ∫(4x - 2y) dx - 2x^2 dy

From the given line integral, we can find that the integrand is of the form f.dr + g.ds, where

f = (4x - 2y) and

g = -2x^2 and

dr = dx i + dy j + dz k and

ds = √(dx^2 + dy^2 + dz^2)

So, we need to convert the given integral into the form of a line integral of the second kind to evaluate it.

L.I = ∫(4x - 2y) dx - 2x^2 dy

= ∫f.dr + g.ds

Now, let us find the differential elements of the path function,

dr = dx i + dy j + dz kds

= √(dx^2 + dy^2 + dz^2)

We need to find the limits of integration to evaluate the line integral,

The given curve is, r(0) = (-1, -2, -2) and r(1) = (1, 2, 1)

=> the limits of integration are 0 and 1

Let us find the line integral,L.I = ∫f.dr + g.ds

= ∫{(4x - 2y) dx - 2x^2 dy}

=> using Stokes' theorem.

= ∫(∂Q/∂x - ∂P/∂y) dy + (∂P/∂z - ∂R/∂x) dz + (∂R/∂y - ∂Q/∂z) dz

where P, Q, R are the components of f(x, y, z), and here,

P = 0, Q = 4x - 2y, and R = 0

Since P = R = 0,

∂P/∂y = ∂R/∂x = 0

L.I = ∫{(4x - 2y) dx - 2x^2 dy}

=> ∫(∂Q/∂x - ∂P/∂y) dy+ (∂P/∂z - ∂R/∂x) dz + (∂R/∂y - ∂Q/∂z) dz

=> ∫(∂Q/∂x) dy

=> ∫(∂(4x - 2y)/∂x) dy

=> ∫4 dy

= 4y, between 0 and 1

=> L.I = 4

Therefore, the value of the given line integral is 4.

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Related Questions

The number of tenths in 3 3/10

Answers

Answer:

0.3 tenths(so 3)

hope this helps

have a good day :)

Step-by-step explanation:

which of these random samples represents a representative sample of the systolic blood pressure of all patients in a hospital?

Answers

A representative sample based on the hospital scenario is option A

What is representative sample?

A subset of a larger population that accurately reflects the traits, diversity, and distribution of the total population is referred to as a representative sample.

Due to time, financial, or logistical limitations, it is frequently not possible or practical to investigate an entire population when conducting research or gathering data. In these situations, researchers choose a representative sample from which to deduce generalizations about the total population.

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which of these random samples represents a representative sample of the systolic blood pressure of all

a certain newspaper provides the net asset value, the year-to-date percent return, and the three-year percent return for 882 mutual funds at the end of 2017. assume that a simple random sample of 12 of the 882 mutual funds will be selected for a follow-up study on the size and performance of mutual funds. use the third column of the table of random numbers, beginning with 71744, to select the simple random sample of 12 mutual funds. begin with mutual fund 744 and use the last three digits in each row of column 3 for your selection process. what are the numbers of the 12 mutual funds in the simple random sample? (enter your answers as a comma-separated list.)

Answers

The 12  mutual funds in the simple randοm samples are

714, 41, 535, 358, 191, 378, 290, 518, 520, 421, 240, 488

What is a simple randοm sample?

A simple randοm sample is a subset οf persοns picked at randοm, all with the same prοbability, frοm a larger set οf individuals. It is a methοd οf chοοsing a sample at randοm.

Here, we have

Given: a certain newspaper prοvides the net asset value, the year-tο-date percent return, and the three-year percent return fοr 882 mutual funds at the end οf 2017. assume that a simple randοm sample οf 12 οf the 882 mutual funds will be selected fοr a fοllοw-up study οn the size and perfοrmance οf mutual funds. use the third cοlumn οf the table οf randοm numbers, beginning with 71744, tο select the simple randοm sample οf 12 mutual funds.

The last three digits in each rοw οf cοlumn 6 less than 882 are

714, 041, 535, 358, 191, 378, 290, 518, 520, 421, 240, 488

Hence, The 12  mutual funds in the simple randοm samples are

714, 41, 535, 358, 191, 378, 290, 518, 520, 421, 240, 488.

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What is the value of x in the equation −x = 6 − 3x + 8?−14−7147

Answers

S={7}

1) Let's solve for x, for the given equation :

-x = 6 -3x +8 Add 3x to both sides

3x-x=-3x+3x +6 +8

2x =14 Divide both sides by 2

x= 7

S={7}

And that is the answer

Constructed response (5 points)
Jayden's best friend brought him 10 packs of bottle rocket fireworks for his
birthday that he launched for July 4th weekend. The height of the fireworks
can be modeled by the function h(x) = -x² + 10.5x + 2 where h is the heig
in feet and t is the time in seconds.

a. Determine the initial height at which the fireworks were launched.
proper units.

Answers

The initial height which the fireworks was launched from the quadratic equation is 2 feet

What is the initial height which the fireworks was launched?

To determine the initial height at which the fireworks were launched, we need to find the value of h(0), since that represents the height at time t=0 (when the fireworks were launched).

In this giving quadratic equation, all we need to do is put x = 0 to determine the initial height

setting the function to 0

\(h(x) = -x^2 + 10.5x + 2\\h(0) = -(0)^2 + 10.5(0) + 2\\= 2 feet\)

Therefore, the initial height at which the fireworks were launched was 2 feet.

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If an independent variable is added to a multiple regression model, the R-squared value:
a. Becomes larger or smaller depending on the statistical significance of the variable
b. Becomes larger even if the variable added is not statistically significant
c. Might or might not become larger even if the variable added is statistically significant
d. Is not affected by the variable added even if it is statistically significant

Answers

C. May or may not increase in size even if the added variable has statistical significance.

The R-squared value measures the proportion of variance in the dependent variable that is explained by the model, including the independent variable.

Therefore, if an independent variable is added to the model and it is statistically significant, then it will increase the R-squared value. However, if the variable added is not statistically significant, then it will not have an effect on the R-squared value.

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find the area under the standard normal curve over the interval specified below to the right of z=3

Answers

The standard normal curve, also known as the standard normal distribution or the z-distribution, is a specific probability distribution that follows a bell-shaped curve. The area under the standard normal curve to the right of z = 3 is approximately 0.0013.

For the area under the standard normal curve to the right of z = 3, we need to calculate the cumulative probability from z = 3 to positive infinity.

The standard normal distribution, also known as the z-distribution, has a mean of 0 and a standard deviation of 1. It is a symmetric bell-shaped curve that represents the distribution of standard scores or z-scores.

Using statistical tables or software, we can find the cumulative probability associated with z = 3, which represents the area under the curve to the left of z = 3.

The cumulative probability for z = 3 is approximately 0.9987.

For the area to the right of z = 3, we subtract the cumulative probability from 1.

Therefore, the area to the right of z = 3 is approximately 1 - 0.9987 = 0.0013.

In conclusion, the area under the standard normal curve to the right of z = 3 is approximately 0.0013.

This means that the probability of randomly selecting a value from the standard normal distribution that is greater than 3 is approximately 0.0013 or 0.13%.

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You have a mortagege of $275,000
after down payment with an interest
rate of 3% for 30 years.
What does P, r,n, and t are equal to?

You have a mortagege of $275,000after down payment with an interestrate of 3% for 30 years.What does

Answers

Answer:

Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this

Step-by-step explanation:

Mercedes can download new songs for $1.39 each. Write an equation to show how many songs she can download for $15.00. NEEED HELP PLZ :(

A 15x = 1.39
B 15 + x = 1.39
C 1.39x = 15
D 1.39 + x = 15

Answers

Answer:    C. 1.39x=15

Step-by-step explanation:

each song is worth 1.39 dollars

If there are x songs, the total value would be 1.39x

1.39x=15

After how many hours was the temperature at 12
degrees F?

After how many hours was the temperature at 12degrees F?

Answers

Answer:

2 hours

Step-by-step explanation:

It was at 12 for 2 hours.

the radius of a circle is changing at .5 cm/sec. find the rate of change of the area when the radius is 4 cm.

Answers

The rate of change of the area of a circle when the radius is 4 cm is 4π cm2/sec.

This can be calculated using the formula for the area of a circle (A = πr2) and the chain rule for derivatives. The chain rule states that when the radius (r) changes, the area of a circle (A) is equal to 2πr times the rate of change of the radius (dr/dt).

Therefore, the rate of change of the area of a circle when the radius is 4 cm is equal to 2π(4 cm) × (0.5 cm/sec) = 4π cm2/sec.

Note that if the rate of change of the radius were different, the rate of change of the area would also be different. This formula can be used to calculate the rate of change of the area of a circle at any given radius, as long as the rate of change of the radius is known.

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let be the tangent plane to the graph of (,)=26−132−262 at the point (4,2,−286). let (,)=26−2−2. find the point on the graph of where the tangent plane is parallel to .

Answers

The point on the graph where the tangent plane is parallel is (52, 52, -5382).

What is the tangent plane?

The surface that contains all tangent lines of the curve at a point, $P$, that lies on the surface and passes through the point is represented by the tangent plane. We discovered earlier in our talks of derivatives and tangent lines that we can use tangent lines to mimic the behavior of a graph. We may employ tangent planes for a similar reason now that we're working with multivariable functions and three-dimensional coordinate systems.

Here, we have

Given: Let P be the tangent plane to the graph of g(x, y) = 26 – 13x² – 26y² at the point (4, 2, –286). Let f(x, y) = 26 – x² - y².

We have to find the point on the graph where the tangent plane is parallel.

Let P be the tangent plane to the graph z = g(x, y) = 26 – 13x² – 26y² at the point (4, 2, –286).

φ(x,y,z) = 13x² + 26y² + z - 26

Δφ = 26xi + 52yj + k

Δφ(4, 2, –286) = 104i + 104j + k

Then,

P: 104(x-4) + 104(y-2)+1(z+286) = 0

104x + 104y + z = 338...(1)

Now, Let

ψ(x,y,z) =  x² + y² + z - 26

Δψ = 2xi + 2yj + k

Let (x₀,y₀,z₀) be the point of the graph z = f(x,y) = 26 – x² - y² where the tangent plane in the plane is parallel to equation (1).

Δψ (x₀,y₀,z₀)  =  (2x₀,2y₀,1)

= 2x₀/104 = 2y₀/104 = 1/1

x₀ = 52 = y₀

Now, z₀ = 26 – x₀² - y₀² = 26 – 52² - 52²= -5382

Hence,  the point on the graph where the tangent plane is parallel is (52, 52, -5382).

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A group of 75 math students were asked whether they
like algebra and whether they like geometry. A total of
45 students like algebra, 53 like geometry, and 6 do
not like either subject.
Algebra vs. Geometry
Likes Algebra
Does Not
Like Algebra
Total
Likes
Geometry
Mark this and return
a
3
53
Does Not
Like Geometry
b
6
e
Total
45
P
75
What are the correct values of a, b, c, d, and e?
a 16, b = 29, c = 22, d = 30, e = 24
a = 29, b = 16, c = 30, d = 22, e = 24
a 16, b = 29, c = 24, d = 22, e = 30
H
a = 29, b = 16, c = 24, d = 30, e = 22

Answers

The correct values for a, b, c, d, and e are a = 16, b = 29, c = 24, d = 22, and e = 30 for group of 75 students on asking whether they like Algebra or Geometry.

For the values of a, b, c, d, and e, we can use the information provided in the table. Let's break it down step-by-step:

We are given that a total of 75 math students were surveyed. Therefore, the total number of students should be equal to the sum of the students who like algebra, the students who like geometry, and the students who do not like either subject.

75 = 45 (Likes Algebra) + 53 (Likes Geometry) + 6 (Does Not Like Either)

Simplifying this equation, we have:

75 = 98 + 6

75 = 104

This equation is incorrect, so we can eliminate options c and d.

Now, let's look at the information given for the students who do not like geometry. We know that a + b = 6, where a represents the number of students who like algebra and do not like geometry, and b represents the number of students who do not like algebra and do not like geometry.

Using the correct values for a and b, we have:

16 + b = 6

b = 6 - 16

b = -10

Since we can't have a negative value for the number of students, option a is also incorrect.

The remaining option is option e, where a = 29, b = 16, c = 24, d = 22, and e = 30. Let's verify if these values satisfy all the given conditions.

Likes Algebra: a + c = 29 + 24 = 53 (Matches the given value)

Does Not Like Algebra: b + d = 16 + 22 = 38 (Matches the given value)

Likes Geometry: c + d = 24 + 22 = 46 (Matches the given value)

Does Not Like Geometry: b + e = 16 + 30 = 46 (Matches the given value)

All the values satisfy the given conditions, confirming that option e (a = 29, b = 16, c = 24, d = 22, and e = 30) is the correct answer.

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A single die is rolled two times. What is the probability that the next roll will produce a number less than 3

Answers

Answer:

\(\dfrac{1}3\)

Step-by-step explanation:

When rolling a die successively, the probability of rolling a certain number(s) does not change because the die stays the same.

In this problem, we need to find the probability that a die roll will produce a number less than 3. First, we can list out those numbers:

all numbers:

123456

numbers less than 3:

12

We can see that there are 6 total numbers and 2 numbers less than 3.

Therefore, we can represent the probability of rolling a number less than 3 as:

\(\dfrac{2}{6}\)

\(\boxed{=\dfrac{1}3}\)

First, we'll find the probability that a die is rolled only once.

There are 2 numbers that are less than 3, which are 1 and 2.

This makes the fraction 2/6, or simplified to 1/3.

The probability is 1/3.

Which number is greater than 555,621,000? A. 5.0 x 10 B. 6.2 x 10 C. 5.55621 x 10 D. 9.99 x 10

Answers

Answer:

None of these

Step-by-step explanation:

None of these are correct because you would need to multiply 5 x 10 to a certain power. 5.55621 x 10 to the 8th power would do it.

Answer: I believe D is correct

Step-by-step explanation:

If a fast food workers pay for hour is 80 dollars how many dollars will he have in a week?

Answers

Answer:

the answer is 13,440. you are welcome

Please help me

Solve the inequality.
8(x - 2) + 9<3(x - 1) + 5x

A. x <-7

B. X<-3

C. no solution

D. all real numbers

Answers

Answer:

D

Step-by-step explanation:

All real numbers are solution

Step 1: Simplify both sides of the inequality.

8x−7<8x−3

Step 2: Subtract 8x from both sides.

8x−7−8x<8x−3−8x

−7<−3

Step 3: Add 7 to both sides.

−7+7<−3+7

0<4

hope this help:)

Which of the following is the best example of a statistical question?
Group of answer choices

What was the best-selling single in 2018?

What are students’ favorite types of music?

What artist won a Grammy in 2012?

Where is the Rock-and-Roll Hall of Fame located?

Answers

The answer is the first question: What was the best-selling single in 2018?

What is the next number in the sequence 11/12,5/6,3/4,2/3

Answers

The next number in the sequence is 1/2

which equations would you use the subtraction property of equality to solve? check all that apply. 5 y

Answers

answer 5y - 12 = 8.

In order to use the subtraction property of equality to solve equations, the subtraction of the same quantity should be done on both sides of the equation.

Here are the equations in which you can use the subtraction property of equality to solve:7x + 2 = 25-2y = 10-4r = 28-1/3p = 15+9z = -27

The only equation from the options given in the question is 5y - 12 = 8. So, we can use the subtraction property of equality to solve this equation as follows:5y - 12 = 8Add 12 to both sides5y - 12 + 12 = 8 + 125y = 20Divide both sides by 55y/5 = 20/5y = 4 Therefore, the equation in which we can use the subtraction property of equality to solve is 5y - 12 = 8.

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Select the correct answer from the drop-down menu.
Triangle ABC is shown with angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees.
In this triangle, the product of tan A and tan C is
.

Answers

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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What is the value of x? enter your answer in the box. x = cm

Answers

The value of x in the given equation will be 2/5

From the data,

We have to determine the value of x.

The given equation is: 18x-16=-12x-4

For determining the value of x, we will first shift the like terms on one side of the equation.

So, for solving the value of x we will shift the terms containing x and the constant on both sides of the equation.

So, shifting -12x from the right-hand side of the equation to the left-hand side of the equation,

We will get it as:

18x+12x = -4+16

30x=12

Now for solving the value of x we will shift x from the left side of the equation to the right side of the equation.

So, the value of x will be = 12/30 = 2/5

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The correct question may be:

What is the value of x

18x-16=-12x-4

Enter your answer in the box.

factor the trinomial below. x^2+13x+42

Answers

Answer:

(x + 6)(x + 7)

Step-by-step explanation:

To factor the trinomial x^2 + 13x + 42, we need to find two numbers that multiply to 42 and add up to 13.

One way to do this is to list all the pairs of factors of 42 and see which pair adds up to 13:

1, 42 -> 1 + 42 = 43

2, 21 -> 2 + 21 = 23

3, 14 -> 3 + 14 = 17

6, 7 -> 6 + 7 = 13

So the pair of factors that we want is 6 and 7. We can use these numbers to rewrite the middle term of the trinomial:

x^2 + 13x + 42 = x^2 + 6x + 7x + 42

Next, we can group the first two terms and the last two terms:

x^2 + 6x + 7x + 42 = (x^2 + 6x) + (7x + 42)

Now, we can factor out the greatest common factor from each group:

x(x + 6) + 7(x + 6)

Notice that we have a common factor of (x + 6) in both terms. We can factor this out:

(x + 6)(x + 7)

What exactly does it mean when a question says "consecutive integers"?

Answers

Answer:

Consecutive integers are those numbers that follow each other. They follow in a sequence or in order. For example, a set of natural numbers are consecutive integers.

hope this helps

have a good day :)

Step-by-step explanation:

Please answer correctly !!!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!

Please answer correctly !!!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

X+123°=180°(BEING DUM OF CO INTEROIOR ANGLES IS EQUAL TO 180°)

X=180°-123°

X=57°

Hi!

x = 57 degrees.

Explanation:

There is a straight line, so that must mean there is a linear pair. We know the first part of that pair is 123 degrees. The linear pair adds up to 180 degrees. Subtract 123 from 180 to get 57.

That angle and x are alternate interior angles, so they are equivalent.

Kaelyn has 14 coins that have a value if $1.20. she only had dimes and nickles. How many nickels does kaelyn have?​

Answers

Answer:

24

Step-by-step explanation:

At an assembly 7 out of the first 10 students who entered the gym were carrying a backpack.
Based on this information, if 700 students were at the assembly, how many students could be
expected to be carrying a backpack?____

Answers

Answer:

490 students.

Step-by-step explanation:

7 out of 10 students would be a percentage of 70% which is 0.7 in decimal form. To find out how many students would be expected to be carrying a backpack out of 700 students, 700 * 0.7 = 490 students.

please help work this out

please help work this out

Answers

Answer:

Area=190.091 cm^2

Step-by-step explanation:

Area = 1/2(Pi x r^2)    one-half because it's a semi-circle

Area=1/2(3.14 x 11^2)

11^2=121 so, Area=1/2(3.14 x 121)

Area=1/2(379.94)

Area=189.97 cm^2

adjustment:

Area=1/2(3.142 x 11^2)

Area=1/2(3.142 x 121)

Area=1/2(380.182)

Area=190.091

I thought I lost my account

Anyways, who made pythagorean theorem

Answers

Answer: Nevertheless, the theorem came to be credited to Pythagoras. It is also proposition number 47 from Book I of Euclid's Elements. According to the Syrian historian Iamblichus (c. 250–330 ce), Pythagoras was introduced to mathematics by Thales of Miletus and his pupil Anaximander.

Step-by-step explanation:

The red function is a representation of y=f(x) which equation represents the blue function

The red function is a representation of y=f(x) which equation represents the blue function

Answers

Blue Graph has the point: (-2,2) and Red Graph has the point: (-2,0). Therefore, when you remove 2 units of y for blue graph you represent the red graph.

Answer Letter A

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In other words, what was wrong with Shanelle's experiment that could have led to this? The Second Great a awakening could best be described as? which feature of a balanced chemical equation demonstrates the law of conservation of mass? iron manufacturers made two announcements concerning its common stock today. first, the company announced that the next annual dividend will be $2.10 a share. secondly, all dividends after that will increase by 2.5 percent annually. what is the maximum amount you should pay to purchase a share of this stock today if you require a 10 percent rate of return? Answer this question please and thank you Can everyone tell the answer can y'all help me out I'm not good at science! I'll make Brainliest!!!! Write an algebraic expression for each verbal expression: the difference of 10 and u 10-u 10+u 10u 10/u Which area of Georgia has the highest population density Conflict:Explain in detail the following conflicts. Include in yourexplanation how the turmoil may have started and how itevolved. Also, state the significance it will play in the secondhalf of the book.Ralph vs. JackBoys vs. NatureBoys vs. PiggyLord of the FliesJack vs. SocietyBoys vs. the Beastie Help me find each. All 4! A large semi-truck, with mass 31x crashes into a small sedan with mass x . If the semi-truck exerts a force F on the sedan, what force will the sedan exert on the semi-truck Public announcement of earnings news that makes the company worth $5 more according to average investor. It takes a few days for the company's stock price to go up by $5, so the market is efficient.Group of answer choicesFalse. Prices should never change under the EMH.True. Eventually, the price reflects available news, implying efficiency.True. Information availability always impact prices.False. Prices should reflect all available information, so delayed price movement implies inefficiency who is pop urban specifically identifying as the enemy to the Catholic faith Fill in the blankBoth of these studies have to do with the sky. However,_______ focuses on space and structures within it, like stars and meteorolds, and ______focuses on weather elements, like wind currents and cold fronts.The first blank can be1.geology 2. astronomy 3.oceanography 4.meteorology The second blank can be1.oceanography 2.astronomy3.geology4.meteorology Which of the following was not a cause of the Renaissance?Group of answer choicesA. The creation of the Holy Roman EmpireB. The discovery of ancient Roman and Greek textsC. Less warfare since the end of the CrusadesD. Increase in economic well-being in Italy If you could help me with the questions it would be greatly appreciated. WILL GIVE BRAINLY Which of these sentences uses punctuation correctly to show a direct quote?"I don't care what you say about me" P.T. Barnum always said "just spell my name right."'I don't care what you say about me," P.T. Barnum always said, "just spell my name right.""I don't care what you say about me." P.T. Barnum always said, just spell my name rightdon't care what you say about me, P.T. Barnum always said, just spell my name right. How is the process shown in the picture going to affect the daughter cells? (a) Let Y be the simple returns on Asset A and Y follows a stationary AR(1) modelIt = 0.5 + 0.377-1 + exwhere et ~ i.i.d. (0, 4) . Derive, step-by-step, the variance of Yt (b) Let Xt be the simple returns on Asset B and Xt follows a stationary AR(1) modelX+ = 0.3 Xt-1 + etwhere et ~ i.i.d. (0, 9) . Derive, step-by-step, the variance of Xt. HURRY PLEASEQ.1Read the following excerpt from Dr. Martin Luther King, Jr.'s "Letter from Birmingham," then answer the question."I guess it is easy for those who have never felt the stinging darts of segregation to say wait. But when you have seen vicious mobs lynch your mothers and fathers at will and drown your sisters and brothers at whim; when you have seen hate filled policemen curse, kick, brutalize, and even kill your black brothers and sisters with impunity; when you see the vast majority of your twenty million Negro brothers smothering in an air-tight cage of poverty in the midst of an affluent society; when you suddenly find your tongue twisted and your speech stammering as you seek to explain to your six-year-old daughter why she can't go to the public amusement park that has just been advertised on television, and see tears welling up in her little eyes when she is told that Funtown is closed to colored children, and see the depressing clouds of inferiority begin to form in her little mental sky, and see her begin to distort her little personality by unconsciously developing a bitterness toward white people then you will understand why we find it difficult to wait. There comes a time when the cup of endurance runs over, and men are no longer willing to be plunged into an abyss of injustice where they experience the bleakness of corroding despair. I hope, sirs, you can understand our legitimate and unavoidable impatience."The purpose of including this paragraph in the letter is toA. cite facts and statistics to prove that change must occur quicklyB. mobilize his readers and incite them to action through the use of motifC. motivate his readers by describing the progress they have madeD. offer an emotional argument to show that change must happen soon