3. [W] Consider the following data from NASA about the density of the sun. • When you are 10% of the way out from the center of the sun (use x = 0.1), the density is approximately 82.9619 g/cm3 . • When you are 20% of the way out of the sun, the density is approximately 38.7504 g/cm3 . • When you are 70% of the way out of the sun, the density is approximately 1.7819 g/cm3 . • When you are 80% of the way out of the sun, the density is approximately 1.9824 g/cm3 . • When you are 90% of the way out of the sun, the density is approximately 0.7859 g/cm3 . We want to use this data to find a quartic (4th degree) interpolating polynomial for the density of the sun throughout. y = Ax4 + Bx3 + Cx2 + Dx + E (a) Set up this problem as a system of linear equations. (b) Find the quartic polynomial that goes through these data points. (c) Use this polynomial to approximate the density 50% of the way out of the sun.

Answers

Answer 1

Answer:

a)

A(0.1)^4 + B(0.1)^3 + C(0.1)^2 + D(0.1) + E = 82.9619  ----------1

A(0.2)^4 + B(0.2)^3 + C(0.2)^2 + D(0.2) + E = 38.7504 -------2

A(0.7)^4 + B(0.7)^3 + C(0.7)^2 + D(0.7) + E = 1.7819   ----------3

A(0.8)^4 + B(0.8)^3 + C(0.8)^2 + D(0.8) + E = 1.9824 ----------4

A(0.9)^4 + B(0.9)^3 + C(0.9)^2 + D(0.9) + E = 0.7859 ----------5

b)  y = 519x^4 - 1630x^3 + 1844x^2 - 889x + 155

c)  0.1875

Step-by-step explanation:

a)

Let y = Ax^4 + Bx^3 + Cx^2 + Dx + E

Setting up the problem as a system of linear equations

when x=(10%)=0.1, y = 82.9619

therefore

A(0.1)^4 + B(0.1)^3 + C(0.1)^2 + D(0.1) + E = 82.9619  ----------1

when x=(20%)=0.2, y = 38.7504

A(0.2)^4 + B(0.2)^3 + C(0.2)^2 + D(0.2) + E = 38.7504 -------2

when x=(70%)=0.7, y = 1.7819

A(0.7)^4 + B(0.7)^3 + C(0.7)^2 + D(0.7) + E = 1.7819   ----------3

when x=(80%)=0.8, y = 1.9824

A(0.8)^4 + B(0.8)^3 + C(0.8)^2 + D(0.8) + E = 1.9824 ----------4

when x=(90%)=0.9, y = 0.7859

A(0.9)^4 + B(0.9)^3 + C(0.9)^2 + D(0.9) + E = 0.7859 ----------5

b)

Find the quartic polynomial that goes through these data points

Now to find the values ( A,B,C,D,E)

[MATRIX]

║A║         ║   (0.1)^4  (0.1)^3    (0.1)^2   (0.1)    1    ║^-1    ║ 82.9619  ║

║B║         ║     (0.2)^4  (0.2)^3  (0.2)^2   (0.2) 1   ║         ║ 38.7504 ║

║C║     =  ║    (0.7)^4  (0.7)^3  (0.7)^2   (0.7)   1   ║         ║ 1.7819     ║

║D║         ║    (0.8)^4  (0.8)^3  (0.8)^2  (0.8)   1   ║         ║ 1.9824    ║

║E║         ║    (0.9)^4  (0.9)^3  (0.9)^2  (0.9)   1   ║         ║ 0.7859    ║

║A║      ║  29.7619  -47.619  166.667   -238.095   89.2857 ║ ║ 82.9619║

║B║      ║  -77.381  119.048  -333.333   452.381 -160.714      ║ ║ 38.7504║

║C║  =  ║   71.131  -102.381  208.333  -269.048 91.9643      ║ ║ 1.7819    ║

║D║      ║  -26.369 33.0952  -41.6667  52.619  -17.6786     ║ ║ 1.9824   ║

║E║       ║   3.00      -2.4         -2.4        -3.00          -1.00       ║  ║ 0.7859  ║

║A║       ║ 519   ║

║B║       ║ -1630║

║C║  =   ║ 1844 ║ ,         y = 519x^4 - 1630x^3 + 1844x^2 - 889x + 155

║D║       ║ -889 ║

║E║       ║ 155    ║

c)

approximate the density 50% of the way out of the sun

so at 50% (0.5) x=0.5

we substitute

y = 519(0.5)^4 - 1630(0.5)^3 + 1844(0.5)^2 - 889(0.5) + 155

= 0.1875


Related Questions

If all else remains constant and the values of two variables move in the same direction it indicates a Group of answer choices negative slope relationship. inverse slope relationship. the values of the two variables will move in the same direction then move in opposite directions. positive slope relationship.

Answers

Answer:

positive slope relationship.

Step-by-step explanation:

When two variables move in the same direction, they are positively related. An increase in one variable would lead to an increase in the other variable.

For example, price and quantity supplied are positively correlated. An increase in price, leads to an increase in quantity supplied and a decrease in price leads to a decrease in quantity supplied.

Please check the attached image for a positively correlated curve

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Answers

Answer:

The student needs a minimum score of 81 on the fourth test to ensure a grade of at least a C in the class.

Step-by-step explanation:

Remember what an average is. (Look at the hint at the bottom of the problem.)

To find the average of a set of numbers, add all the numbers and divide by the number of numbers.

For example, if in a class you took 8 tests, the average of the 8 tests is the sum of the 8 scores divided by 8.

In this case, the student took 3 tests and is taking one more, so in the end there will be 4 scores. The number of tests is 4.

We know 3 of the 4 scores. We don't know the fourth score because he has not taken the test yet, so we use a variable to represent the unknown score. Let's call the score of the fourth test x.

To find the average of the 4 scores, we add them and divide the sum by 4.

The three known scores are 63, 62, 74.

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[tex] \dfrac{63 + 62 + 74 + x}{4} [/tex]

The expression above is the average of the 4 scores. We want the average to be at least 70, so we need the average to be greater than or equal to 70.

We get this inequality.

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Multiply both sides by 4.

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Subtract 199 from both sides.

x = 81

Answer: The student needs a minimum score of 81 on the fourth test to ensure a grade of at least a C in the class.

Factor x3 – 7x2 – 5x + 35 by grouping. What is the resulting expression? o
(x2 – 7)(x - 5)
(x2 – 7)(x + 5) •
(x2 – 5)(x – 7)
(x2 + 5)(x – 7)​

Answers

Answer: C

.................................................................

The expression is a polynomial expression, and the factored expression of x³ - 7x² - 5x + 35 is (x² - 5)(x - 7)

How to factor the expression?

The expression is given as:

x³ - 7x² - 5x + 35

Factorize the expression

x²(x - 7) - 5(x - 7)

Factor out x - 7 in the expression

(x² - 5)(x - 7)

The above expression cannot be further factorized.

Hence, the factored expression of x³ - 7x² - 5x + 35 is (x² - 5)(x - 7)

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Find the unknown length y in the pair of similar triangles.

Answers

Step-by-step explanation:

If 2 triangles are similar then the ratio of any 2 sides of one triangles will be equal to the ratio of any 2 sides of the another triangle.

So,

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What are the coordinates of the vertices of AA'B'C' after each movement?

Answers

Answer:

The answer is in the picture attached.

Step-by-step explanation:

Edmentum Sample Answer

Answer:

Step-by-step explanation:

(1-,1, (2,0), ( 3,-2 )

(-4, 2),(-3,3),(2,1)

(-3,-3), (-2,-2), (-1,4)

what the facters of 18​

Answers

☽------------❀-------------☾

Hi there!

~

[tex]1, 2, 3, 6, 9, 18[/tex]

The factor pairs of 18 are:

[tex]1 \times 18 = 18\\2 \times 9 = 18\\3 \times 6 = 18[/tex]

❀Hope this helped you!❀

☽------------❀-------------☾

Answer:

1, 2, 3, 6, 9, 18

Step-by-step explanation:

1*18=18

2*9=18

3*6=18

There are no other factors, Hope this helps!!

Which of the following is/are units of velocity? Can select more than one answer A) m/s B) m/s^2 C) km/hr D) km/hr/s E) m/s/s

Answers

Answer:

The answer to your question is m/s which is the A

Answer:

m/s is the answer

Step-by-step explanation:

because

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Answers

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Step-by-step explanation:

9+x=10

x=1

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Answers

Answer: one

Step-by-step explanation:

Answer:

Step-by-step explanation:

If 9 was underlined it would be 9 ones

If it was 5, 5 tenths

If it was 2, 2 hundreths

If it was 1, 1 thousandth

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Andrew was making a science project for school. He worked for 6.6 hours the first week, 2.75 hours the second week, and 4.4 hours the third week.

Andrew used the following mental math strategy to find the total number of hours he worked on his project.

Answers

Answer:

Step-by-step explanation:

its wierd but 2.22

The probability that Chloe is happy given that she has had dinner by 6pm is 0.9. The probability that Chloe is not happy given that she has not had dinner by 6pm is 0.8. Assume that there is a 60% chance that Chloe eats dinner by 6pm on a given day. a) If Chloe is not happy at 6pm, find the probability that she has not had dinner yet. b) If Chloe is happy at 6pm, find the probability that she has already had dinner.

Answers

Answer:

a) If Chloe is not happy at 6pm,  the probability that she has not had dinner yet =P(B/D)= 0.8

b) If Chloe is happy at 6pm,the probability that she has already had dinner= P(A/C) = 0.9

Step-by-step explanation:

Let A be an event that Chloe is happy given that she has had dinner by 6pm

P(A) =  0.9

Let B be an event that  Chloe is not happy given that she has not had dinner by 6pm

P(B) = 0.8.

Let C be an event that Chloe eats dinner by 6pm on a given day

P(C) = 60%=0.6

Let D be an event that Chloe does not eat dinner by 6pm on a given day

P(D) = 1- 60%=1- 0.6= 0.4

This requires conditional probability .

Part a

P(B/D)=P(B∩D)/P(D)

P(B∩D) = 0.8 *0.4=0.32

P(D) = 0.4

P(B/D)=P(B∩D)/P(D)

         = 0.32/0.4= 0.8

P(B)= P(B/D)

0.8 is equal to 0.8

This shows that the  events are independent.

b)

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Answers

Answer: SEE BELOW

If you need further explanation about how to graph, please let me know.

Hope this helps!! :)

this is the answerisjsjdndjdn

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Answers

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Answers

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Answers

Answer:

The numerical length of UW is 27

Step-by-step explanation:

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Answers

Answer:

Hope you understand not to sure but that's what I got

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Answers

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Answers

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Answers

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Step-by-step explanation:

Step 1: Write out expression

(x - 4)²

Step 2: Expand

(x - 4)(x - 4)

Step 3: FOIL

x² - 4x - 4x + 16

Step 4: Combine like terms

x² - 8x + 16

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Answers

Answer:

5

Step-by-step explanation:

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Parallel lines have same slope.

So, slope of required line = 5

Solve for x and check: 1/2x - 3 =25

Answers

Answer:

14

Step-by-step explanation:

Step 1:

1/2x - 3 = 25

Step 2:

1/2x = 28

Answer:

x = 14

Hope This Helps :)

What is the y-intercept of:
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Answers

Answer:

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Step-by-step explanation:

(0,5)

Plug x=0 to get your y-intercept

Brainliest?

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What was the price yesterday?

Answers

$481 is 74%
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481 x 100 = 48100
48100 / 74 = 650

the price was $650

Answer:

The price yesterday was 650

Step-by-step explanation:

X is the price yesterday

There is a 26% discount

That means today we pay 100 -26 = 74 %

x* 74% = 481

.74x = 481

Divide each side by .74

.74x/.74 = 481/.74

x = 650

The price yesterday was 650

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Answers

Answer:

i think its rational.  

Step-by-step explanation:

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Its 4 PARTS​

Answers

Angle 1 = 44
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Angle 3 = 44
Angle 4 = 136
Angle 5 = 62

The measure of angle ∠1 is 44 degrees and the measure of angle ∠5 is 62 degrees.

What is an angle?

Angle is the space between the line or the surface that meets.  And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.

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∠1 + 46° = 90°

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∠1 = ∠3 = 44°

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Answers

Answer:

x = -1

Step-by-step explanation:

7^(3x+7) = 7^(-8x-4)

First Step: Cancel out like bases.

3x + 7 = -8x - 4

Second Step: Add 8x on both sides.

11x + 7 = -4

Third Step: Subtract 7 on both sides.

11x = -11

Fourth Step: Divide by 11 on both sides.

x = -1

PLEASE HURRY IM GIVING BRAINLIEST AND 50 POINTS!!! for the function g(x) = x - 2x^2, find g(-3) + 13

Answers

Hey there! I'm happy to help!

If we have g(-3) we plug -3 into our function as x.

-3-2(-3)²

-3-2(9)

-3-18

-21

g(-3) is -21, so now we just add 13.

-21+13=-8

The answer is -8.

Have a wonderful day! :D

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Answers

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Step-by-step explanation: In math a equal sign put in between two expressions is called an equation.    :)

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