1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Savatey [412]
3 years ago
7

Help ASAP!!!!!!!!!!!! Show your work!!!!!!!!!!!

Mathematics
1 answer:
Mariulka [41]3 years ago
3 0

Answer:

x = -0.846647 or x = -0.177346 or x = 0.841952 or x = 1.58204

Step-by-step explanation:

Solve for x:

5 x^4 - 7 x^3 - 5 x^2 + 5 x + 1 = 0

Eliminate the cubic term by substituting y = x - 7/20:

1 + 5 (y + 7/20) - 5 (y + 7/20)^2 - 7 (y + 7/20)^3 + 5 (y + 7/20)^4 = 0

Expand out terms of the left hand side:

5 y^4 - (347 y^2)/40 - (43 y)/200 + 61197/32000 = 0

Divide both sides by 5:

y^4 - (347 y^2)/200 - (43 y)/1000 + 61197/160000 = 0

Add (sqrt(61197) y^2)/200 + (347 y^2)/200 + (43 y)/1000 to both sides:

y^4 + (sqrt(61197) y^2)/200 + 61197/160000 = (sqrt(61197) y^2)/200 + (347 y^2)/200 + (43 y)/1000

y^4 + (sqrt(61197) y^2)/200 + 61197/160000 = (y^2 + sqrt(61197)/400)^2:

(y^2 + sqrt(61197)/400)^2 = (sqrt(61197) y^2)/200 + (347 y^2)/200 + (43 y)/1000

Add 2 (y^2 + sqrt(61197)/400) λ + λ^2 to both sides:

(y^2 + sqrt(61197)/400)^2 + 2 λ (y^2 + sqrt(61197)/400) + λ^2 = (43 y)/1000 + (sqrt(61197) y^2)/200 + (347 y^2)/200 + 2 λ (y^2 + sqrt(61197)/400) + λ^2

(y^2 + sqrt(61197)/400)^2 + 2 λ (y^2 + sqrt(61197)/400) + λ^2 = (y^2 + sqrt(61197)/400 + λ)^2:

(y^2 + sqrt(61197)/400 + λ)^2 = (43 y)/1000 + (sqrt(61197) y^2)/200 + (347 y^2)/200 + 2 λ (y^2 + sqrt(61197)/400) + λ^2

(43 y)/1000 + (sqrt(61197) y^2)/200 + (347 y^2)/200 + 2 λ (y^2 + sqrt(61197)/400) + λ^2 = (2 λ + 347/200 + sqrt(61197)/200) y^2 + (43 y)/1000 + (sqrt(61197) λ)/200 + λ^2:

(y^2 + sqrt(61197)/400 + λ)^2 = y^2 (2 λ + 347/200 + sqrt(61197)/200) + (43 y)/1000 + (sqrt(61197) λ)/200 + λ^2

Complete the square on the right hand side:

(y^2 + sqrt(61197)/400 + λ)^2 = (y sqrt(2 λ + 347/200 + sqrt(61197)/200) + 43/(2000 sqrt(2 λ + 347/200 + sqrt(61197)/200)))^2 + (4 (2 λ + 347/200 + sqrt(61197)/200) (λ^2 + (sqrt(61197) λ)/200) - 1849/1000000)/(4 (2 λ + 347/200 + sqrt(61197)/200))

To express the right hand side as a square, find a value of λ such that the last term is 0.

This means 4 (2 λ + 347/200 + sqrt(61197)/200) (λ^2 + (sqrt(61197) λ)/200) - 1849/1000000 = (8000000 λ^3 + 60000 sqrt(61197) λ^2 + 6940000 λ^2 + 34700 sqrt(61197) λ + 6119700 λ - 1849)/1000000 = 0.

Thus the root λ = (-3 sqrt(61197) - 347)/1200 + 1/60 (-i sqrt(3) + 1) ((3 i sqrt(622119) - 4673)/2)^(1/3) + (19 (i sqrt(3) + 1))/(3 2^(2/3) (3 i sqrt(622119) - 4673)^(1/3)) allows the right hand side to be expressed as a square.

(This value will be substituted later):

(y^2 + sqrt(61197)/400 + λ)^2 = (y sqrt(2 λ + 347/200 + sqrt(61197)/200) + 43/(2000 sqrt(2 λ + 347/200 + sqrt(61197)/200)))^2

Take the square root of both sides:

y^2 + sqrt(61197)/400 + λ = y sqrt(2 λ + 347/200 + sqrt(61197)/200) + 43/(2000 sqrt(2 λ + 347/200 + sqrt(61197)/200)) or y^2 + sqrt(61197)/400 + λ = -y sqrt(2 λ + 347/200 + sqrt(61197)/200) - 43/(2000 sqrt(2 λ + 347/200 + sqrt(61197)/200))

Solve using the quadratic formula:

y = 1/40 (sqrt(2) sqrt(400 λ + 347 + sqrt(61197)) + sqrt(2) sqrt(347 - sqrt(61197) - 400 λ + 172 sqrt(2) 1/sqrt(400 λ + 347 + sqrt(61197)))) or y = 1/40 (sqrt(2) sqrt(400 λ + 347 + sqrt(61197)) - sqrt(2) sqrt(347 - sqrt(61197) - 400 λ + 172 sqrt(2) 1/sqrt(400 λ + 347 + sqrt(61197)))) or y = 1/40 (sqrt(2) sqrt(347 - sqrt(61197) - 400 λ - 172 sqrt(2) 1/sqrt(400 λ + 347 + sqrt(61197))) - sqrt(2) sqrt(400 λ + 347 + sqrt(61197))) or y = 1/40 (-sqrt(2) sqrt(400 λ + 347 + sqrt(61197)) - sqrt(2) sqrt(347 - sqrt(61197) - 400 λ - 172 sqrt(2) 1/sqrt(400 λ + 347 + sqrt(61197)))) where λ = (-3 sqrt(61197) - 347)/1200 + 1/60 (-i sqrt(3) + 1) ((3 i sqrt(622119) - 4673)/2)^(1/3) + (19 (i sqrt(3) + 1))/(3 2^(2/3) (3 i sqrt(622119) - 4673)^(1/3))

Substitute λ = (-3 sqrt(61197) - 347)/1200 + 1/60 (-i sqrt(3) + 1) ((3 i sqrt(622119) - 4673)/2)^(1/3) + (19 (i sqrt(3) + 1))/(3 2^(2/3) (3 i sqrt(622119) - 4673)^(1/3)) and approximate:

y = -1.19665 or y = -0.527346 or y = 0.491952 or y = 1.23204

Substitute back for y = x - 7/20:

x - 7/20 = -1.19665 or y = -0.527346 or y = 0.491952 or y = 1.23204

Add 7/20 to both sides:

x = -0.846647 or y = -0.527346 or y = 0.491952 or y = 1.23204

Substitute back for y = x - 7/20:

x = -0.846647 or x - 7/20 = -0.527346 or y = 0.491952 or y = 1.23204

Add 7/20 to both sides:

x = -0.846647 or x = -0.177346 or y = 0.491952 or y = 1.23204

Substitute back for y = x - 7/20:

x = -0.846647 or x = -0.177346 or x - 7/20 = 0.491952 or y = 1.23204

Add 7/20 to both sides:

x = -0.846647 or x = -0.177346 or x = 0.841952 or y = 1.23204

Substitute back for y = x - 7/20:

x = -0.846647 or x = -0.177346 or x = 0.841952 or x - 7/20 = 1.23204

Add 7/20 to both sides:

Answer: x = -0.846647 or x = -0.177346 or x = 0.841952 or x = 1.58204

You might be interested in
The school store opened on the first day of school with 45 notebooks and 15 pencils. Within two days it sold all of these items.
malfutka [58]

The number of pencils sold on the first day  is 5 pencils.

The number of notebooks sold on the first day  is 10 notebooks.

The number of pencils sold on the second day 10 pencils.

The number of notebooks sold on the second day   35 notebooks.

<u>Step-by-step explanation:</u>

Given data,

  • The total number of notebooks in the store = 45 notebooks.
  • The total number of Pencils in the store = 15 pencils.
  • The number of days that all items were sold = 2 days.

Now, you have to calculate the no.of notebooks and no. of pencils sold each day.

<u>In the first day :</u>

The number of sale of notebooks and pencils are given by,

Twice as many notebooks were sold as pencils.

Let us take, the number of pencils sold on the first day  = x

And,  the number of notebooks sold on the first day  = 2x (Twice as pencils).

<u>In the second day :</u>

The number of sale of notebooks and pencils are given by,

For every 7 notebooks​ sold, 2 pencils were sold.

The number of pencils sold on the second day =   2y

The number of notebooks sold on the second day   = 7y

<u> The equation is framed for number of notebooks sold on each day :</u>

The number of notebooks sold ⇒ 2x + 7y = 45   -------(1)

<u> The equation  is framed for number of pencils sold on each day :</u>

The number of pencils sold: x + 2y = 15  ----------(2)

Solving the equations by multiplying eq(2) by 2 and subtract it from eq(1),

  2x + 7y = 45

-<u> (2x + 4y) = 30</u>

   <u>        3y = 15  </u>

⇒ y = 15/3

⇒ y = 5

The value of y is 5.

Substitute y=5 in eq (2),

⇒ x + 2(5) = 15

⇒ x + 10 = 15

⇒ x = 15 - 10

⇒ x = 5

The value of x is 5.

First day sale,

The number of pencils sold on the first day  = x ⇒ 5 pencils

The number of notebooks sold on the first day  = 2x ⇒ 10 notebooks

Second day sale,

The number of pencils sold on the second day =   2y ⇒ 10 pencils

The number of notebooks sold on the second day   = 7y ⇒ 35 notebooks.

8 0
2 years ago
Latoya made 2 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for both necklaces
denis23 [38]

Answer:

its 2.60 for each pendent

7 0
3 years ago
PLEASE HELPPP!!!!
dybincka [34]

Answer:

A. The point (0,0) shows that the cost is $0 for 0 kg of cashews.

C. The point (2,60) shows that it cost $60 for 2 kg of cashews.

B. The constant of proportionality for this graph is 30.

Step-by-step explanation:

D is wrong

7 0
3 years ago
A can of hairspray has a
lara [203]

Answer:

2inches=5.08cm

TSA of cylinder=2πr(r+h)

2×22/7×5.08(5.08+5.08)

6×5.08×10.16

324.42cm^3

7 0
2 years ago
Write the equation of the line that passes through the points
Vikki [24]

Answer:

y = 5x + 8

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍

8 0
3 years ago
Read 2 more answers
Other questions:
  • if Mr hansons motorcycle drives 432 miles on 6 gallons of gas how much gas will he need to drive 738​
    13·1 answer
  • Answer all for points
    8·1 answer
  • Solve 3(x + 2) &gt; x.
    6·1 answer
  • Type your answer in decimal form. Do not round.<br><br> 230 ounces = <br> how many cups
    5·2 answers
  • It took a plane 2 hours to go from Dallas to NY with the head wind and 1.5 hours to get back with the tail wind. If the speed of
    6·1 answer
  • 309×29 solve it by using regrouping and partial products
    8·1 answer
  • What is 10/18 equivalent to
    11·1 answer
  • 2. A bowling alley charges $3.00 to rent shoes and $1.50 per game bowled.
    11·1 answer
  • Courtney walks 5 laps around 1/4 mile track. how far does she walk?
    8·1 answer
  • Simplify this exponential expression:<br><br> (-49) 2/5
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!