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3 years ago

100 point giveaway!!

Mathematics

2 answers:

melomori [17]3 years ago

8 0

Answer:

tysm!! :D ack

Step-by-step explanation:

keeps saying server is swamped, wait for your answer to load. scream scream, guess i'm here typing gibberish then-

jeyben [28]3 years ago

3 0

Thank you!
Have a good day!

You might be interested in

If:

PSYCHO15rus [73]

Take some trinomial expansions to find some useful expressions and their values.

• 2nd degree expansion

$x + y + z = 7 \\\\ \implies (x+y+z)^2 = x^2+y^2+z^2+2(xy+xz+yz) = 7^2 \\\\ \implies xy+xz+yz = \dfrac{49-33}2 = 8$

• 3rd degree expansion

$x+y+z=7 \implies (x+y+z)^3 = 7^3 \\\\ \implies \\ 243 = x^3+y^3+z^3+3(x^2y+x^2z+xy^2+y^2z+xz^2+yz^2) + 6xyz \\\\ \implies \\ x^2y+x^2z+xy^2+y^2z+xz^2+yz^2 + 2xyz = \dfrac{343 - 145}3 = 66$

• 4th degree expansion

$x+y+z=7 \implies (x+y+z)^4 = 7^4 \\\\ \implies \\ 2401 = x^4+y^4+z^4+4(x^3y+x^3z+xy^3+y^3z+xz^3+yz^3) \\\\ ~~~~~~~~~~~~+ 6(x^2y^2+x^2z^2+y^2z^2) + 12(x^2yz+xy^2z+xyz^2) \\\\ \implies \\\\ x^4+y^4+z^4 = 2401 - 4(x^3y+x^3z+xy^3+y^3z+xz^3+yz^3) \\\\ ~~~~~~~~~~~~~~~~~~~~~~- 6(x^2y^2+x^2z^2+y^2z^2) - 12(x^2yz+xy^2z+xyz^2)$

Simplify:

$x^3y+x^3z+xy^3+y^3z+xz^3+yz^3 \\\\ ~~~~ = x^2 (xy+xz) + y^2 (xy+yz) + z^2 (xz + yz) \\\\ ~~~~ = x^2 (xy+xz+yz) + y^2 (xy+xz+yz) + z^2 (xy + xz + yz) - (x^2yz + xy^2z + xyz^2) \\\\ ~~~~ = (x^2+y^2+z^2) (xy+xz+yz) - xyz (x+y+z) \\\\ ~~~~ = 264 - 7xyz$

$x^2y^2+x^2z^2+y^2z^2 \\\\ ~~~~ = xy\cdot xy + xz \cdot xz + yz \cdot yz \\\\ ~~~~ = xy(xy+xz+yz) + xz(xy+xz+yz) + yz(xy+xz+yz) - 2(x^2yz+xy^2z+xyz^2) \\\\ ~~~~ = (xy+xz+yz)^2 - 2xyz(x+y+z) \\\\ ~~~~ = 64 - 14xyz$

$x^2yz+xy^2z+xyz^2 = xyz (x + y + z) = 7xyz$

Then the equation we got from the 4th degree expansion reduces to

$x^4+y^4+z^4 = 2401 - 4(264-7xyz) - 6(64-14xyz) - 12(7xyz) \\\\ ~~~~~~~~~~~~~~~~~= 961 + 28xyz$

and all we need now is the value of $xyz$ .

In the 3rd degree expansion, we have

$x^2y+x^2z+xy^2+y^2z+xz^2+yz^2 \\\\ ~~~~ = x(xy + xz) + y(xy + yz) + z(xz + yz) \\\\ ~~~~ = x(xy+xz+yz) + y(xy+xz+yz) + z(xy+xz+yz) - 3xyz \\\\ ~~~~ = (x+y+z)(xy+xz+yz) - 3xyz \\\\ ~~~~ = 56 - 3xyz \\\\ \implies (56 - 3xyz) + 2xyz = 66 \\\\ \implies xyz = -10$

So, we end up with

$x^4+y^4+z^4 = 961 - 280 = \boxed{681}$

4 0

1 year ago

Previous balance = $179.32 Annual rate = 16% Finance charge = $ New purchases = $117.42 Payments/credits = $85.00 New balance =

sdas [7]

First we should calculate the amount of the finance charge
Finance charge=179.32×(0.16÷12months)
=2.39

New balance= previous balance-payments/credit+finance change+New purchases

New balance=179.32−85+2.39+117.42
=214.13

Good luck!

8 0

3 years ago

Read 2 more answers

Solve the equation and this is an assignment btw

lilavasa [31]

Answer:

z=6 and z=-6

Step-by-step explanation:

$7z^2=252$

Divide both sides by 7

$\frac{7z^2}{7} =\frac{252}{7} \\z^2=36$

Find the square root

z=±√36

z=±6

Therefore, z=6 and z=-6.

I hope this helps!

4 0

3 years ago

5. Michael and his family went on a four-day hiking trip. On the first day, they walked 32.1

oee [108]

Answer:its about the exact answer the answer is 78.76

Step-by-step explanation:

I chose exact answer becase the answer is 78.76

4 0

3 years ago

A bicycle costs $240 and loses 35 of its value each year. What is the value of the bike after 3 years?

Svetlanka [38]

Answer:

135 In the 3rd year

Step-by-step explanation:

240-35= 205

205-35=170

170-35=135 (Or just use a calculator)

3 0

3 years ago