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Setler [38]
3 years ago
7

What is the solution to the system of equations?

Mathematics
1 answer:
Dovator [93]3 years ago
4 0

Answer:

<h2>(-10, 2, 6)</h2>

Step-by-step explanation:

\left\{\begin{array}{ccc}x+3y+2z=8&(1)\\3x+y+3z=-10&(2)\\-2x-2y-z=10&(3)\end{array}\right\qquad\text{subtract both sides of the equations (1) from (2)}\\\\\underline{-\left\{\begin{array}{ccc}3x+y+3z=-10\\x+3y+2z=8\end{array}\right }\\.\qquad2x-2y+z=-18\qquad(4)\qquad\text{add both sides of the equations (3) and (4)}\\\\\underline{+\left\{\begin{array}{ccc}-2x-2y-z=10\\2x-2y+z=-18\end{array}\right}\\.\qquad-4y=-8\qquad\text{divide both sides by (-4)}\\.\qquad\qquad y=2\qquad\text{put the value of y to (1) and (3)}

\left\{\begin{array}{ccc}x+3(2)+2z=8\\-2x-2(2)-z=10\end{array}\right\\\left\{\begin{array}{ccc}x+6+2z=8&\text{subtract 6 from both sides}\\-2x-4-z=10&\text{add 4 to both sides}\end{array}\right\\\left\{\begin{array}{ccc}x+2z=2&\text{multiply both sides by 2}\\-2x-z=14\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2x+4z=4\\-2x-z=14\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad3z=18\qquad\text{divide both sides by 3}\\.\qquad\qquad z=6\qquad\text{put the value of z to the first equation}

x+2(6)=2\\x+12=2\qquad\text{subtract 10 from both sides}\\x=-10

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3 years ago
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There are four children in the Velez family. Alano is 1 and 1/2 times as tall as Lupe, and 6 inches taller than Olivia. Nelia is
balu736 [363]

Step-by-step explanation:

If you think about Nelia's age you can see that Olivia is 54 inches

Alano is 6 inches tall than Olivia which equals 60.

Then you would do 60 x 1 then x 30 to get Alano's height

4 0
3 years ago
The sum of three numbers is 113 . The second number is 3 times the third. The first number is 7 less than the third . What are t
OLga [1]
Number 1 = 17
number 2 = 72
number 3 = 24


work:

the three numbers are symbolized as x, y, and z

x + y + z = 113

number 2 (y) is 3 times the third number (z) so 

y = 3z

so x + 3z + z = 113

the first number (x) is 7 less than than the third number (z) so

x = z - 7

so z -7 + 3z + z = 113

5z - 7 = 113
5z = 120

z = 24

x = 17
y = 72

Hope this helped :)
8 0
3 years ago
Find the nth taylor polynomial for the function, centered at c. f(x) = ln(x), n = 4, c = 5
masha68 [24]

The nth taylor polynomial for the given function is

P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴

Given:

f(x) = ln(x)

n = 4

c = 3

nth Taylor polynomial for the function, centered at c

The Taylor series for f(x) = ln x centered at 5 is:

P_{n}(x)=f(c)+\frac{f^{'} (c)}{1!}(x-c)+  \frac{f^{''} (c)}{2!}(x-c)^{2} +\frac{f^{'''} (c)}{3!}(x-c)^{3}+.....+\frac{f^{n} (c)}{n!}(x-c)^{n}

Since, c = 5 so,

P_{4}(x)=f(5)+\frac{f^{'} (5)}{1!}(x-5)+  \frac{f^{''} (5)}{2!}(x-5)^{2} +\frac{f^{'''} (5)}{3!}(x-5)^{3}+.....+\frac{f^{n} (5)}{n!}(x-5)^{n}

Now

f(5) = ln 5

f'(x) = 1/x ⇒ f'(5) = 1/5

f''(x) = -1/x² ⇒ f''(5) = -1/5² = -1/25

f'''(x) = 2/x³  ⇒ f'''(5) = 2/5³ = 2/125

f''''(x) = -6/x⁴ ⇒ f (5) = -6/5⁴ = -6/625

So Taylor polynomial for n = 4 is:

P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴

Hence,

The nth taylor polynomial for the given function is

P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴

Find out more information about nth taylor polynomial here

brainly.com/question/28196765

#SPJ4

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2 years ago
PLEASE HELP ME!! due soon
lisabon 2012 [21]
Re post the picture
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3 years ago
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