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fgiga [73]
1 year ago
11

Factorize that x^4+4y^4​

Mathematics
1 answer:
ipn [44]1 year ago
4 0

Answer:

  • (x² + 2y² + 2xy)(x² + 2y² - 2xy)

Step-by-step explanation:

<h3>Given binomial:</h3>

x⁴ + 4y⁴

In order to factorize it, follow the steps:

<h3>Complete the square:</h3>

  • x⁴ + 4y⁴ =
  • (x²)² + 2*(x²)*(2y²) + (2y²)² - 2*(x²)*(2y²) =
  • (x² + 2y²)² - (2xy)² =
  • (x² + 2y² + 2xy)(x² + 2y² - 2xy)

Used identities:

  • (a + b)² = a² + 2ab + b²
  • a² - b² = (a + b)(a - b)
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Ax-bx+y=z solve for x​
Eddi Din [679]

ax - bx + y = z \\ \Leftrightarrow x(a - b) =  - y + z \\ \Leftrightarrow x =  -  \frac{y - z}{a - b}

3 0
3 years ago
Joey is running an experiment with a mass on a spring. Joey models the height of the mass above the table he is working on using
galben [10]

Answer: 1.8 s

Step-by-step explanation:

Given

The height of the spring mass system above the table is given by

h(t)=6.85\cos (3.42t)+9

The mass is performing S.H.M with frequency \omega =3.42

and \omega T=2\pi

\therefore T=\dfrac{2\pi }{\omega}

time when mass returns to its original position

T=\dfrac{2\pi }{3.42}\\\\T=1.8\ s

5 0
2 years ago
Valentina has a tray where she keeps all of her important papers. The tray is in the shape of a rectangular prism with no top.
yulyashka [42]
The answer is 300 as 2.5x10x12=300
4 0
2 years ago
Read 2 more answers
If x2 + y2 = 14 and xy = 5, find the value of (1/2 x + 1/2 y)2.
aleksley [76]

Answer:

(½x+½y)²=6

Step-by-step explanation:

x^2 + y^2 = 14, xy=5

(A+B)^2=A^2 +2AB+B^2... (*)

(1/2x+1/2y)^2 =(*)

(1/2x)^2 +2(1/2x)(1/2y)+(1/2y)^2 =

1/4x^2 +1/2xy+1/4y^2=

1/4(x^2 +y^2) +1/2(xy)=

1/4*14+1/2*5=

14/4+5/2=

14/4+10/4=

24/4=6

let me know if I'm wrong.

5 0
2 years ago
Read 2 more answers
An elementary ntimesn scaling matrix with k on the diagonal is the same as the ntimesn identity matrix with _______ exactly one
Dafna11 [192]

Answer:

exactly one, 0's, triangular matrix, product and 1.

Step-by-step explanation:

So, let us first fill in the gap in the question below. Note that the capitalized words are the words to be filled in the gap and the ones in brackets too.

"An elementary ntimesn scaling matrix with k on the diagonal is the same as the ntimesn identity matrix with EXACTLY ONE of the (0's) replaced with some number k. This means it is TRIANGULAR MATRIX, and so its determinant is the PRODUCT of its diagonal entries.​ Thus, the determinant of an elementary scaling matrix with k on the diagonal is (1).

Here, one of the zeros in the identity matrix will surely be replaced by one. That is to say, the determinants = 1 × 1 × 1 => 1. Thus, it is a a triangular matrix.

3 0
3 years ago
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