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
QveST [7]
2 years ago
9

No links, provide full answer

Mathematics
1 answer:
AURORKA [14]2 years ago
4 0

The value of M is:

M = ± (1 / 2) · √[(k² + 5)² /(4 · k²) - 5] ∓ (1 / 2) · √[(k² / 100) · (25 / k² + 5)² - 5] + √3, for k ≠ 0.

<h3>What are the family of solutions behind an equation of the form p · q = k?</h3>

In this question we have a product of two <em>nonzero</em> <em>real</em> numbers equal to 5, whose mathematical form is:

p · q = 5, where p = 2 · x + √(4 · x² + 5) = k and q = 2 · y + √(4 · y² + 5) = 5 / k

Then, we proceed to find the solutions for x and y in terms of k:

2 · x + √(4 · x² + 5) = k

2 · x = k - √(4 · x² + 5)

4 · x² = k² - 2 · k · √(4 · x² + 5) + 4 · x² + 5

2 · k · √(4 · x² + 5) = k² + 5

4 · k² · (4 · x² + 5) = (k² + 5)²

4 · x² + 5 = (k² + 5)² /(4 · k²)

4 · x² = (k² + 5)² /(4 · k²) - 5

x = ± (1 / 2) · √[(k² + 5)² /(4 · k²) - 5], for k ≠ 0.

2 · y = 5 / k - √(4 · y² + 5)

4 · y² = 25 / k² - (10 / k) · √(4 · y² + 5) + 4 · y² + 5

(10 / k) · √(4 · y² + 5) = 25 / k² + 5

(100 / k²) · (4 · y² + 5) = (25 / k² + 5)²

4 · y² + 5 = (k² / 100) · (25 / k² + 5)²

4 · y² = (k² / 100) · (25 / k² + 5)² - 5

y = ∓ (1 / 2) · √[(k² / 100) · (25 / k² + 5)² - 5], for k ≠ 0.

Therefore, the value of M is:

M = ± (1 / 2) · √[(k² + 5)² /(4 · k²) - 5] ∓ (1 / 2) · √[(k² / 100) · (25 / k² + 5)² - 5] + √3, for k ≠ 0.

To learn more on radical equations: brainly.com/question/8606917

#SPJ1

You might be interested in
If 2k, 5k-1 and 6k+2 are the first 3 terms of an arithmetic sequence, find k and the 8th term​
Klio2033 [76]

Answer:

see explanation

Step-by-step explanation:

The common difference d of an arithmetic sequence is

d = a_{2} - a_{1} = a_{3} - a_{2}

Substitute in values and solve for k, that is

5k - 1 - 2k = 6k + 2 - (5k - 1)

3k - 1 = 6k + 2 - 5k + 1

3k - 1 = k + 3 ( subtract k from both sides )

2k - 1 = 3 ( add 1 to both sides )

2k = 4 ⇒ k = 2

--------------------------------------------------------

The n th term of an arithmetic sequence is

a_{n} = a_{1} + (n - 1)d

a_{1} = 2k = 2 × 2 = 4 and

d = 5k - 1 - 2k = 3k - 1 = (3 × 2) - 1 = 5

Hence

a_{8} = 4 + (7 × 5) = 4 + 35 = 39

4 0
3 years ago
How many ML are in 7L
sergeinik [125]
Hello,
7l=7×1000=7000 ml

Bye :-)
8 0
3 years ago
Read 2 more answers
Angles that share a vertex, but not a side are called
djyliett [7]
Adjacent angles-
  2 angles that share a common vertex, a common side and no common interior points.

The answer is ADJACENT ANGLE

7 0
3 years ago
Pls answer now<br> i gave you brainlest
slava [35]

1) A

2) B

3) C

4) C

5) D

5 0
2 years ago
HELP!! 4 people work an event where they make $156, They split the money evenly
Marina CMI [18]

Answer:

$34

-----------------------

6 0
3 years ago
Other questions:
  • A cone with volume 5000 m³ is dilated by a scale factor of 15.
    7·1 answer
  • How to solve -w+4(w+3)=-12
    14·2 answers
  • In a scale model of the Eiffel Tower, 10 centimeters represent 65 meters. If the real Eiffel Tower is approximately 325 meters t
    8·1 answer
  • A new car loses value at a constant rate. You purchase a new car for $21,500. After 3 years the value of the car was $14,120. Wh
    12·1 answer
  • How do you convert euros to Mexican pesos in part b ii
    10·1 answer
  • What is the solution set of fx x&gt;-5) u {xx&lt;5)?
    7·1 answer
  • What is the volume please this is for a quiz​
    13·1 answer
  • Match the sides based on their relationship to A<br><br> PLEASE ANSWER ASAP
    15·2 answers
  • If x = (7+4√3), then the value of x^2 + 1/x^2 is​
    9·1 answer
  • What is the value of the expression n(8n/10) when n =<br> 5?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!