Determine the value of $x$ from the following equations:

3. $\sqrt{(4 - x^2)^3} + 3x^2\sqrt{4 - x^2} = 0$
    
4. $\dfrac{1}{3x - 2} - \dfrac{8}{\sqrt{3x - 2}} = 9$
    

Solve for $x$ from the following equations

1. $\sqrt{3 - x} + \sqrt{4 - 2x} = \sqrt{3 - 3x}$
    
2. $\sqrt{\dfrac{2x + 4}{x - 5}} + 8\sqrt{\dfrac{x - 5}{2x + 4}} = 6$

Problem 3
A man bought a cellphone and laptop for P50,000.00, paying three times as much for the laptop as for the cellphone. How much did each cost?
 

Problem 4
Two boys, counting their money, found that together they had P372, and that Rody had five times as much as Mar. How much had each?
 

Problem 1
The sum of two numbers is 120. If the greater number is four times the less, what are the numbers?
 

Problem 2
The greater of two numbers is twice the less, and the sum of the numbers is 96. What are the numbers?
 

Problem
What is the equation of the curve passing through the point (3, -2) and having a slope at any point (x, y) equal to (x² + y²) / (y³ - 2xy)?
 

Problem
Point P is inside the isosceles right triangle ABC. AP is 15 cm, BP is 9 cm and CP is 12 cm as shown. Determine the area of the triangle ABC.
 

Problem 604
Determine the magnitude of the resultant, its pointing, and its direction cosines for the following system of non-coplanar concurrent forces. 200 lb (4, 5, –3); 400 lb (–6, 4, –5); 300 lb, (4, –2, –3).
 

Problem 603
Determine the magnitude of the resultant, its pointing, and its direction cosines for the following system of non-coplanar concurrent forces. 100 lb (2, 3, 4); 300 lb (–3, –4, 5); 200 lb, (0, 0, 4).
 

Problem 602
Determine the magnitude of the resultant, its pointing and its direction cosines for the following system of non-coplanar, concurrent forces. 300 lb (+3, -4, +6); 400 lb (-2, +4, -5); 200 lb (-4, +5, -3).
 

Problem 864
An 18-ft beam, simply supported at 4 ft from each end, carries a uniformly distributed load of 200 lb/ft over its entire length. Compute the value of EIδ at the middle and at the ends.