MATHalino

Problem
Two flat belt pulleys have a center to center distance of 137 cm, and diameters of 72 cm and 36 cm, respectively. Neglecting the sagging of belt...

1. compute the length of belt if both pulleys will rotate in the same direction.
   

   A.   464.5 cm	C.   446.0 cm
   B.   553.1 cm	D.   535.4 cm

2. compute the length of belt if the belt will be cross-connected to make the pulleys rotate in opposite directions.
   

   A.   654.1 cm	C.   564.2 cm
   B.   465.2 cm	D.   645.1 cm

3. determine the distance of the point from the center of the bigger pulley where the belt will cross when cross-connected.
   

   A.   91.3 cm	C.   89.4 cm
   B.   100.4 cm	D.   98.7cm

Problem 7
Determine the value of $x$ from $\sqrt[4]{3^{x^2}\sqrt{3^{x - 1}}} = \sqrt[8]{9^{x + 1}}$
 

Solve for the value of x from each of the following equations:

3. 9^x - 6(9^-x) - 1 = 0
4. 2^{x + 1} · 3^x = 5^{x + 3}

Solve for x from the following:

1. $\log_6 (x - 2) + \log_6 (x + 3) = 1$
    
2. $x^{\log x} = 10\,000$

Problem
Solve for $x$ and $y$ from the given system of equations.
$\dfrac{3}{x^2} - \dfrac{4}{y^2} = 2$   ←   Equation (1)

$\dfrac{5}{x^2} - \dfrac{3}{y^2} = \dfrac{17}{4}$   ←   Equation (2)
 

Problem
Solve for $x$ and $y$ from the given system of equations.
$x^2y + y = 17$   ←   Equation (1)

$x^4y^2 + y^2 = 257$   ←   Equation (2)
 

Problem
Solve for x and y from the given system of equations.
$x + 2y = 6$   ←   Equation (1)

$\sqrt{x} + \sqrt{y} = 3$   ←   Equation (2)
 

Solve for $x$ from the following equations:

5. $\left( \dfrac{x^2 - 15}{x} \right)^2 - 16\left( \dfrac{15 - x^2}{x} \right) + 28 = 0$
    
6. $\dfrac{x}{\sqrt{x} + \sqrt{9 - x}} + \dfrac{x}{\sqrt{x} - \sqrt{9 - x}} = \dfrac{24}{\sqrt{x}}$

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