# Tutor profile: Mark Jude A.

## Questions

### Subject: Trigonometry

What is the sin θ if cos θ = 1/4?

In order to solve this, we make use of one of the Pythagorean identities. sin^2 (θ) + cos^2 (θ) = 1. Since cos θ is 1/4, cos^2 (θ) = 1/16. sin^2 (θ) would therefore be 1 - 1/16 or 15/16. Finally, sin θ = sqrt(15)/ 4.

### Subject: Civil Engineering

A hollow steel tube with an inside diameter of 100 mm must carry a tensile load of 400 kN. Determine the outside diameter of the tube if the stress is limited to 120 MN/m2.

The tensile stress is equal to the tensile force divided by the area unto which the force is applied. In order to solve for the outside diameter of the hollow tube, we formulate σ = P/A where σ = 120 MPa, P = 400 kN and A = π/4 ( D^2 - 0.1^2), where D is the outside diameter. Solving for D, outside diameter = 0.11935 m or 119.35 mm.

### Subject: Algebra

Solve for x: (3x+2-5(6x+6))/(3x+2) = 7

First, inspect operations and operative symbols on both side of the equation. Notice that the LHS is divided by 3x+2. To put the equation in simpler form, transpose 3x+2 to the right hand side by multiplying 3x+2 on both sides of the equation. 3x+2-5(6x+6)=7(3x+2). Perform operations.3x+2-30x-30=21x+14. Segregate the terms with x to to the left hand side while the rest on the right hand side. 3x-30x-21x=14-2+30. Perform operations. -48x = 42. x = -7/8.

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