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Rafeed R.

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Trigonometry

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Question:

The lengths of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively. The size of angle C is 59o. Find the length of side AC.

Rafeed R.

Answer:

Let x be the length of side AC. Use the cosine law 122 = 82 + x2 - 2*8*x*cos(59o) Solve the quadratic equation for x: x = 14.0 and x = -5.7 x cannot be negative and therefore the solution is x = 14.0 (rounded to one decimal place).

Geometry

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Question:

ABCD is a parallelogram such that AB is parallel to DC and DA parallel to CB. The length of side AB is 20 cm. E is a point between A and B such that the length of AE is 3 cm. F is a point between points D and C. Find the length of DF such that the segment EF divide the parallelogram in two regions with equal areas.

Rafeed R.

Answer:

Let A1 be the area of the trapezoid AEFD. Hence A1 = (1/2) h (AE + DF) = (1/2) h (3 + DF) , h is the height of the parallelogram. Now let A2 be the area of the trapezoid EBCF. Hence A2 = (1/2) h (EB + FC) We also have EB = 20 - AE = 17 , FC = 20 - DF We now substitute EB and FC in A2 = (1/2) h (EB + FC) A2 = (1/2) h (17 + 20 - DF) = (1/2) h (37 - DF) For EF to divide the parallelogram into two regions of equal ares, we need to have area A1 and area A2 equal (1/2) h (3 + DF) = (1/2) h (37 - DF) Multiply both sides by 2 and divide thm by h to simplify to 3 + DF = 37 - DF Solve for DF 2DF = 37 - 3 2DF = 34 DF = 17 cm

Algebra

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Question:

solve the equation 5(-3x - 2) - (x - 3) = -4(4x + 5) + 13

Rafeed R.

Answer:

Given the equation 5(-3x - 2) - (x - 3) = -4(4x + 5) + 13 Multiply factors. -15x - 10 - x + 3 = -16x - 20 +13 -16x - 7 = -16x - 7 Add 16x + 7 to both sides and write the equation as follows 0 = 0 The above statement is true for all values of x and therefore all real numbers are solutions to the given equation.

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