Solve.If the three lengths of the sides of a triangle are known, Heron's formula can be used to find its area. If a, b, and c are the three lengths of the sides, Heron's formula for area is: A = 
where s is half the perimeter of the triangle, or s = 
(a + b + c).Use this formula to find the area of the triangle if a = 6 cm, b = 8 cm and c = 10 cm. 
A. 24
sq. cm
B. 48
sq. cm
C. 24 sq. cm
D. 4
sq. cm
Answer: C
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Find the center of mass of a thin plate of constant density covering the given region.The region bounded by the parabola y = 81 - x2 and the x-axis
A. 
= 0, 
= 
B. 
= 0, 
= 
C. 
= 
, 
= 0
D. 
= 0, 
= 
Find the linear approximating polynomial for the function centered at a.f(x) = sin x, a = 0
A. p1(x) = -x B. p1(x) = 0 C. p1(x) = 2x + 1 D. p1(x) = x
Secret messages can be encoded by using a code and an encoding matrix. If we have the code:
and an encoding matrix E, we can encode a message by taking every two letters of the message, converting them to their corresponding numbers, creating a 2 × 1 matrix, and then multiplying each two numbers by E. The message may be unscrambled with a decoding matrix which is the inverse of the coding matrix, E-1. Determine if the given pair of encoding matrices are inverses of each
other.
and 
What will be an ideal response?
Write the expression as a logarithm of a single expression. Assume that variables represent positive numbers.(logax - logay) + 2logaz
A. loga
B. loga
C. loga
D. logaxz2y