Response:
Detailed explanation:
The timing data for each lap will form an arithmetic progression (AP) with a first term of 25 s and a common difference of 1.6 s.
a )
first term a = 25
common difference d = 1.6.
The 10th term of the sequence can be found using the formula
a₁₀ = 25 + (10-1) x 1.6
= 25 + 1.6 x 9
= 39.4 s
b )
Let n be the final lap
a(n) = a + (n-1) x d
55.4 = 25 + (n-1) x 1.6
n - 1 = 19
n = 20.
c )
The total for all terms in the AP
=(first term + last term) x number of terms / 2
= (25 + 55.4) x 20 / 2
= 804 s.
= 804 / 60 min
= 13.4 min.
Begin by subtracting 8x from both sides of the inequality.
To analyze the situation step-by-step, observe that the angle is situated in the fourth quadrant (between 3π/2 and 2π). It is essential to remember that in this quadrant, both tangent and cosine functions yield positive values while the sine function is negative. This is critical given that the tangent of an angle is defined as the sine function of that angle divided by its cosine. Since the tangent of the specified angle is -1, we recognize that the corresponding angle where sine and cosine are equal must exist in the fourth quadrant, leading us to identify the specific angle that gives us that ratio.
