Question

1. what is the area (in units²) of a rectangle in the (x,y) - coordinate?

a) 12 units²
b) 16 units²
c) 24 units²
d) 64 units²

1. what is the missing term x in the geometric sequence below?

-1/3, 2, x, 72,...
a) -27
b) -12
c) 6
d) 12

1. in a right triangle, if cscθ = √2, what is the measure of θ?

a) 30°
b) 45°
c) 60°
d) 90°

Explanation:

Question 92:

Since no dimensions of the rectangle are given in the problem - statement, we assume this is a multiple - choice elimination problem. We know that the area of a rectangle is \(A = l\times w\) (length times width). The area of a rectangle must be a non - negative real number. But without further information, we can't calculate it directly. However, we can analyze the options.

Question 93:

For a geometric sequence, the common ratio \(r\) is constant. The formula for the \(n\)th term of a geometric sequence is \(a_n=a_1r^{n - 1}\), and also \(r=\frac{a_{n+1}}{a_n}\). Given \(a_1 =-\frac{1}{3}\), \(a_2 = 2\), then \(r=\frac{a_2}{a_1}=\frac{2}{-\frac{1}{3}}=- 6\). To find \(x=a_3\), we use the formula \(a_3=a_2r\). Substitute \(a_2 = 2\) and \(r=-6\) into the formula, we get \(a_3=2\times(-6)=-12\).

Question 94:

Recall that \(\csc\theta=\frac{1}{\sin\theta}\). Given \(\csc\theta=\sqrt{2}\), then \(\sin\theta=\frac{1}{\csc\theta}=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}\). In the range of \(0^{\circ}<\theta<90^{\circ}\) (for a right - triangle), when \(\sin\theta=\frac{\sqrt{2}}{2}\), \(\theta = 45^{\circ}\).

Answer:

1. No answer can be determined from the given information.
2. B. - 12
3. B. \(45^{\circ}\)