If sin(x) = 12, what is cos(x) and tan(x)?

To find cos(x) and tan(x) given that sin(x) = 12, we first need to recognize an important fact about the sine function. The value of sine, sin(x), must always fall within the range of -1 to 1 for real numbers. Therefore, sin(x) = 12 is not possible in the context of real angles. Since sin(x) […]

What are metric units? Explain with examples.

Metric units are a standardized system of measurement used around the world, known as the metric system. It is based on powers of ten, making it easier to convert between units. The metric system includes units for measuring length, mass, volume, and temperature, among others. For example: Length: The meter (m) is the base unit […]

What is the recursive rule for the geometric sequence 10, 80, 640, 5120?

A recursive rule for a geometric sequence is used to express each term based on the previous term. In the case of the sequence 10, 80, 640, 5120, we start by identifying the common ratio between the terms. To find the common ratio, we divide the second term by the first term: Common ratio = […]

How many ways can 7 books be arranged on a shelf 5 at a time?

To determine how many ways 7 books can be arranged on a shelf 5 at a time, we need to calculate the number of permutations of 7 books taken 5 at a time. The formula for permutations is given by: P(n, r) = n! / (n – r)! Where: n = total number of items […]

How do you simplify the expression 8 9 x 16 7?

To simplify the expression 8 9 x 16 7, we first need to clarify the operations involved. Assuming that this means we are performing a multiplication (as indicated by the ‘x’), the expression can be rewritten as: 8 * 9 * 16 * 7 Next, we proceed with the multiplication step-by-step. Let’s break this down: […]

If A and B are Independent Events, Show That A and B Are Also Independent

To show that events A and B are independent, we need to demonstrate that the occurrence of one does not affect the occurrence of the other. By definition, two events A and B are considered independent if: P(A and B) = P(A) * P(B) Now, let’s understand why the independence of A and B implies […]

Find the value of t in the equation t + 5 = 3t + 1

To find the value of t in the equation t + 5 = 3t + 1, we first need to rearrange the equation to isolate t on one side. Step 1: Start by subtracting t from both sides of the equation: t + 5 – t = 3t + 1 – t This simplifies to: […]