X=-2 y=-1 these are x and y values
Answer: k = 4
Step-by-step explanation: greatest k, which 5^k is a factor of
the product of the integers from 1 through 24
From 1.2.3...24, if we factor all these numbers to prime integers, we can find 5 in: 5, 10, 15 and 20.
5; 2.5; 3.5; 4.5, so 5^4 is a factor of this product.
This way, k = 4
We know that the area of a rectangle can be written as: length x width
so:
l x (1/5) = 9/20
9/20 x 5/1 = 45/20, which can be reduced to 9/4
So the length is 9/4 miles
Step-by-step explanation:
1. All the trigonometric values can be found using the unit circle. See attached table.
2. Graph:
desmos.com/calculator/10n7yrm3tm
3. All trig functions are periodic functions. The period of secant and cosecant is 2π. The period of cotangent is π.
4. Using the table from step 1 and the graph from step 2, secant has a domain of x ≠ pi/2, 3pi/2 and a range of x ≤ -1, x ≥ 1. Cotangent has a domain of x ≠ 0, pi, 2pi and a range of -∞ < x < ∞.
5. Graph:
desmos.com/calculator/tldiqt7qra
Cosecant has the same graph as secant shifted π/2 to the right. So they have different domains, but the same range.