Since x - 3 < 0 for -2 < x < 3, |x-3| = -(x-3)
Since x + 2 > 0 for -2 < x < 3, |x+2| = x+2
Since x - 5 < 0 for -2 < x < 3, |x-5| = -(x-5).
So y = -(x-3) + (x+2) -(-(x-5)) = 3 - x + x + 2 + x - 5 = x.
y = x, if -2 < x < 3.
Step-by-step explanation:
If it helps, write as a product of fractions, grouped by variable.
Now reduce using exponent rules.
The trigonometric expression tan² x + 1 = sec² x is proved by using the fundamental trigonometric formula and the definition of tangent and secant.
<h3>How to prove a derivate trigonometric formula</h3>
In this problem we must prove the existence of a trigonometric formula by means of definitions of trigonometric functions and the fundamental trigonometric formula.
Step 1 - Introduce the fundamental trigonometric formula and the definitions of tangent and secant:
sin² x + cos² x = 1, tan x = sin x / cos x, sec x = 1 / cos x
Step 2 - Divide each side of the formula by cos² x:
sin² x / cos² x + cos² x / cos² x = 1 / cos² x
(sin x / cos x)² + 1 = (1 / cos x)²
Step 3 - Use the definition of the two trigonometric functions:
tan² x + 1 = sec² x
To learn more on trigonometric functions: brainly.com/question/14746686
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To determine the total time it needs for the two painters to completely paint the whole wall space, we need to relate the total area of the wall to be painted and the time they need. So, base from the problem, the relation would just be a linear function. We do as follows:
let A = total area of the wall space
t = total time they both need
Painter 1 = <span>190 square feet per hour
Painter 2 = </span><span>130 square feet per hour
total area = 1200 ft^2 (3) = 3600 ft^2
The function would be:
A = 190t + 130t
3600 = 190t + 130t
3600 = 320t
t = 11.25 hrs
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