Vectorcardiography Suppose the voltage vector of a healthy heart is given by [0.3, 20.2]. Cardiac abnormalities result in change
s to this vector. Each abnormality can be viewed as a change of a healthy heart voltage vector into a pathological voltage vector through matrix multiplication. For each of the following heart pathologies, find a matrix that produces the pathological voltage vector from a healthy voltage vector. (a) Left anterior hemiblock: h =[0.3, 0.2], (b) Left posterior hemiblock: h =[20.3, 20.2]
(c) Apical ischemia: h =[20.3, 0.2]
(d) Chronic obstructive pulmonary disease:h =[0.1, 20.0667]
(c) Apical ischemia: h =[20.3, 0.2]
(d) Chronic obstructive pulmonary disease:h =[0.1, 20.0667]
1 answer:
You might be interested in
You can use the definition of logarithm and the fact that a positive number raised to any power will always stay bigger than 0.
The domain of the given function is {x | x > 1 and a real number }
The range of the given function is (set of real numbers)
If a is raised to power b is resulted as c, then we can rewrite it that b equals to the logarithm of c with base a.
Or, symbolically:
Since c was the result of a raised to power b, thus, if a was a positive number, then a raised to any power won't go less or equal to zero, thus making c > 0
<h3>How to use this definition to find the domain and range of given function?</h3>Since log(x-1) is with base 10 (when base of log isn't specified, it is assumed to be with base 10) (when log is written ln, it is log with base e =2.71828.... ) thus, we have a = 10 > 0 thus the input x-1 > 0 too.
Or we have:
x > 1 as the restriction.
Thus domain of the given function is {x | x > 1 and a real number }
Now from domain, we have:
(log(x-1) > -infinity since log(0) on right side have arbitrary negatively large value which is denoted by -infinity)
Thus, range of given function is whole real number set (since all finite real numbers are bigger than negative infinity)
Thus, the domain of the given function is {x | x > 1 and a real number }
The range of the given function is (set of real numbers
Learn more about domain and range here: