HELP Solve the formula E = /(R + r) for r.
1 answer:
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By some properties of logarithms, rewrite the equation as
so that
(<em>a</em> - 2<em>b</em>)² = <em>ab</em>
Expand the left side:
<em>a</em> ² - 4<em>ab</em> + 4<em>b</em> ² = <em>ab</em>
Rearrange terms to get a quadratic equation in <em>a</em>/<em>b</em> :
<em>a</em> ² - 5<em>ab</em> + 4<em>b</em> ² = 0
<em>b</em> must be greater than 0, otherwise log(<em>b</em>) doesn't exist, and the same goes for <em>a</em>. So we can divide by <em>b</em> ² to get
<em>a</em> ²/<em>b</em> ² - 5<em>a</em>/<em>b</em> + 4 = 0
Factorize and solve for <em>a</em>/<em>b</em> :
(<em>a</em>/<em>b</em> - 4) (<em>a</em>/<em>b</em> - 1) = 0
==> <em>a</em>/<em>b</em> = 4 or <em>a</em>/<em>b</em> = 1
However, if <em>a</em>/<em>b</em> = 1, then <em>a</em> = <em>b</em> makes <em>a</em> - 2<em>b</em> = -<em>b</em>. But we must have <em>b</em> > 0, so we omit the second solution and end up with
<em>a</em>/<em>b</em> = 4
Graphs can be used to represent functions.
See attachment for the graphs of: <em>y =x - 2, y = 0.4x - 2, y =-x - 2</em>
The function is given as:
When k = 1,
We have:
----- substitution property of equations
So, the equation is: when k = 1
When k = 0.4,
We have:
----- substitution property of equations
So, the equation is: when k = 0.4
When k = -1,
We have:
----- substitution property of equations
So, the equation is: when k = -1
See attachment for the graphs of: ,
and
Read more about graphs and functions at:
Answer:
The angle of depression of an object becomes the angle between the horizontal and the line of sight from the object to the observer's eye. The angle of depression will be below the observer's eyes.
Step-by-step explanation:
