Given: Circle M with inscribed Angle K J L and congruent radii JM and ML Prove: mAngle M J L = One-half (measure of arc K L) Cir
cle M is shown. Line segment J K is a diameter. Line segment J L is a secant. A line is drawn from point L to point M. What is the missing reason in step 8?
2 answers:
Answer:
We need to demontrate
As you can see in the figure below, angle MJL is an inscribed angle for Circle M, that means we can use the inscribed angle theorem to demonstrate the proposition above.
<h3>Therorem.</h3><em>The angle formed by two intersecting chords with vertex on the circumference is equal to one-half of the intercepted arc.</em>
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Notice that the theorem says a chord. However, a diameter is a chord by definition, because a chord is a segment that unites to points of the circumference, and a diameter does that too.
Therefore, based on the inscribed angle arc theorem, we have
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Answer:
Collin: about $401 thousand
Cameron: about $689 thousand
Step-by-step explanation:
A situation in which doubling time is constant is a situation that can be modeled by an exponential function. Here, you're given an exponential function, though you're not told what the variables mean. That function is ...
In this context, P0 is the initial salary, t is years, and d is the doubling time in years. The function gives P(t), the salary after t years. In this problem, the value of t we're concerned with is the difference between age 22 and age 65, that is, 43 years.
In Collin's case, we have ...
P0 = 55,000, t = 43, d = 15
so his salary at retirement is ...
P(43) = $55,000(2^(43/15)) ≈ $401,157.89
In Cameron's case, we have ...
P0 = 35,000, t = 43, d = 10
so his salary at retirement is ...
P(43) = $35,000(2^(43/10)) ≈ $689,440.87
___
Sometimes we like to see these equations in a form with "e" as the base of the exponential. That form is ...
If we compare this equation to the one above, we find the growth factors to be ...
2^(t/d) = e^(kt)
Factoring out the exponent of t, we find ...
(2^(1/d))^t = (e^k)^t
That is, ...
2^(1/d) = e^k . . . . . match the bases of the exponential terms
(1/d)ln(2) = k . . . . . take the natural log of both sides
So, in Collin's case, the equation for his salary growth is
k = ln(2)/15 ≈ 0.046210
P(t) = 55,000e^(0.046210t)
and in Cameron's case, ...
k = ln(2)/10 ≈ 0.069315
P(t) = 35,000e^(0.069315t)