The sum of a polygon's angles are 540.
When you add all the angles together here, you get 456.
Now subtract 456 from 540.
540 - 456 = 84
(a) The radius of the circle is the distance the wave travels since it first formed, so if <em>g(t)</em> is the radius of the circle at time <em>t</em>, then it changes at a rate according to
d<em>g</em>/d<em>t</em> = 60 cm/s
Integrate both sides with respect to <em>t</em> to solve for <em>g</em> :
∫ d<em>g</em>/d<em>t</em> d<em>t</em> = ∫ (60 cm/s) d<em>t</em>
<em>g(t)</em> = (60 cm/s) <em>t</em> + <em>C</em>
but <em>C</em> = 0 since the radius at <em>t</em> = 0 must be 0.
<em>g(t)</em> = (60 cm/s) <em>t</em>
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(b) The area of any circle with radius <em>r</em> is <em>πr</em> ². So
<em>f(r)</em> = <em>πr</em> ²
(c) The composition of <em>f</em> with <em>g</em> represents the area of water encircled by the wave at time <em>t</em> :
<em>(f</em> o <em>g)(t)</em> = <em>f(g(t))</em> = <em>π</em> <em>g(t) </em>²
<span>The arithmetic sequences have a constant difference between two terms. This sequence does not match this criterion, look: 12-8 = 4; 8-5=3; 5-3=2. Then it is not arithmetic. Let's examine whether it is geometric. Geometric sequences have a constant ration between adjacent terms: given that 3/2 is different to 5/3, and both are different to 8/5 and so on, this sequence does not either match this requirement. Then the sequence is not arithmetic or geometric.</span>
Answer:
Step-by-step explanation:
We want to find the equation of the line tangent to the graph of:
So, we will find the derivative of our equation first. Applying the chain rule, we acquire that:
Simplify:
We can factor out the denominator within the square root:
Simplify:
So, we can find the slope of the tangent line at <em>x</em> = 5/2. By substitution:
Evaluate:
We will also need the point at <em>x</em> = 5/2. Using our original equation, we acquire that:
So, a point is (5/2, π/6).
Finally, by using the point-slope form, we can write:
Distribute:
Isolate. Hence, our equation is:
