The exact value of cos120 if the measure 120 degrees intersects the unit circle at point (-1/2,√3/2) is 0.5
<h3>Solving trigonometry identity</h3>
If an angle of measure 120 degrees intersects the unit circle at point (-1/2,√3/2), the measure of cos(120) can be expressed as;
Cos120 = cos(90 + 30)
Using the cosine rule of addition
cos(90 + 30) = cos90cos30 - sin90sin30
cos(90 + 30) = 0(√3/2) - 1(0.5)
cos(90 + 30) = 0 - 0.5
cos(90 + 30) = 0.5
Hence the exact value of cos120 if the measure 120 degrees intersects the unit circle at point (-1/2,√3/2) is 0.5
Learn more on unit circle here: brainly.com/question/23989157
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<span>h<span>(t)</span>=<span>t<span>34</span></span>−3<span>t<span>14</span></span></span>
Note that the domain of h is <span>[0,∞]</span>.
By differentiating,
<span>h'<span>(t)</span>=<span>34</span><span>t<span>−<span>14</span></span></span>−<span>34</span><span>t<span>−<span>34</span></span></span></span>
by factoring out <span>34</span>,
<span>=<span>34</span><span>(<span>1<span>t<span>14</span></span></span>−<span>1<span>t<span>34</span></span></span>)</span></span>
by finding the common denominator,
<span>=<span>34</span><span><span><span>t<span>12</span></span>−1</span><span>t<span>34</span></span></span>=0</span>
<span>⇒<span>t<span>12</span></span>=1⇒t=1</span>
Since <span>h'<span>(0)</span></span> is undefined, <span>t=0</span> is also a critical number.
Hence, the critical numbers are <span>t=0,1</span>.
I hope that this was helpful.
A is the correct answer, NOT c. You don't list elements of the domain each time they occur, you enter each element of the domain only once
9514 1404 393
Answer:
779.4 square units
Step-by-step explanation:
You seem to have several problems of this type, so we'll derive a formula for the area of an n-gon of radius r.
One central triangle will have a central angle of α = 360°/n. For example, a hexagon has a central angle of α = 360°/6 = 60°. The area of that central triangle is given by the formula ...
A = (1/2)r²sin(α)
Since there are n such triangles, the area of the n-gon is ...
A = (n/2)r²sin(360°/n)
__
For a hexagon (n=6) with radius 10√3, the area is ...
A = (6/2)(10√3)²sin(360°/6) = 450√3 ≈ 779.4 . . . . square units
