Answer:
Answer in picture attached
Step-by-step explanation:
If the surface area of the rectangular prism is 224 cm 2, what is the height?
2 answers:
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These are a huge pain. First set up your initial triangle with A and B as your base angles and C as your vertex angle. Now drop an altitude and call it h. You need to solve for h. Use sin 56 = h/13 to get that h = 10.8. The rule is that if the side length of a is greater than the height but less than the side length of b, you have 2 triangles. h<a<b --> 10.8<12<13. Those are true statements so we have 2 triangles. Side a is the side that swings, this is the one we "move", forming the second triangle. First we have to solve the first triangle using the Law of Sines, then we can solve the second. 
to get that angle B is 64 degrees. Now find C: 180-56-64=60. And now for side c: 
and c=12.5. That's your first triangle. In the second triangle, side a is the swinging side and that length doesn't change. Neither does the angle measure. Angle B has a supplement of 180-64 which is 116. So the new angle B in the second triangle is 116, but the length of b doesn't change, either. I'll show you how you know you're right about that in just a sec. The only angle AND side that both change are C and c. If our new triangle has angles 56 and 116, then C has to be 8 degrees. Using the Law of Sines again, we can solve for c:
and c = 2.0. We can look at this new triangle and determine the side measures are correct because the longest side will always be across from the largest angle, and the shortest side will always be across from the smallest angle. The new angle B is 116, which is across from the longest side of 13. These are hard. Ugh.
Answer:
5 amperes will produce the maximum power of 300 watts.
Step-by-step explanation:
The general form of a quadratic function presents the function in the form
The vertex of a quadratic function is the highest or lowest point, also known as the maximum or minimum of a quadratic function.
We can define the vertex by doing the following:
- Identify a, b, and c
- Find, the x-coordinate of the vertex, by substituting a and b into
- Find, the y-coordinate of the vertex, by evaluating
We know that the power generated by an electrical circuit is modeled by
This function is a quadratic function.
To find the current that produce the maximum power you must
- Identify a and b
a = -12 and b = 120
- Find, the maximum current of the vertex, by substituting a and b into
- Find, the maximum-power, by evaluating
5 amperes will produce the maximum power of 300 watts.
We can check our work with the graph of the function and see that the maximum is (5, 300).
