The volume of the triangular prism is 54 cubic units.
1 answer:
Answer:
x = 3
Step-by-step explanation:
Given:
- The volume of the triangular prism : 54 cubic units
- The base length: 4 unit
- The height of the base: x
- The height of the prism : 3x
As we know that, the formula used to find out the volume of a triangular prism is:
V = 1/2 * The base length * The height of the base * The height of the prism
<=> V = 1/2*4*x*3x
In this question we have V = 54 cubic units
<=> 1/2*4*x*3x = 54
<=> = 9
<=> x = 3
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Answer:
2.375 inches
Step-by-step explanation:
<u>Main Steps</u>
1. Identifying important parts of the question
2. Solving the problem
<u>Step 1. - Identifying important parts of the question</u>
In the question, there is some extraneous information. For instance, the question introduces the terms "diameter" and "loaded in shear" and "with a safety factor of 1.5". However, given the information in the problem, and the question asked, it isn't necessary to know that it is "loaded in shear" means, or to know what a diameter is (since everything stays with diameters, and doesn't involve another dimension), and the problem gives the result that will satisfy "a safety factor of 1.5".
<u>Sifting through the problem/question, these are the important parts:</u>
- "to the nearest 1/8 inch" (meaning round to the nearest 1/8th of a unit)
- with "units of inches to 3 decimal places"
- The number to round is "2.4183 inches
<u>Step 2. - Solving the Problem</u>
To round to the nearest 1/8 inch, we can divide the number 2.4183 by 1/8.
Recall that dividing by a fraction is the same as multiplying by the reciprocal
19.3464
So, there are approximately 19, one-eighth-inches in the measurement. (Note that 19.3464 is closer to 19 than it is to 20). To find the final rounded measurement, multiply 19 by 1/8
2.375 inches
So, the diameter of the bolt that should be used (if rounded to the nearest 1/8 inch, to allow for a factor of safety of 1.5) is 2.375 inches
Answer:
Step-by-step explanation:
So an ellipse can be expressed in two different but very similar forms:
<u><em>Horizontal Major Axis:</em></u>
<u><em>Vertical Major Axis</em></u>:
In both equations the length of the major axis is "2a" and the length of the minor axis is "2b"
In the equation you provided, the major axis is horizontal, and the minor axis is vertical.
So looking at the horizontal length, you can see that it's 6, and since this ellipse has a horizontal major axis, that means 2a=6, which means a=3
Looking at the vertical length, you can see that it's 4, and since the ellipse has a vertical minor axis, that means 2b=4, which means b=2
The last thing to note is that the center of an ellipse is (h, k) in the equation, and since here the center is (0, 0) it's (x-0)^2 and (y-0)^2 in the denominator which is just x^2 and y^2
So let's plug in the values into the equation:
(h, k) = (0, 0)
a = 3
b = 2