can someone help me understand this, please? For some reason my answer is correct but I need to understand how did I found the c
orrect answer
1 answer:
Answer with step-by-step explanation:
The way the question is worded, this actually shouldn't be correct. The correct answer should be .
Because the trapezoids are similar, we can find the ratio of their perimeters by actually just finding the ratio of their sides.
Why?
By definition, the corresponding sides of a polygon are in a constant proportion. The perimeter is simply the sum of all sides of the polygon. Since we're just adding the sides, the proportion will still be maintained.
Therefore, we'll just need to ratio of their corresponding sides. The only two corresponding sides that are marked are and
.
The ratio of is
.
The reason why it ideally should be and not
is because the question states
, which mentions
first, so our answer should follow this respective order. I believe you were marked right anyways because the specific order is not specified, but generally, you want to give your answer respectively by default.
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Answer:
Hence, none of the options presented are valid. The plane is represented by .
Step-by-step explanation:
The general equation in rectangular form for a 3-dimension plane is represented by:
Where:
,
,
- Orthogonal inputs.
,
,
,
- Plane constants.
The plane presented in the figure contains the following three points: (2, 0, 0), (0, 2, 0), (0, 0, 3)
For the determination of the resultant equation, three equations of line in three distinct planes orthogonal to each other. That is, expressions for the xy, yz and xz-planes with the resource of the general equation of the line:
xy-plane (2, 0, 0) and (0, 2, 0)
Where:
- Slope, dimensionless.
,
- Initial and final values for the independent variable, dimensionless.
,
- Initial and final values for the dependent variable, dimensionless.
- x-Intercept, dimensionless.
If ,
,
and
, then:
Slope
x-Intercept
The equation of the line in the xy-plane is or
, which is equivalent to
.
yz-plane (0, 2, 0) and (0, 0, 3)
Where:
- Slope, dimensionless.
,
- Initial and final values for the independent variable, dimensionless.
,
- Initial and final values for the dependent variable, dimensionless.
- y-Intercept, dimensionless.
If ,
,
and
, then:
Slope
y-Intercept
The equation of the line in the yz-plane is or
.
xz-plane (2, 0, 0) and (0, 0, 3)
Where:
- Slope, dimensionless.
,
- Initial and final values for the independent variable, dimensionless.
,
- Initial and final values for the dependent variable, dimensionless.
- z-Intercept, dimensionless.
If ,
,
and
, then:
Slope
x-Intercept
The equation of the line in the xz-plane is or
After comparing each equation of the line to the definition of the equation of the plane, the following coefficients are obtained:
,
,
,
Hence, none of the options presented are valid. The plane is represented by .