Exponent laws and pythagorean theorem quiz
1 answer:
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Answer:
<u>False </u>Any three points are always coplanar
<u>False </u>Two points are always collinear
<u>False </u>Two planes intersect at a point
Read explanations, as the answer to these questions, is subjective.
Step-by-step explanation:
The definition of coplanar is; figures that exist on the same plane. Any three points might not always be colinear, as some points might exist on one plane, but other points could exist on other planes. To visualize this phenomenon, refer to the attached image. Two points could be on the red plane, but the third could be on the green. Therefore, while there are three points, not all of them exist on the same plane. However, another plane can be constructed to connect these points, bear in mind certain problems might specifically indicate that three points are not coplanar, therefore, the answer is false.
The definition of collinear is existing on the same line. This statement is a little subject, it can be both true and false depending on the way one looks at it. A line can be drawn to connect any two points, one only needs two points to determine a line. So technically two points are always collinear. However, it also depends on the circumstance. Certain geometry problems might specifically indicate that two points are not collinear. Thus, it really depends on the context. Therefore, the answer is technically false.
Two planes usually intersect on a line. To understand this, please refer to the image attached. Tehcnailly, if a corner of one plane intersects another, then one can state that the plane intersects on a point, but typically, planes intersect on lines. Therefore, technically the answer to this problem is false, as two planes usually intersect on a line.
Images credits: Geogebra
Answer:
Step-by-step explanation:
The shape of an arch corresponds to a parabola.
the general equation for a parabola is:
we're given three coordinates: (-7,-13),(7,-13) and (0,0)
so we can plug these values in the general equation to make 3 separate equations:
(x,y) = (-7,-13)
(x,y) = (7,-13)
(x,y) = (0,0)
so we have three equations. and we can solve them simultaneously to find the values of a,b, and c.
we've already found c = 0, let's use substitute it to other equations.
we can solve these two equation using the elimination method, by simply adding the two equations
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Now we can plug this value of a in any of the two equations.
We have the values of a,b, and c. We can plug them in the general equation to find the equation of the arch.
This our equation of the arch!