Mathematics, 13.03.2022 14:00 olamagdziak2007

1. How does the distance formula help me know if two or three sides of a triangle are equal?

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Answer from: dani3112

If we consider what the distance formula really tells you, we can see the similarities. It is more than just a similar form.
The distance formula is commonly seen as:
D= √(x1−x2)2+(y1−y2)2
We commonly write the Pythagorean Theorem as:
c= √a2+b2
Consider the following major points (in Euclidean geometry on a Cartesian coordinate axis):
The definition of a distance from
x
to ±c is |x−c|
.
There is the relationship where
√(x−c)2=|x−c|=x−c
AND −x+c
The distance from one point to another is the definition of a line segment.
Any diagonal line segment has an
x
component and a
y
component, due to the fact that a slope is
Δy/Δx
. The greater the
y
contribution, the steeper the slope. The greater the
x
contribution, the flatter the slope.
What do you see in these formulas? Have you ever tried drawing a triangle on a Cartesian coordinate system? If so, you should see that these are two formulas relating the diagonal distance on a right triangle that is composed of two component distances
x
and
y
.
Or, we could put it another way through substitutions based on the distance definitions above. Let:
x1−x2=±ay1−y2=±b

(depending on if x1>x2 or x1

Answer from: Quest

step-by-step explanation:

we can use this expression to calculate the energy gain as a particle moves with a field or the energy loss as it moves against it. (note that it is also used to define the electron-volt, a unit of energy equal to that gained by an electron as it falls through a pd of 1 v, i.e. w = 1 ev = 1.6 10-19 c 1 v = 1.6 10-19j).in fact this expression is really nothing more than the statement that potential is the potential energy per unit charge. in this case, v= w/qis simply stating that the change in potential energy(or work done) per unit charge is equal to the change in potential (or potential difference), v.student questions: uniform electric fields2electron beamcathode+5 kvanode0 v

Answer from: Quest

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

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