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frozen [14]
3 years ago
15

Explain how the segment addition postulate can be modeled using a real-world object

Mathematics
2 answers:
IgorC [24]3 years ago
6 0

To determine the length of AB, one must subtract BC from AC. If the length of AC is 18 and the length of BC is 4, then using this formula yields 18 - 4 = 14, so the length of AB is 14.

This postulate also allows a line segment that has only two known points to be broken into two line segments with the addition of a third point in between the endpoints. This is useful for proofs in geometry and analysis.


Pavel [41]3 years ago
4 0

Segment Addition Postulate States that, if there are three Points A, B and C , such that, point C lies between A and B, then

  This Postulate states that

AC + BC=AB

Real World Object(Model)

Consider a wooden block , located at the base of floor and it touches the ceiling of roof .At a point a Nail is thrashed inside it, at a distance of 40 cm from the base.And Height of the nail from ceiling is 60 cm.The total height of Wooden Block is 100 cm.Proof Segment addition postulate for this Problem.

Proof:

Total Height of wooden Block=100 cm(PQ)

Height of nail from base =40 cm(PR)

Height of nail from Ceiling= 60 cm(QR)

⇒100=40+60

⇒PR+QR=PQ

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Decide whether Rolle's Theorem can be applied to f(x) = x2 + 5 on the interval [0, 3]. If Rolle's Theorem can be applied, find a
kap26 [50]
F(x)= x² + 5, is just a parabola shfited upwards by 5 units, so, is a smooth graph and no abrupt edges, so from 0 to 3, is indeed differentiable and continuous.  So Rolle's theorem applies, let's check for "c" by simply setting its variable to 0, bear in mind that, looking for "c" in this context, is really just looking for a critical point, since we're just looking where f'(c) = 0, and is a horizontal tangent line.

\bf f(x)=x^2+5\implies \cfrac{df}{dx}=2x\implies 0=2x\implies \boxed{0=x}\leftarrow c
7 0
3 years ago
Circle A has center of (4, 5), and a radius of 3 and circle B has a center of (1, 7), and a radius of 9. What steps will help sh
Katarina [22]

Answer:

Dilate Circle A by a scale factor of 3

Step-by-step explanation:

Circle A has a radius of 3, Circle B has a radius of 9. By dilating Circle a by a scale factor of 3, it will make it the same size as Circle B, showing that the two circles are similar.

Rotating and reflecting does nothing because both circles are in the same quadrant and rotating a circle does nothing to the placement.

Translating the circle (x+3, y-2) does not put it in the same place as circle B.

8 0
3 years ago
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(Problem in two-dimensions.) Given the line: L1 : y = 2x , (2) find the equation of the line L2 perpendicular to L1 passing thro
kirill115 [55]

Given :

Equation of line 1 , y = 2x .

A point (1 , 2) .

To Find :

The equation of the line L2 perpendicular to L1 passing through the point P = (1, 2) .

Solution :

Let , equation of line 2 is :

y = mx + c     .....eq 1 ( here , m is slope and c is a constant )

Now , we know when two lines are perpendicular product of their slope is -1 .

Slope of given line is 2 .

Therefore ,

2m=-1\\\\m=\dfrac{-1}{2}

Now putting value of m in equation 1 , we get :

y=\dfrac{-1}{2}x+c

Now , it is given that this point (1,2) satisfy the above equation .

So ,

2=\dfrac{-1}{2}(1)+c\\\\c=\dfrac{5}{2}

Putting value of c in above equation , we get :

y=-\dfrac{1}{2}x+\dfrac{5}{2}\\\\2y=-x+5

Therefore , the equation of the line L2 perpendicular to L1 passing through the point P = (1, 2) is 2y = -x +5 .

Hence , this is the required solution.

7 0
3 years ago
What is the range of this relation?<br> (-5,0)<br> (8,9)<br> (-10, 2)<br> (-1, -3)
aniked [119]

Answer:

{0,9,2,-3}

Step-by-step explanation:

the range is all the ys.

these are all in the format (x, y)

Hope this helps.

PS-If it's a multiple choice question, the numbers might not be in the same order. just pick the one with those numbers.

3 0
3 years ago
14. Compare the graph below to the function
Dahasolnce [82]

Answer:

Option (2)

Step-by-step explanation:

Parent function has been given as,

f(x) = \sqrt{x}

When translated by 3 units left,

f(x + 3) = \sqrt{(x+3)}

g(x) = \sqrt{(x+3)}

If the translated function is stretched vertically by a scale factor = k

New function will be,

g'(x) = k\sqrt{(x+3)}

Since a point (1, 4) passes lies on the transformed function.

g'(1) = k\sqrt{(1+3)}

4 = 2k

k = 2

Therefore, transformed function represents the translation by 3 units in the negative side of the x-axis and stretched vertically by 2 units.

Option (2) will be the answer.

5 0
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