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Cloud [144]
3 years ago
8

Beth is writing out the steps using the "Shortest Route Algorithm". She just finished writing out all

Mathematics
1 answer:
JulijaS [17]3 years ago
5 0

Answer:

ACBD; 7

Step-by-step Explanation:

The Route Algorigtm finds the short route that is efficient, in order to find the solution following pathways.

From the pictures from the complete question,

STEP #1, there exist, three routes, which are:

AB

AC,

and AD.

*AB is not viable because of the negative distance, so it can be removed .

* the AC distance is 3,and AD distance is 8. Therefore, AC can be selected and circled.is because of AC efficiency is high compare to AD.

*from selected AC, the possible routes are ACB; 3 and ACE; 6. which are route shown in #2

* ACB is circled, because it's more shorter than ACE

*The possible routes are ACBE; 8 and ACBD; 7. which are route shown in #3 . Therefore, route ACBD is circled because it's more shorter.

From the analysis of the algorithm, the route ACBD route is the shortest and the most efficient

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dentify all of the following solutions of square root of x minus 8 end root plus 8 equals x. (1 point)
viva [34]

Answer:gh

Step-by-step explanation:

3 0
3 years ago
Find the partial fraction decomposition of the rational expression with prime quadratic factors in the denominator
SpyIntel [72]
\dfrac{5x^4-7x^3-12x^2+6x+21}{(x-3)(x^2-2)^2}=\dfrac{a_1}{x-3}+\dfrac{a_2x+a_3}{x^2-2}+\dfrac{a_4x+a_5}{(x^2-2)^2}
\implies 5x^4-7x^3-12x^2+6x+21=a_1(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(a_4x+a_5)(x-3)

When x=3, you're left with

147=49a_1\implies a_1=\dfrac{147}{49}=3

When x=\sqrt2 or x=-\sqrt2, you're left with

\begin{cases}17-8\sqrt2=(\sqrt2a_4+a_5)(\sqrt2-3)&\text{for }x=\sqrt2\\17+8\sqrt2=(-\sqrt2a_4+a_5)(-\sqrt2-3)\end{cases}\implies\begin{cases}-5+\sqrt2=\sqrt2a_4+a_5\\-5-\sqrt2=-\sqrt2a_4+a_5\end{cases}

Adding the two equations together gives -10=2a_5, or a_5=-5. Subtracting them gives 2\sqrt2=2\sqrt2a_4, a_4=1.

Now, you have

5x^4-7x^3-12x^2+6x+21=3(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(x-5)(x-3)
5x^4-7x^3-12x^2+6x+21=3x^4-11x^2-8x+27+(a_2x+a_3)(x-3)(x^2-2)
2x^4-7x^3-x^2+14x-6=(a_2x+a_3)(x-3)(x^2-2)

By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that a_2x^4=2x^4 and a_3(-3)(-2)=6a_3=-6. These alone tell you that you must have a_2=2 and a_3=-1.

So the partial fraction decomposition is

\dfrac3{x-3}+\dfrac{2x-1}{x^2-2}+\dfrac{x-5}{(x^2-2)^2}
7 0
3 years ago
Hey I hope this helps many people but how do you do this problem <br><br> 5x=0.4
Scrat [10]
X=0.08 hope it helps love
4 0
3 years ago
Read 2 more answers
Convert 7,200 in scientific notation​
Nitella [24]

Answer:

7.2*10^3.

7,200 in scientific notation, is 7.2*10^3

8 0
3 years ago
TU = 3, RS = 15, TW = 4, TR = 9; Assume that the sides of triangle TUW are proportional to the sides of triangle TRS. What is th
VMariaS [17]

Answer:

  WS=8\ units

Step-by-step explanation:

we know that

If two triangles are similar

then

the ratio of their corresponding sides are equal and the corresponding angles are also equal

In this problem

\frac{TU}{TR}=\frac{UW}{RS}=\frac{TW}{TS}

we have

TU=3\ units, RS=15\ units, TW=4\ units,TR=9\ units

Find the value of TS

\frac{TU}{TR}=\frac{TW}{TS}

substitute

\frac{3}{9}=\frac{4}{TS}

TS=36/3=12\ units

WS=TS-TW

WS=12-4=8\ units

see the attached figure to better understand the problem

3 0
3 years ago
Read 2 more answers
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