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mixer [17]
3 years ago
5

If m ∆ n means m²-2mm+n³, determine the value of 3∆2.​

Mathematics
2 answers:
Novay_Z [31]3 years ago
6 0

\large\underline{\underline{ \sf\maltese Correct \ Question :- }}

If m ∆ n means m²-2mm+n², determine the value of 3∆2.

\large\underline{\underline{ \sf\maltese Answer :- }}

Here we are given that m ∆ n means m² -2mn +n². And we need to find the value of 3∆2 . So let's find out what does the " ∆ " operator does.

Here we can see that m² - 2mn - n² is the whole square of ( m - n)² . A inference can be taken out that the operator " ∆ " first subtracts the two numbers and then squares the obtained value to get the result . That is ,

\sf\implies m \Delta n = ( m - n )^2

Now similarly let's simplify out 3 ∆ 2.

Step 1 : <u> </u><u>Subtra</u><u>ct</u><u> </u><u>the </u><u>two</u><u> </u><u>numbers</u><u> </u><u>:</u><u>-</u><u> </u>

This means we need to subtract 2 from 3 . This will give result as ,

\sf\implies Result_1 = 3 - 2 =\pink{1}

Step 2 : <u>Square </u><u>the</u><u> </u><u>obta</u><u>ined</u><u> </u><u>val</u><u>ue</u><u> </u><u>:</u><u>-</u><u> </u>

Here , the value obtained from step 1 is 1 and the square of 1 is 1 . So our final result would be,

\sf\implies Result_{(final)}= 1^2 = \boxed{\pink{ 1 }}

jeka943 years ago
5 0

since m▲n=m^2-2mn+n^3

3▲2=3^2-2*3*2+2^3

=9-12+8

=17-12

=15

Done!

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<u><em>12 feet.
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6 0
3 years ago
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A village was founded four hundred years ago by a group of 20 people. In this village, the population triples every one hundred
Paha777 [63]

Answer:

Step-by-step explanation:

Treat this like compound interest:  Use A = P(1 + r)^t.

Here, P is the initial population and A is 3 times that, or 3P.  Since P = 20 people, 3P = 60 people,

and this population is reached after 100 years.

We need to determine r, substitute its value into the formula A = P(1 + r)^t, and then determine the population of the village after 400 years.

60 = 20(1 + r)^100

Simplifying, 3 = (1 + r)^100.

Taking the natural log of both sides,

ln 3 = 100 ln (1 + r), or

                   ln 3

ln (1 + r) = ---------------

                    100

              = 1.0986 / 100 = 0.01986

We must solve this for r.  Raising e to the power ln (1 + r), on the left side of an equation, and raising e to the power 0. 01986 on the right side, we get:

1 + r = 3, so r must = 2.

Now find the pop of the village today.  Use the same equation:  A = P (1+r)^t.

A = 20(1 +2)^4 (hundreds),

or

A = 20(3)^4, or

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The population after 400 years is 81.

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3 years ago
Use always, sometimes or never to make a true statement:
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Answer:

1. Intersecting lines are <u>always</u> coplanar

2. Two planes <u>never</u> intersect in exactly one point

3. Three points are <u>always</u> coplanar

4. A plane containing two points of a line <u>always</u> contains the entire line

5. Four points are <u>sometimes</u> coplanar

6. Two lines <u>never</u> meet in more than one point.

7. Two skew lines are <u>never</u> coplanar

8. Line TQ and Line QT are <u>always</u> the same line.

Step-by-step explanation:

Note: Coplanar means "In the same plane"

1. Each line exist in many planes. But different lines must share at least one plane for them to intersect. That is why intersecting lines are always coplanar.

2. Two planes never intersect at exactly one point because only lines intersect at a point. Planes can only intersect along a line.

3.Three points are always coplanar because in geometry, a group of points are coplanar because there is a geometric plane that they all lie on.

4. A plane containing two points of a line always contains the entire line. Yes

5. Four points are only sometimes coplanar because there is a probability that they may all not lie on the same plane

6. Two lines never meet in more than one point because lines are basically straight and cannot bend over to intersect at another point

7. Two skew lines are never coplanar because skews lines are lines that do not intersect and are never parallel.

8. Line TQ and Line QT are always the same line because a line is straight and extends from one point to the other. So, if a line is labelled TQ calling it QT means the same thing

4 0
3 years ago
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Paha777 [63]

Answer: Angle HAB= 66 and Angle CAB= 44

Step-by-step explanation:

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5x=110

x=22

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HAB= 3(22)=66 degrees

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Galina-37 [17]

Answer:

(4, 5 )

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substitute x = 4 into either of the 2 equations and solve for y

substituting into (1)

4 + y = 9 ( subtract 4 from both sides )

y = 5

solution is (4, 5 )

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