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4 years ago

6 (Picture) CONVERGENT AND DIVERGENT SERIES PLEASE HELP!!

Mathematics

1 answer:

V125BC [204]4 years ago

3 0

Answer:

The progression is Option A. convergent.

Step-by-step explanation:

The given series is( $-\frac{8}{5}+\frac{32}{25}-\frac{128}{125}+......$ )

= $(-\frac{8}{5})(1-\frac{4}{5}+(\frac{4}{5})^{2}-.....)$

Now we can write this series as $\sum_{n=0}^{n=\oe}(-\frac{8}{5})(-\frac{4}{5})^{n}$

In this expression common ration is 4/5= 0.8

As we know that in geometric progression if common factor is less than one then the progression converges.

Therefore we can say that this progression is convergent.

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The line segments that connect 2nd base to 1st base' & 2nd base to 3rd base form a right angle. Marcus on 3rd base and he is

Stells [14]

Answer: The correct answer is option C; 90√2

Step-by-step explanation: The line segments are labelled as base 1, base 2 and base 3 respectively. This we shall call point 1, point 2 and point 3. These three points form a right angle. Also we have been told that Marcus is on point 3 and Jean is on point 2. They are both 90 feet apart. Also Joel is on point 1 and he is 90 feet away from Jean. The unmeasured distance therefore is from point 1 to point 3, which is the distance from Joel to Marcus (or Marcus to Joel).

The distance from point 1 to point 3 is the hypotenuse of the right angled triangle derived. Using the Pythagoras' theorem, the distance from Joel to Marcus (or JM) is calculated as follows;

JM² = JC² + JL²

Where JM is the distance between Joel and Marcus (hypotenuse), JC is the distance from Jean to Marcus and JL is the distance from Jean to Joel.

JM² = 90² + 90²

JM² = 8100 + 8100

JM² = 16200

Add the square root sign to both sides of the equation

√JM = √16200

JM = √100*√81*√2

The right hand side of the equation can be further solved as

JM = 10*9*√2

JM = 90√2

Therefore the distance between Marcus and Joel is calculated as 90√2 feet

6 0

3 years ago

In which of the tables below x and y are inversely proportional? Find the constant of variation.

sertanlavr [38]

Answer:

In Table (b)

$k=30$

Step-by-step explanation:

By definition, Inverse proportion equations have he following form:

$y=\frac{k}{x}$

Where "k" is the Constant of proportionality.

Solving for "k":

$k=yx$

Having the values of "x" and "y" given in each table, you can check if the products of "x" and "y" is equal to a constant value.

Then:

(a) For $x=3;y=8$ :

$(8)(3)=24$

For $x=4;y=6$ :

$(6)(4)=24$

For $x=5;y=4.8$ :

$(4.8)(5)=24$

For $x=5.5;y=4$ :

$(4)(5.5)=22$

Since the product of the values of "x" and "y" is not constant, they are not inversely proportional.

(b) For $x=0.1;y=300$ :

$(300)(0.1)=30$

For $x=0.5;y=60$ :

$(60)(0.5)=30$

For $x=75;y=0.4$ :

$(0.4)(75)=30$

For $x=100;y=0.3$ :

$(100)(0.3)=30$

Notice that the Constant of proportionality is:

$k=30$

Therefore "x" and "y" are inversely proportional.

8 0

3 years ago

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In-s [12.5K]

I think C is the answer

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4 years ago