Show the conjecture is false by the counterexample any number is divisible by 2 is divisible by 4

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s

serg [7]

solution:

s( t ) = ( 2 )sin( πt ) + ( 2 )cos(πt )

v( t ) = s'( t ) = ( 2π )cos( πt) - ( 2π )sin( πt )

vavg = 1 / ( b - a ) Integral a to b [ v( t ) ] dt

( a )

vavg

= 1 / ( 2 - 1 ) Integral 1 to 2 [ ( 2π)cos( πt ) - ( 2π )sin( πt ) ] dt

= [ ( 2)sin( πt ) + ( 2 )cos( πt ) ] 1to 2

= [ ( 2)sin( 2π ) + ( 2 )cos( 2π ) ] - [ ( 2 )sin( π ) + ( 2 )cos( π) ]

= 4 cm / s

( b )

vavg

= 1 / ( 1.1 - 1 ) Integral 1 to 1.1 [ ( 2π)cos( πt ) - ( 2π )sin( πt ) ] dt

= 10 [ ( 2 )sin( πt ) + ( 2 )cos( πt ) ] 1 to 1.1

= 10 [ [ ( 2 )sin( 1.1π ) + ( 2)cos( 1.1π ) ] - [ ( 2 )sin( π) + ( 2 )cos( π ) ] ]

-5.20 cm /s

( c )

vavg

= 1 / ( 1.01 - 1 ) Integral 1 to 1.01 [ ( 2π)cos( πt ) - ( 2π )sin( πt ) ] dt

= 100 [ ( 2 )sin( πt ) + ( 2 )cos( πt ) ] 1 to 1.01

= 100 [ [ ( 2 )sin( 1.01π ) + (2 )cos( 1.01π ) ] - [ ( 2 )sin( π) + ( 2 )cos( π ) ] ]

-6.18 cm /s

( d )

vavg

= 1 / (1.001 - 1 ) Integral 1 to 1.001 [ ( 2π )cos( πt ) - ( 2π )sin(πt ) ] dt

= 1000 [ ( 2 )sin( πt ) + ( 2 )cos( πt ) ] 1 to 1.001

= 1000 [ [ ( 2 )sin( 1.001π ) + (2 )cos( 1.001π ) ] - [ ( 2 )sin(π ) + ( 2 )cos( π ) ] ]

-6.27 cm /s

8 0

3 years ago

Are the graphs of the lines in the pair parallel? Explain.

myrzilka [38]

Either A or C since the slopes are different.

5 0

4 years ago

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Suppose you loan $320 to a friend and charge them 11% annual interest. If they don't pay you back, how much will they owe you af

RSB [31]

Answer:

Step-by-step explanation:

You want to calculate the interest on $320 at 11% interest per year after 5 year(s).

The formula we'll use for this is the simple interest formula, or:

Where:

P is the principal amount, $320.00.

r is the interest rate, 11% per year, or in decimal form, 11/100=0.11.

t is the time involved, 5....year(s) time periods.

So, t is 5....year time periods.

To find the simple interest, we multiply 320 × 0.11 × 5 to get that:

The interest is: $176.00

Usually now, the interest is added onto the principal to figure some new amount after 5 year(s),

or 320.00 + 176.00 = 496.00. For example:

If you borrowed the $320.00, you would now owe $496.00

If you loaned someone $320.00, you would now be due $496.00

8 0

3 years ago

A rectangle and a square have the same perimeter. the rectangle is of length 6cm and has an area of 48cm², find the length of th

EleoNora [17]

<em>The length of the square that has the same perimeter as the rectangle is of length 6cm and area of 48cm² is 7cm</em>

<h2>Explanation:</h2>

Let's call:

$A_{s}:Area \ of \ square \\ \\ A_{r}:Area \ of \ rectangle \\ \\ P_{s}:Perimeter \ of \ square \\ \\ P_{r}:Perimeter \ of \ rectangle$

From the question, we know that:

<em>A rectangle and a square have the same perimeter.</em>

So:

$P_{s}=P_{r}$

Moreover:

<em>The rectangle is of length 6cm and has an area of 48cm²</em>

Accordingly:

$For \ Rectangle: \\ \\ L:Length \\ W:Width \\ \\ A_{r}=L\times W \\ \\ 48=6W \\ \\ W=8$

Also:

$A_{s}=s^2 \\ \\ S:Side \ of \ square$

From the statement of perimeters:

$P_{s}=P_{r} \\ \\ \\ But: \\ \\ P_{s}=4s \\ \\ P_{r}=2W+2L \\ \\ \\ Then: \\ \\ 4s=2W+2L \\ \\ \\ But: \ W=8 \ and \ L=6 \\ \\ 4s=2(8)+2(6) \\ \\ 4s=16+12 \\ \\ 4s=28 \\ \\ \boxed{s=7cm}$

Finally, <em>the length of the square that has the same perimeter as the rectangle is of length 6cm and area of 48cm² is 7cm</em>

<h2>Learn more:</h2>

Perimeter: brainly.com/question/9969486

#LearnWithBrainly

6 0

3 years ago

PLEASE WILL GIVE BRAINLEST \

Lesechka [4]

Answer:

First statement is wrong

Step-by-step explanation:

Forgive me if I am wrong

7 0

3 years ago

Read 2 more answers