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kakasveta [241]

4 years ago

10

jakes map shows the distance from the bake stars cafe to the restaurant supply store as 3 centimeters. if the scale of the map i

s 1 centimeter to 8 kilometers, what is the distance from the shop to the store

1 answer:

Mila [183]4 years ago

6 0

Answer:

It would be 24 kilometers.

Step-by-step explanation:

This is because 1 centimeter on the map equals 8 kilometers in real life.

Since the cafe's distance is 3 centimeters, it would be 24 kilometers.

<em>3 * 1 = 3 centimeters</em>

<em>3 * 8 = 24 kilometers</em>

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Statements can be proved by contrapositive, contradiction or by induction.

<em>2.21 and 2.23 are proved by contrapositive</em>
<em>2.22 is proved by induction</em>

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<u>2.21: If </u> $n^3$ <u> is even, then n is even (By contrapositive)</u>

The contrapositive of the above statement is that:

<em>If n is odd, then </em> $n^3$ <em> is odd</em>

Represent the value of n as:

$n = 2k + 1$ , where $k \ge 0$

Take the cube of both sides

$n^3 = (2k + 1)^3$

Expand

$n^3 = 8k^3 + 6k^2 + 6k + 1$

Group

$n^3 =[ 8k^3 + 6k^2 + 6k] + 1$

Factor out 2

$n^3 =2[4k^3 + 3k^2 + 3k] + 1$

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The constant term (i.e. 1) means that $n^3$ is odd.

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<u>2.22 </u> $3n + 4$ <u> is even, if and only if n is even</u>

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<u>2.22: </u> $s \ne -1$ <u> and </u> $t \ne -1$ <u>, then </u> $s + t + st \ne -1$ <u />

To do this, we prove by contrapositive.

The contrapositive of the above statement is:

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$s + t + st = -1$

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