Consider the cylinder with a volume of 132 cm3.

What is the value of the expression i 0 × i 1 × i 2 × i 3 × i 4?

astraxan [27]

ANSWER

The value of the expression is
$- 1$

EXPLANATION

Method 1: Rewrite as product of
${i}^{2}$

The expression given to us is,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4}$

We use the fact that
${i}^{2} = - 1$
to simplify the above expression.

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{0} \times {i}^{1} \times {i}^{3} \times {i}^{2} \times {i}^{4}$

This implies,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{0} \times {i}^{2} \times {i}^{2} \times {i}^{2} \times {i}^{2} \times {i}^{2}$

We substitute to obtain,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = 1\times - 1 \times - 1 \times - 1\times - 1 \times - 1$

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = 1\times 1 \times 1 \times - 1 = - 1$

Method 2: Use indices to solve.

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{0 + 1 + 2 + 3 + 4}$

This implies that,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{10}$

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = ( {{i}^{2}} )^{5}$

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = ( - 1 )^{5} = - 1$

8 0

3 years ago

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5 t shirts cost $25.00 how much do 15 t shirts cost if you can please show work!!:)

motikmotik

Answer:

Step-by-step explanation: ok so counting my 5’s .. 5, 10, (15) it’s 3 times soo 5 shirts cost 25 you are gonna do 25x3 so it’s 75

7 0

3 years ago

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Which expression is equivalent to

bazaltina [42]

Answer:

Step-by-step explanation:

6m+9q-3mq+4m= 10m + 9q - 3mq = C

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3 years ago

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A random sample of 300 balls hit into play in college baseball games is taken. For each ball hit into play, it is recorded wheth

AlekseyPX

Answer:

Null hypothesis: There is no relationship between direction of the ball and if it resulted in a hit or an out.

Step-by-step explanation:

In this case, the experiment conducted is to determine whether there is any relationship between the direction of the ball and if it resulted in a hit or an out.

A random sample of 300 balls hit into play in college baseball games is taken. For each ball hit into play, it is recorded whether the ball was hit to the left, center, or right of the field, and whether the ball resulted in a hit or an out.

The regression analysis would be used to determine whether there is any relationship between direction of the ball and if it resulted in a hit or an out.

The hypothesis for the regression analysis is defined as follows:

H₀: There is no relationship between direction of the ball and if it resulted in a hit or an out.

Hₐ: There is a significant relationship between direction of the ball and if it resulted in a hit or an out.

5 0

3 years ago

The volume for a rectangular prism is given by the formula V = l · w · h, where l is the length of the prism, w is the width of

Charra [1.4K]

Answer:

4

Step-by-step explanation:

devide 144 by 9

get 16

The base squared is 16

find the root of 16

get 4

4 is your awnser

4 0

3 years ago