The perimeter of a rectangular garden is 372 feet. if the width of the garden is 88 feet, what is its length?

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

Read 2 more answers

Im almost done with my test just need 2 more :) and please help me

creativ13 [48]

Answer:

░░░░░▐▀█▀▌░░░░▀█▄░░░

░░░░░▐█▄█▌░░░░░░▀█▄░░

░░░░░░▀▄▀░░░▄▄▄▄▄▀▀░░

░░░░▄▄▄██▀▀▀▀░░░░░░░

░░░█▀▄▄▄█░▀▀░░

░░░▌░▄▄▄▐▌▀▀▀░░ This is Bob

▄░▐░░░▄▄░█░▀▀ ░░

▀█▌░░░▄░▀█▀░▀ ░░ Copy And Paste Him onto all of ur brainly answers

░░░░░░░▄▄▐▌▄▄░░░ So, He Can Take

░░░░░░░▀███▀█░▄░░ Over brainly

░░░░░░▐▌▀▄▀▄▀▐▄░░

░░░░░░▐▀░░░░░░▐▌░░

░░░░░░█░░░░░░░░█

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Least to greatest 0.386 0.3 0.683 0.836

m_a_m_a [10]

0.3, 0.386, 0.683, 0.836

7 0

3 years ago

Renting a room at the Willow tree resort costs $125 for 2 people. Each additional person is $25. Write an expression that shows

Mama L [17]

Answer:

Let C be the cost for the people staying

if n <= 2 ; C = $125

If n >2 ; C = $125 + $25 * (n-2)

Step-by-step explanation:

If the number of people is more than two, we need to add $25 for each of them.

Since n will be the number of people staying, we need to make sure that we substract two from this term to avoid overcharging the guests when there is less than two people.

So

(n-2) is the term that should be multiplied by a factor of 25.

5 0

3 years ago

59÷2<br><img src="https://tex.z-dn.net/?f=59%20%5Cdiv%202" id="TexFormula1" title="59 \div 2" alt="59 \div 2" align="absmiddle"

zubka84 [21]

The answer is 29.5

Okkkkkkkkrrrrrrrr It is a long division just use calculator

7 0

3 years ago