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1 year ago

What is the value of i4?

Mathematics

1 answer:

natima [27]1 year ago

8 0

Answer:

Step-by-step explanation:

You want to know the value of i^4.

<h3>Powers of i</h3>

The fourth power of i, √(-1), can be found the same way the value of any fourth power can be found: carry out the multiplication.

i^4 = i·i·i·i = -1·i·i = -i·i = -(-1) = 1

The fourth power of i is 1.

<em>Additional comment</em>

As you can see from the evaluation process, ...

i¹ = i

i² = -1 . . . . . definition of i

i³ = -i

i⁴ = 1

The sequence repeats for higher powers.

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What are the angle measures of triangle ABC?

Schach [20]

The angle measures of triangle ABC is ∠A=90°, ∠B= 60°, ∠C = 30°. Thus, the correct option is B.

<h3>What is a triangle?</h3>

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

As it is known that the angles of the triangle are 30°, 60°, and 90°. Therefore, the largest angle is 90° which will be the opposite of the largest side of the triangle, therefore, the measure of ∠A=90°.

Also, the shortest angle of the triangle is 30°, which will lie at the opposite of the smallest side of the triangle, therefore, the measurement of the ∠C=30°.

Now, the angle left is ∠B therefore, the measure of ∠B=60°.

Hence, the angle measures of triangle ABC is ∠A=90°, ∠B= 60°, ∠C = 30°. Thus, the correct option is B.

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4 0

2 years ago

X = 10<br><br> x = 2<br><br> x = two divided by five.<br><br> x = 11

KengaRu [80]

Answer:

x = 10

Step-by-step explanation:

You can try the answers to see which works. (The first one does.)

Or, you can solve for the variable:

Divide by 75

... (1/5)^(x/5) = 3/75 = 1/25

Recognize that 25 = 5^2, so ...

... (1/5)^(x/5) = (1/5)^2

Equating exponents, you have

... x/5 = 2

... x = 10 . . . . . multiply by 5

_____

You can also start by taking logarithms:

... log(75) +(x/5)log(1/5) = log(3)

... (x/5)log(1/5) = log(3) -log(75) = log(3/75) = log(1/25) . . . . simplify the log

... x/5 = log(1/25)/log(1/5) = 2 . . . . . simplify (or evaluate) the log expression

... x = 10 . . . . . multiply by 5

_____

"Equating exponents" is essentially the same as taking logarithms.

5 0

3 years ago

Noah has $50. He wants to buy a cell phone case for $20 and some accessories. Each accessory costs $8. How many accessories (x)

levacccp [35]

Answer:

Noah can buy 2 accessories.

Step-by-step explanation:

Given:

Money Noah has = $50

Cost of Cell phone case = $20

Cost of each accessory =$8

Amount he wants to be left = $8

So Total Amount he he wants to spend on accessories and Cell phone case will be equal to Money Noah has minus Amount he wants to be left.

framing in equation form we get;

Total Amount he he wants to spend on accessories and Cell phone case = $\$50-\$8 =\$42$

No we need to find the number of accessories Noah can buy.

Let the number of accessories be 'x'.

Now we can say that;

Cost of Cell phone case plus Cost of each accessory multiplied by number of accessories should be less than or equal to Total Amount he he wants to spend on accessories and Cell phone case.

framing in equation form we get;

$20+8x\leq 42$