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Gnoma [55]
3 years ago
10

Simplify 24x^3 y^4 % 4xy^3

Mathematics
1 answer:
Aleksandr-060686 [28]3 years ago
6 0
24x^3 y^4 ÷ 4xy^3 = (24/4)x^(3 - 1)y^(4 - 3) = 6x^2y
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Which simplifications of the powers of i are correct?
OleMash [197]

The correct simplifications of powers of i are:

a. i^27=−i

d. i^8=1

e. i^5=i

Step-by-step explanation:

We know that

i^2=-1\\i^3=-i\\i^4=1

We can use the smaller powers of i to solve the larger powers.

a. i^27=−i

i^{27}\\={i^{24}}.i^3\\={i^{4*6}}.-i\\=(i^4)^6.-i\ \ \ \ As\ we\ know\ i^4=1\\=(1)^6.-i\\=1*-i\\=-i

b. i^28=i

i^{28}\\=i^{4*7}\\=(i^4)^7\\=(1)^7\\=1

c. i^14=1

i^{14}\\=i^{12}.i^2\\=(i^{4*3}).i^2\\=> i^2=-1\\=(i^4)^3.-1\\=(1)^3*-1\\=-1

d. i^8=1

i^8\\=i^{4*2}\\=(i^4)^2\\=(1)^2\\=1

e. i^5=i

i^5\\=i^{2*2*1}\\=i^2*i^2*i\\=(-1)(-1)(i)\\=i

Hence,

The correct simplifications of powers of i are:

a. i^27=−i

d. i^8=1

e. i^5=i

Keywords: Imaginary units, Iota

Learn more about imaginary units at:

  • brainly.com/question/8806598
  • brainly.com/question/8805387

#LearnwithBrainly

6 0
3 years ago
Matthew writes this sentence:   Two less than eight times a number is 22.   Which equation represents Matthew's sentence? DIS EA
Salsk061 [2.6K]
8x - 2 = 22
 x is "the number"
4 0
3 years ago
Read 2 more answers
The volume of a sphere with radius r is 4 3 πr 3 . what is the volume of a sphere with radius 5
MA_775_DIABLO [31]
Sphere volume = (4/3) PI * radius ^ 3
sphere volume = (4/3) PI * 5 ^ 3
sphere volume = (4/3) PI * 125
<span><span><span>sphere volume = 523.5987755983 </span> </span> </span>
<span>sphere volume = 523.6 (rounded)

</span>

3 0
3 years ago
What is the variable "x" in the equation, 7/2=x/2, and why?
love history [14]
X is equal to 7. Since you are trying to make them equal to each other, the denominator is already the same, so you just need to make the numerator the same too.
7 0
3 years ago
A shirt is on sale for $42. If this is of the original price of the shirt, what was the original price of the shirt?
bixtya [17]

Answer:

C. $70.00

Step-by-step explanation:

First convert the discount rate of 60% into a decimal (0.6)

Remember that the original price(x) times the discount rate(0.6) is the sale price(42).

0.6x=42

divide both sides by 0.6 to get

x=70

The original price was $70.00

7 0
3 years ago
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