Could someone help me solve for this question? I have a hard time

Understanding. Thanks, the question is


Which statement describes the end behavior of the exponential equation y = 3^x?

A as x -> - ♾ , y -> - ♾

B as x -> - ♾ , y -> 0

C as x - > ♾ , y -> - ♾

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Explanation:

We use De Moivre's Theorem. It says that if you started with

[tex]z = r*\left[\cos\left(\theta\right)+i*\sin\left(\theta\right)\right][/tex]

then raising both sides to the nth power leads to

[tex]z^n = r^n*\left[\cos\left(n*\theta\right)+i*\sin\left(n*\theta\right)\right][/tex]

The term out front r is raised to the nth power. We also have copies of n inside the trig functions.

The square root operation undoes the squaring operation, so we'll be dealing with n = 2.

If you were to go through each answer choice, then you'll find that squaring choice B will lead to the original expression given.

[tex]z = \sqrt{3}*\left[\cos\left(\frac{\pi}{4}\right)+i*\sin\left(\frac{\pi}{4}\right)\right]\\\\\\z^2 = (\sqrt{3})^2*\left[\cos\left(2*\frac{\pi}{4}\right)+i*\sin\left(2*\frac{\pi}{4}\right)\right]\\\\\\z^2 = 3*\left[\cos\left(\frac{\pi}{2}\right)+i*\sin\left(\frac{\pi}{2}\right)\right]\\\\\\[/tex]

Note that working this process in reverse means we apply the square root and we'll go from the expression in choice B to the original expression again.

The complex number Z =  √3[cosπ/4 + i sinπ/4] represents the complex number √(3[cosπ/2 + i sinπ/2]) after using the De Moivre's theorem option (B) is correct.

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number in the trigonometric form:

Z = √(3[cosπ/2 + i sinπ/2])

It is required to find the square root of the complex number.

To find the square root of the complex number we can use the De Moivre's theorem:

If

Z = r[cosθ + i sinθ]

Zⁿ = rⁿ[cosnθ + i sinnθ]

Using the above theorem:

Z =  √3[cos[(1/2)π/2] + i sin[(1/2)π/2]]

Z =  √3[cosπ/4 + i sinπ/4]

Thus, the complex number Z =  √3[cosπ/4 + i sinπ/4] represents the complex number √(3[cosπ/2 + i sinπ/2]) after using the De Moivre's theorem option (B) is correct.

Learn more about the complex number here:

brainly.com/question/10251853

#SPJ5

If you are asking for the value of x, then x = not defined because dividing a value by 0 will always give you a non-defined answer. So, x can be equal to any number (there can be infinite values).

Next, if you want to prove that both the statements are true, then yes it's true because RHS = LHS = 0.

Check the 2 attachments for the steps.

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RainbowSalt2222 ☔

Answer:

infinite number of solutions

Step-by-step explanation:

x - ([tex]\frac{x}{5}[/tex] + 60) = [tex]\frac{4}{5}[/tex] x - 60 ← distribute parenthesis on left by - 1

x - [tex]\frac{x}{5}[/tex] - 60 = [tex]\frac{4}{5}[/tex] x - 60 , collect like terms on left side

[tex]\frac{4}{5}[/tex] x - 60 = [tex]\frac{4}{5}[/tex] x - 60

Since expressions on both sides are equal then any value of x is a solution.

That is there is an infinite number of solutions

Answer:

you multiple two numbers and you devide both sides you get the answer

Step-by-step explanation:

area of triangle,=1/2*base*height

30=1/2*10/h

h=6cm

Answer:  Height=6cm

Step-by-step explanation:

Area of triangle =30cm²

Base=10cm

Height=?

Area=1/2*base*height

30=1/2*10*height

Height=30*2/10

Height=6cm

Answer:

each company will earn $38 when they ship a 12-pound package

Step-by-step explanation:

you can solve this algebraically by setting up two equations:

let 'c' = charges per pound

Lone Star:  y = 2c + 14

Discount:  y = 1.5c + 20

now set each equation equal to the other to solve for 'c':

2c + 14 = 1.5c + 20

subtract 14 from each side to get:

2c = 1.5c + 6

subtract 1.5c from each side to get:

0.5c = 6

c = 6/0.5

c = 12

if you plug 12 in for 'c' in each equation you will get y = 38

(12,38) is the point where these two companies would each earn $38 for shipping a 12-pound package

We have a group of 169 students that needs to be seated in a square formation. Then, the number of rows has to be the square root of 169 :-

[tex]r = \sqrt{169} = 13[/tex]

Then, a square of 13 rows and 13 columns will fit the 169 students.

If the number of students is 1024, then the number of rows N can be calculated as :-

[tex] {N}^{2} = 1024[/tex]

[tex]N = \sqrt{1024} [/tex]

[tex]N = 32[/tex]

169 students will seat in a 13×13 formation.

1024 students will seat in a 32×32 formation (N=32)

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Answer:

33 1/3%

Step-by-step explanation:

Answer:

33.3%

Step-by-step explanation:

We can also work this out in a simpler way by first converting the fraction 1/3 to a decimal. To do that, we simply divide the numerator by the denominator:

1/3 = 0.33333333333333

Once we have the answer to that division, we can multiply the answer by 100 to make it a percentage:

0.33333333333333 x 100 = 33.3333%

(Hope this helps can I pls have brainlist (crown)☺️)

78

Step-by-step explanation:

23+28+16+11=78

people who was interested in the restaurant

Answer:

A

Step-by-step explanation:

Answer:

conversion from gram to kilogram

u divide the gram by 1000

which is 722/ 1000

=0.722kilograms

i.e answer is A

Answer:

140 inches

Step-by-step explanation:

one decagon has 10 sides

14*10= 140

Answer:

1)36

2)1/36

Step-by-step explanation:

Hope it can help you lovelots

Answer:

-7

Step-by-step explanation:

Y2 - Y1 / X2 - X1

-1-6/2-1

-7/1

= -7

Answer:

Maybe 34cm

Sana makatulong..

Answer:

Well to calculate slope you just do

y2-y1/ X2-x1

In this case

9-8/3-2

Which is 1/1

THe slope is 1

Answer:

1

Step-by-step explanation:

The slope is going to be the ratio between the difference of y coordinates, and the difference in x coordinates.

[tex]m= \frac{\Delta y}{\Delta x} = \frac{3-2}{9-8} = \frac11 = 1[/tex]

Answer:

yes I would like to hope on a meet that will be fun

Answer:

10.75 miles

Step-by-step explanation:

Step-by-step explanation:

Given,

The product of Algebraic Expression is equal to the ________ of their H.C.F& L.C.M.

Solution,

Consider the the numbers are a, b.

a \times b = LCM\,of\,\left( {a,b} \right) \times HCF\,of\,\left( {a,b}Given,

Answer:

thx for points ....,..................

[tex]\large\boxed{\tt\:Question}[/tex]

x² - 8x + 12 = 0

Hello meremyj! Here's your answer with explanation.

[tex]\large\boxed{\tt\:Answer\:with\:Explanation}[/tex]

[tex]x ^ { 2 } - 8 x + 12[/tex]

Use the biquadratic formula =》 [tex]x=\frac{-b±\sqrt{\left(-b\right)^{2}-4 ac}}{2}[/tex]

Now,

Using the biquadratic formula & substituting the values....

[tex]x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 12}}{2} \\x=\frac{-\left(-8\right)±\sqrt{64-4\times 12}}{2} \\x=\frac{-\left(-8\right)±\sqrt{64-48}}{2} \\x=\frac{-\left(-8\right)±\sqrt{16}}{2} \\x=\frac{-\left(-8\right)±4}{2} \\\underline{\underline{x=\frac{8±4}{2}} }[/tex]

Now, solve when  [tex]x=\frac{8+4}{2}[/tex]

[tex]x=\frac{8+4}{2}\\x=\frac{12}{2} \\\boxed{\bf\:x=6 }[/tex]

Now, solve when [tex]x = \frac{8-4}{2}[/tex]

[tex]x = \frac{8-4}{2}\\x = \frac{4}{2}\\\boxed{\bf\:x=2}[/tex]

______________

______________

Hope it'll help you!

Lucäžž

Answer:

14.1372 m

Step-by-step explanation:

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Work Shown:

The first four terms are: -4, 14, -22, 50

The idea is to start with the first term (-4) and use the template [tex]\text{nth term} = -2*(\text{previous term}) + 6[/tex] to generate each new term. We multiply the previous term by -2, then add on 6. This is exactly what the recursive equation [tex]a_n = -2(a_{n-1})+6[/tex] is indicating.

Answer:

4800$

Step-by-step explanation:

1 day = 600

7 years = 600 x 2 = 1200$

14 years = 1200 x 2 = 2400$

21 years = 2400 x 2 = 4800$

Answer:

6

Step-by-step explanation:

when calculating (g of f)(3) you first have to substitute 3 in the f(x) equation which would be -2(3)+8=-6+8=2. then you have to do g of f, which is g(2) in this case, and 3(2)=6.

hope this helps! :D

Answer:

576

Step-by-step explanation:

5 + 3 = 8

5 - 2 = 3

8 x 3 = 24

24 to the second power is 576

Answer:

27x+5

Step-by-step explanation:

5+3x(5-2)^2

5+3x(3)^2

5+3x*9

5+27x

27x+5

Answer:

4/7

Step-by-step explanation:

6 -2/2+5 = 4/7

thats it simple

Answer: 10

Step-by-step explanation:

6-x/x+5

6-(2)/(2)+5

Order of Operations

6-1+5

5+5

10

Answer:

$258

Step-by-step explanation:

Answer:

A^7x^2/B

Step-by-step explanation: