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2 years ago

Write the complex number in polar form with argument between 0 and 2.

Mathematics

1 answer:

pychu [463]2 years ago

5 0

Lets say that √(3+i) is the magnitude of your vector. In polar form, i represents the x component and j represents the y component of the vector. Therefore, the polar form is icosθ√(3+i) + jsinθ√(3+i)

draw a diagram :

z = r(cos θ + i sin θ), where z = complex number, r = modulus, θ = angle of rotation For the given:r = 2θ = π/6 √3 + i = 2(cos π/6 + i sin π/6)

hope thz hlpz ✿

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Find f(x)+g(x), given f(x)=x^2-8 and g(x)=-2-x^2

Gnoma [55]

$\left(x^2-8\right)+\left(-2-x^2\right)=-10$

$\left(x^2-8\right)+\left(-2-x^2\right)$

$=x^2-8-2-x^2$

$=x^2-x^2-8-2$

$=-8-2$

$=-10$

8 0

3 years ago

The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price

likoan [24]

Answer:

A) 3%

B) Product A

Step-by-step explanation:

Exponential Function

General form of an exponential function: $y=ab^x$

where:

a is the initial value (y-intercept)
b is the base (growth/decay factor) in decimal form
x is the independent variable
y is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Part A

Product A

Assuming the function for Product A is exponential:

$f(x) = 0.69(1.03)^x$

The base (b) is 1.03. As b > 1 then it is an increasing function.

To calculate the percentage increase/decrease, subtract 1 from the base:

⇒ 1.03 - 1 = 0.03 = 3%

Therefore, product A is increasing by 3% each year.

Part B

$\sf percentage\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100$

To calculate the percentage change in Product B, use the percentage change formula with two consecutive values of f(t) from the given table:

$\implies \sf percentage\:change=\dfrac{10201-10100}{10100}\times 100=1\%$

Check using different two consecutive values of f(t):

$\implies \sf percentage\:change=\dfrac{10303.01-10201}{10201}\times 100=1\%$

Therefore, as 3% > 1%, Product A recorded a greater percentage change in price over the previous year.

Although the question has not asked, we can use the given information to easily create an exponential function for Product B.

Given:

a = 10,100
b = 1.01
n = t - 1 (as the initial value is for t = 1 not t = 0)

$\implies f(t) = 10100(1.01)^{t-1}$

To check this, substitute the values of t for 1 through 4 into the found function:

$\implies f(1) = 10100(1.01)^{1-1}=10100$

$\implies f(2) = 10100(1.01)^{2-1}=10201$

$\implies f(3) = 10100(1.01)^{3-1}=10303.01$

$\implies f(4) = 10100(1.01)^{4-1}=10406.04$

As these values match the values in the given table, this confirms that the found function for Product B is correct and that Product B increases by 1% per year.

4 0

2 years ago

-1 < x < 4 x is an integer. Write down the possible values of x.

bogdanovich [222]

Answer:

0, 1, 2, 3

Step-by-step explanation:

-1 < x < 4 means that x has to be an integer (whole number aka no fractions) between -1 and 4. Note that the < and > means that x cannot be -1 or 4 since it has to be greater than -1, or smaller than 4.

7 0

2 years ago

10) Given that two tangent lines are constructed from the shared point A outside a circle with the center O and points of tangen

lora16 [44]

Those two angles are congruent.

_____
The angles are corresponding parts of congruent triangles (CPCT). Triangles OBA and OCA are right triangles congruent by the HL postulate. The "H" is segment OA. The "L" is the radius, OB or OC. Of course the angles at B and C are 90° as with any radius and tangent line.

5 0

3 years ago

URGENT FIND THE POINT OF INTERSECTION. 16x+12y=-12 16x-10y=10

Scrat [10]

Answer:

(0, -1)

Step-by-step explanation:

hope this helps :)

6 0

3 years ago