Finance Name: This project has two problems centered around finance - one question about the mathematical explosion of compound interest and the other about the stock market. Problem 1 1. Let's use mathematics to see why time is so important when it comes to saving for retirement. Suppose you have $10,000 to invest in a mutual fund that averages a 12% annual return. a) After 5 years, what is the value of the fund? Explain or show your work. b) After 10 years, what is the value of the fund? Explain or show your work. c) After 20 years, what is the value of the fund? Explain or show your work. d) it looks like time doubles in parts b) and c) from 10 to 20 years. Does the account value also double? if not, why not?

True. A rational expression is undefined whenever its denominator is zero. This is because division by zero is not defined.

In mathematics, a rational expression is defined as the quotient of two polynomials, where the denominator represents the divisor. When the denominator of a rational expression becomes zero, it results in division by zero, which is undefined. Division by zero is not a valid operation in mathematics, and it leads to an undefined value. Therefore, to determine if a rational expression is undefined, we need to check if its denominator evaluates to zero. If the denominator is zero, the rational expression is undefined. Also there is division by zero, or related concepts in mathematics.

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Answer:

5+5=10

Step-by-step explanation:

5+5=10

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(a)  The synchronous reactance of the alternator is 0.001953125 Ω.

The synchronous reactance [tex]X_{s}[/tex] of the alternator can be calculated using the formula:

[tex]X_{s} = (Vt^2) / (3 * VL * S_{base})[/tex]

where [tex]V_{t}[/tex] is the rated line-to-line voltage of the alternator, VL is the rated line-to-neutral voltage of the alternator (which is the same as the rated voltage for a Y-connected alternator), and S_base is the apparent power rating of the alternator (which is equal to the rated power factor of the alternator times the rated apparent power). Substituting the given values, we get:

[tex]X_{s} = (13.5^2) / (3 * 13.5 * 1600) = 0.001953125[/tex] Ω

Therefore, the synchronous reactance of the alternator is 0.001953125 Ω.

(b) The percentage voltage regulation at full-load 0.8 power factor leading is 23.15%.

The percentage voltage regulation (%VR) at full-load 0.8 power factor leading can be calculated using the formula:

%VR = (E - Vl) / Vl * 100%

where E is the generated voltage of the alternator, and Vl is the terminal voltage of the alternator at full-load 0.8 power factor leading. We can assume that the armature resistance and inductance are negligible compared to Xs for this calculation. Using the given values, we first calculate the apparent power S of the load:

S = P / pf = 1280 / 0.8 = 1600 kVA

Since the load is at unity power factor, the current drawn from the alternator is also 1600 A. Therefore, the voltage drop across Xs is:

Vx = Xs * I = 0.001953125 * 1600 = 3.125 V

The generated voltage E is equal to the terminal voltage Vl plus the voltage drop across Xs:

E = Vl + Vx

The percentage voltage regulation is then:

%VR = (E - Vl) / Vl * 100% = (Vl + Vx - Vl) / Vl * 100% = Vx / Vl * 100%

Substituting the given values, we get:

%VR = 3.125 / 13.5 * 100% = 23.15%

Therefore, the percentage voltage regulation at full-load 0.8 power factor leading is 23.15%.

(c) If the %VR value is taken at half-load lagging power factor, it will be higher than the %VR value at full-load 0.8 power factor leading. This is because the load impedance at half-load lagging power factor has a lower magnitude than the load impedance at full-load 0.8 power factor leading, which means that the voltage drop across [tex]X_{s}[/tex] will be a larger fraction of the terminal voltage, resulting in a larger %VR value.

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Answer:

Complementary

x= 60

Step-by-step explanation:

Answer:

The angles are complementary.

X =  60

Step-by-step explanation:

The measure of the third angle, C, is 30 degrees. So, the correct answer is (c) 30.

Let's assume the three angles of the triangle are A, B, and C, where A, B, and C are measured in degrees.

We know that the sum of the angles in a triangle is 180 degrees. Therefore, we can write the equation:

A + B + C = 180

The obtain of two angles is 150 degrees, we can set up another equation:

A + B = 150

To obtain the measure of the third angle, which we'll call C, we can subtract the sum of the other two angles from 180:

C = 180 - (A + B)

Substituting the value of the sum of two angles (150 degrees), we have:

C = 180 - 150

C = 30

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Answer:

answer is x=3 and y=10

Step-by-step explanation:

Forgot to isolate y and x and simplify

Answer:

the second one is 20 i think

Step-by-step explanation:

Answer:

Step-by-step explanation:

(-3)x + (3)(-12)

= -3x -36

or -3(x + 12)

Answer:

Step-by-step explanation:

(-3)x + 3(-12) = (-3) (x + 12)

(-3) is both the two terms. So we can take (-3) as common

Answer:

the answer is 120 degree

Answer:

(A) 30 degree

Step-by-step explanation:

Just subtract 180 with 120 = 60

then add 60 and 90 = 150

after that 180 - 50 = 30

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Answer:

(x+1)^2 + y ^2 = 16

Step-by-step explanation:

center: (-1,0)

radius=4

(x-h)^2 + (y-k)^2 = r^2

(h,k) = center

plug in the center

(x+1)^2 + (y+0) ^2 = r^2

r^2 = (4)^2

r^2=16

(x+1)^2 + y^2 = 16

Solving a set of linear inequalities in several variables is an NP-hard problem, meaning there is no known polynomial-time algorithm to find a satisfying assignment.

Unlike linear equalities, solving a set of linear inequalities in several variables is an NP-hard problem. This means that there is no known polynomial-time algorithm to find a satisfying assignment for all instances of such problems. The complexity arises from the fact that there are infinitely many potential solutions, making it challenging to determine whether a feasible assignment exists or not. To find a satisfying assignment for linear inequalities, algorithms typically use heuristics or approximation techniques that do not guarantee optimality or completeness. Various methods, such as linear programming or constraint satisfaction algorithms, can be employed, but they may have exponential time complexity in the worst case. Therefore, solving a set of linear inequalities generally requires more computational resources and time compared to solving linear equalities.

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Answer:

volume=1yd x 1yd = q cubic yard

Answer:

$135,000

Step-by-step explanation:

108000*1.25

Answer:

lol same facts though

Step-by-step explanation:

Answer:

Your future doesn't really depend on school to be honest, but school is one of the options to a great future. Even college and etc dropouts become successful.

Answer:

If you add teacher plus students which is 490+10=500

you get 500 people in total after that you divide 500 by 50 and you get 10 so you will need 10 busses in total hope this helped!

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

u have it right it increases by 1:75 per time

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

it is A because it is increasing by 1.75 each week

Answer:

Answers is D

Step-by-step explanation:

2x = 60° because they are vertically opposite angles.

x=60÷2=30°

Answer:

Step-by-step explanation:

Answer:

Both commutative and associative

Answer:

19x−14y

Steps:

7x-3y+4x-5y+8x-6y

=19x-3y-5y-6y

= 19x−14y

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Answer:

19x-14y

Step-by-step explanation:

rearrange

7x+4x+8x-3y-5y-6y

solve the coefficient and add the variables

Answer:

6(2x+3)

Step-by-step explanation:

There's really no way to explain this. Take the number that all of the numbers in the equation can be divisible by and then single it out and then yeah.

Hope this helped! :)

Answer:

Step-by-step explanation:

m = [tex]\frac{-1}{4}[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

See the attached.

I will come back to this question when it has been further clarified.

(Honestly I just really need to delete this answer since I misread the question but it doesn't give me an option to delete it).

To find the volume of the glass formed by rotating the shaded region about the y-axis, we can use the method of cylindrical shells.

The volume of a solid of revolution using cylindrical shells is given by the integral:

V = ∫[a,b] 2πx * f(x) * dx

In this case, the function representing the curve that forms the inside of the glass is y = x^4/2. We need to find the limits of integration, a and b, which correspond to the x-values where the shaded region begins and ends.

From the graph, it appears that the shaded region begins at x = -1 and ends at x = 1. So, the limits of integration are -1 to 1.

Now, we can calculate the volume of the glass using the integral formula:

V = ∫[-1,1] 2πx * [tex](x^4/2) * dx[/tex]

V = π * ∫[-1,1] [tex]x^5 dx[/tex]

Using the power rule of integration, we integrate x^5:

V = π * [x^6/6] from -1 to 1

V = π * [[tex](1^6/6) - (-1^6/6)][/tex]

V = π * [(1/6) - (1/6)]

V = π * 0

Therefore, the volume of the glass is 0 cubic units.

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Answer:

11 Seconds

Step-by-step explanation:

Swimming pool volume:

25.8 × 11.9 × 1.1 = 337.722

Time to empty pool:

337.722 ÷ 29.8 = 11.3329530201 ≈ 11 seconds

Answer:

3. Likely

Step-by-step explanation:

Answer: Common factor

common factor. a whole number that is a factor of two or more nonzero whole numbers

Step-by-step explanation:

[tex] \purple{ \tt{ \huge{ \: ✨Answer ✨ \: }}}[/tex]

[tex] \: \: \: \red{ \boxed{ \boxed{ \huge{ \tt{ \: common \: factor \: }}}}}[/tex]