Determinando o valor desconhecido , dividido por 5

$ 20,000 is invested at a rate of 5% compounded quarterly. Identify the compound interest function ta model the situation. Then

liq [111]

Answer:

the balance after 5 years is: 26540.744

Step-by-step explanation:

Given the information:

P = initial balance = $ 20,000
r = interest rate (decimal) = 5% = 0.05
n = number of times compounded annually = 4
t = time = 5

We have the compound interest function ta model the situation is:

$A=P(1+\frac{r}{n} )^{nt}$

<=> A = $20000(1+\frac{0.05}{4} )^{4*5}$

<=> A = $26540.744

Hence, the balance after 5 years is: $26540.744

7 0

3 years ago

Because of their connection with secant lines, tangents, and instantaneous rates, limits of the form ModifyingBelow lim With h

Gre4nikov [31]

Answer:

$\dfrac{1}{2\sqrt{x}}$

Step-by-step explanation:

$f(x) = \sqrt{x} = x^{\frac{1}{2}}$

$f(x+h) = \sqrt{x+h} = (x+h)^{\frac{1}{2}}$

We use binomial expansion for $(x+h)^{\frac{1}{2}}$

This can be rewritten as

$[x(1+\dfrac{h}{x})]^{\frac{1}{2}}$

$x^{\frac{1}{2}}(1+\dfrac{h}{x})^{\frac{1}{2}}$

From the expansion

$(1+x)^n=1+nx+\dfrac{n(n-1)}{2!}+\ldots$

Setting $x=\dfrac{h}{x}$ and $n=\frac{1}{2}$ ,

$(1+\dfrac{h}{x})^{\frac{1}{2}}=1+(\dfrac{h}{x})(\dfrac{1}{2})+\dfrac{\frac{1}{2}(1-\frac{1}{2})}{2!}(\dfrac{h}{x})^2+\tldots$

$=1+\dfrac{h}{2x}-\dfrac{h^2}{8x^2}+\ldots$

Multiplying by $x^{\frac{1}{2}}$ ,

$x^{\frac{1}{2}}(1+\dfrac{h}{x})^{\frac{1}{2}}=x^{\frac{1}{2}}+\dfrac{h}{2x^{\frac{1}{2}}}-\dfrac{h^2}{8x^{\frac{3}{2}}}+\ldots$

$x^{\frac{1}{2}}(1+\dfrac{h}{x})^{\frac{1}{2}}-x^{\frac{1}{2}}=\dfrac{h}{2x^{\frac{1}{2}}}-\dfrac{h^2}{8x^{\frac{3}{2}}}+\ldots$

$\dfrac{x^{\frac{1}{2}}(1+\dfrac{h}{x})^{\frac{1}{2}}-x^{\frac{1}{2}}}{h}=\dfrac{1}{2x^{\frac{1}{2}}}-\dfrac{h}{8x^{\frac{3}{2}}}+\ldots$

The limit of this as $h\to 0$ is

$\lim_{h\to0} \dfrac{f(x+h)-f(x)}{h}=\dfrac{1}{2x^{\frac{1}{2}}}=\dfrac{1}{2\sqrt{x}}$ (since all the other terms involve $h$ and vanish to 0.)

8 0

3 years ago

Find the slope between (8, -2) and (7, -2).

lions [1.4K]

-0.25 is the slope between those two points.

3 0

3 years ago

Is the system of equations consistent and independent, consistent and dependent, or inconsistent? y=4x−4y=−4x 4 Select the corre

Amiraneli [1.4K]

System of equations helps us to compare two different situations. The system is Independent Consistent System.

<h3>What is System of equation?</h3>

Inconsistent System

A system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

A system of the equation to be Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

A system of the equation to be Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.

Given to us

y = 4x - 4

y = -4x + 4

As we have the two equations, substitute the value of y of both the equations,

4x - 4 = -4x + 4

8x = 8

x = 1

We have the value of x as 1, substitute the value of x in the equation of y,

y = 4(1) - 4

y = 0

Since the two equations have a unique solution, therefore, the system is Independent Consistent System.

Learn more about System of equation:

brainly.com/question/12895249

8 0

3 years ago

There are 42 female performers in a dance recital. The ratio of men to women is 4:7. How many men are in the dance recital?

marusya05 [52]

Answer:

Step-by-step explanation:

The first thing I did was divide 42 by 7 to get the equivilant for 1.

42 ^ 7 = 6

So,

1 = 6

This means that all you have to do to get the amount of men is to multiply 4 by 6.

4 * 6 = 24

So, there are 24 men and 42 females.

<u><em>Hope this helps!</em></u>

5 0

3 years ago