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MatroZZZ [7]
4 years ago
13

Maria invests $6,154 in a savings account with a fixed annual interest rate of 8% compounded continuously. What will the account

balance be after 10 years?
Mathematics
1 answer:
VladimirAG [237]4 years ago
3 0

Answer:

$13,695.98

Step-by-step explanation:

Continuously compounded interest formula:

A = Pe^{rt}

where

A = future value

P = principal (present value of amount invested)

e = mathematical constant, the base of natural logarithms

r = interest rate

t = time in years

We have: P = 6154; r = 8% = 0.08; t = 10

A = 6154e^{0.08 \times 10}

A = 6154e^{0.8}

A = 6154 \times 2.2255

A = 13695.98

Answer: $13,695.98

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Given the function f(x) x^2-2x/x^3 +9x^2-10x Find any holes, vertical asymptotes, and horizontal asymptotes there may be.
yulyashka [42]

Answer:

See below

Step-by-step explanation:

I assume you mean f(x)=\frac{x^2-2x}{x^3+9x^2-10x}:

Holes: Since f(x)=\frac{x^2-2x}{x^3+9x^2-10x} reduces to f(x)=\frac{x(x-2)}{x(x^2+9x-10)}, then there is a hole at x=0 as x exists in both the numerator and denominator (however, its limit as x approaches 0 is 1/5).

Vertical Asymptotes: If we further reduce f(x)=\frac{x(x-2)}{x(x^2+9x-10)} to f(x)=\frac{x-2}{(x+10)(x-1)}, then we see that there are vertical asymptotes at x=-10 and x=1

Horizontal Asymptotes: As the degree of the numerator is less than the degree of the numerator (2), then there is a horizontal asymptote at y=0

4 0
2 years ago
Write an equation in which the quadratic expression 3x^2+6x-24 equals 0. Show the expression in factored form and explain what y
mr_godi [17]

Answer:

3x² + 6x - 24 = 0

(3x - 6)(x + 4) = 0

x = -4 , x = 2 when y = 0

Step-by-step explanation:

3x² + 6x - 24 = 0

(3x - 6)(x + 4) = 0

Means

3x - 6 = 0 ⇒ 3x = 6 ⇒ x = 6 ÷ 3 = 2

x + 4 = 0 ⇒ x = -4

The Parabola which represents the quadratic equation intersects x-axis at

points (2 , 0) and (-4 , 0)

5 0
3 years ago
Need help with this math question
anastassius [24]

Answer:

The vertex is: (6, 8)

Step-by-step explanation:

First solve the equation for the variable y

x^2-4y-12x+68=0

Add 4y on both sides of the equation

4y=x^2-4y+4y-12x+68

4y=x^2-12x+68

Notice that now the equation has the general form of a parabola

ax^2 +bx +c

In this case

a=1\\b=-12\\c=68

Add (\frac{b}{2}) ^ 2 and subtract (\frac{b}{2}) ^ 2 on the right side of the equation

(\frac{b}{2}) ^ 2=(\frac{-12}{2}) ^ 2\\\\(\frac{b}{2}) ^ 2=(-6) ^ 2\\\\(\frac{b}{2}) ^ 2=36

4y=(x^2-12x+36)-36+68

Factor the expression that is inside the parentheses

4y=(x-6)^2+32

Divide both sides of the equality between 4

\frac{4}{4}y=\frac{1}{4}(x-6)^2+\frac{32}{4}

y=\frac{1}{4}(x-6)^2+8

For an equation of the form

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

the vertex is: (h, k)

In this case

h=6\\k =8

the vertex is: (6, 8)

5 0
3 years ago
Simplify 2.8-5.8n-3n+5
emmasim [6.3K]

Answer: -8.8n + 7.8

Step-by-step explanation:

2.8 - 5.8n - 3n + 5

Add -5.8n and -3n to get -8.8n

Add 2.8 and 5 together to get 7.8

6 0
4 years ago
Read 2 more answers
HELP WILL MARK YOU BRAINLIEST!! NO FAKE ANSWERS
lara31 [8.8K]
The answer is B

Solution:
Find perimeter (L+B+L+B)
600+300+600+300= 1,800
1,800/3= 600
600x500= 300,000
6 0
3 years ago
Read 2 more answers
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