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3 years ago

Find the sixth term of the geometric sequence 9, 18, 36, ...

Mathematics

1 answer:

timama [110]3 years ago

6 0

Answer:

This is a geometric sequence because any term divided by the previous term is a constant called the common ratio. r=36/18=18/9=2 A geometric sequence is expressed as

\begin{gathered}a_n=ar^{n-1},\text{ where a=initial term, r=common ratio, n=term number}\\ \\ a_n=9(2^{n-1})\\ \\ a_6=9(2^5)\\ \\ a_6=288\end{gathered}an=arn−1, where a=initial term, r=common ratio, n=term numberan=9(2n−1)a6=9(25)a6=288

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Orlando invests $1000 at 6% annual interest compounded daily and Bernadette invests $1000 at 7%

Montano1993 [528]

Answer:

6 Years

Step-by-step explanation:

Orlando invests $1000 at 6% annual interest compounded daily.

Orlando's investment = $A=1000(1+\frac{0.06}{365})^{(365\times t)}$

Bernadette invests $1000 at 7% simple interest.

Bernadette's investment = A = 1000(1+0.07×t)

By trail and error method we will use t = 5

Bernadette's investment will be after 5 years

1000(1 + 0.07 × 5)

= 1000(1 + 0.35)

= 1000 × 1.35

= $1350

Orlando's investment after 5 years

$A=1000(1+\frac{0.06}{365})^{(365\times 5)}$

= $1000(1+0.000164)^{1825}$

= $1000(1.000164)^{1825}$

= 1000(1.349826)

= 1349.825527 ≈ $1349.83

After 5 years Orlando's investment will not be more than Bernadette's.

Therefore, when we use t = 6

After 6 years Orlando's investment will be = $1433.29

and Bernadette's investment will be = $1420

So, after 6 whole years Orlando's investment will be worth more than Bernadette's investment.

8 0

3 years ago

James has to fill 40 water bottles for the soccer team. Each bottle holds 500 milliliters of water. How many liters of water doe

Mandarinka [93]

Answer:

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

A door of a lecture hall is in a parabolic shape. The door is 56 inches across at the bottom of the door and parallel to the flo

Arada [10]

Answer:

The parabolic shape of the door is represented by $y - 32 = -\frac{2}{49}\cdot x^{2}$ . (See attachment included below). Head must 15.652 inches away from the edge of the door.

Step-by-step explanation:

A parabola is represented by the following mathematical expression:

$y - k = C \cdot (x-h)^{2}$

Where:

$h$ - Horizontal component of the vertix, measured in inches.

$k$ - Vertical component of the vertix, measured in inches.

$C$ - Parabola constant, dimensionless. (Where vertix is an absolute maximum when $C < 0$ or an absolute minimum when $C > 0$ )

For the design of the door, the parabola must have an absolute maximum and x-intercepts must exist. The following information is required after considering symmetry:

$V (x,y) = (0, 32)$ (Vertix)

$A (x, y) = (-28, 0)$ (x-Intercept)

$B (x,y) = (28. 0)$ (x-Intercept)

The following equation are constructed from the definition of a parabola:

$0-32 = C \cdot (28 - 0)^{2}$

$-32 = 784\cdot C$

$C = -\frac{2}{49}$

The parabolic shape of the door is represented by $y - 32 = -\frac{2}{49}\cdot x^{2}$ . Now, the representation of the equation is included below as attachment.

At x = 0 inches and y = 22 inches, the distance from the edge of the door that head must observed to avoid being hit is:

$y -32 = -\frac{2}{49} \cdot x^{2}$