Please help me, I have more

Consider the sequence Two-fourths, three-fifths, four-sixths, StartFraction 5 Over 7 EndFraction, ellipsis Which statement descr

Phoenix [80]

Answer:

The sequence converges to 1

Step-by-step explanation:

Given

$\frac{2}{4}. \frac{3}{5}, \frac{4}{6}, \frac{5}{7},...$

Require

Description of the sequence

The given sequence follows:

$\frac{2}{4}. \frac{3}{5}, \frac{4}{6}, \frac{5}{7},... \frac{n+1}{n+3}$

i.e.

$T_n = \frac{n+1}{n+3}$

For every term,

$\frac{n+1}{n+3} < 1$

In other words,

as the value of n increases, $\frac{n+1}{n+3}$ approaches 1

<em>Hence, (c) is true</em>

6 0

3 years ago

Question:

Allisa [31]

We know that 24 is 160% more than some recommended number, let's call it "x." This means 1.6 times the recommended number equals 24. Therefore, all we need to do is solve for x.

$1.6x=24$

$x=\frac{24}{1.6}$

Make sense?

4 0

2 years ago

The area of a circle is increasing at the rate of pi cm^(2)/min. At what rate is the radius increasing when the area is 4pi cm^(

Vikentia [17]

This problem deals the rate of change.
For the formula of the area of a circle, we differentiate both sides with respect to time t.
(A = πr^2) d/dt
dA/dt = 2πr (dr/dt)

Since we don't know yet the radius r, the area of a circle is given.
A = πr^2
r^2 = A/π = 4π/π
r^2 = 4
r = 2 cm

Therefore, the rate of the radius is
dA/dt = 2πr (dr/dt)
dr/dt = (dA/dt)/(2πr)
dr/dt = π/(2π*2)
dr/dt = 0.25 cm/min

Hope this helps.

3 0

3 years ago

Locate the point in the complex plane and express the number in polar form.

EleoNora [17]

Answer:

We kindly invite you to see the result in the image attached below.

The number in polar form is $z = 3\sqrt{5}\cdot e^{i\cdot 0.352\pi}$ .

Step-by-step explanation:

A complex number is represented by elements of the form $a + i\,b$ , for all $a$ , $b$ $\in \mathbb{R}$ . The first part of the sum is the real component of the complex number, whereas the second part of the sum is the imaginary component of the complex number. The real component is located on the horizontal axis and the imaginary component on the vertical axis.

Now we proceed to present the point on the graph: ( $a = 6$ , $b = 3$ ) We kindly invite you to see the result in the image attached below.

The polar form of the complex number is defined by:

$z = r\cdot e^{i\cdot \theta}$ (1)

Where:

$r$ - Magnitude of the complex number, dimensionless.

$\theta$ - Direction of the complex number, measured in radians.

The magnitude and the direction of the complex number are defined by the following formulas:

Magnitude

$r =\sqrt{a^{2}+b^{2}}$ (2)

Direction

$\theta = \tan^{-1} \frac{b}{a}$ (3)

If we know that $a = 6$ and $b = 3$ , then the polar form of the number is:

$r =\sqrt{6^{2}+3^{2}}$

$r = 3\sqrt{5}$

$\theta = \tan^{-1} \frac{6}{3}$

$\theta \approx 0.352\pi \, rad$

$z = 3\sqrt{5}\cdot e^{i\cdot 0.352\pi}$

The number in polar form is $z = 3\sqrt{5}\cdot e^{i\cdot 0.352\pi}$ .

4 0

2 years ago

How to graph y=2^x+3

Mashcka [7]

Answer:

see below

Step-by-step explanation:

It is usually convenient to choose small exponents when graphing an exponential function. You can get a reasonable idea of the shape of the curve using x-values with a magnitude of 3 or less.

The exponential term 2^x has a horizontal asymptote of y=0 for large negative values of x. Adding 3 to that term shifts the horizontal asymptote up to y=3. Of course, everything else is shifted up the same amount.

You know that ...

2^-1 = 1/2

2^0 = 1

2^1 = 2

2^2 = 4

Adding 3 to these values will give you points on the graph for x=-1 to 2.

7 0

3 years ago