PLEASE HELP URGENTTTTT

Determine whether the sequence is geometric. If so, find the common ratio. 3.0, 6.0, 12.0, 24.0

Luba_88 [7]

Answer:

The sequence is geometric and the common ratio is 2

Step-by-step explanation:

A sequence is geometric if each term (after the first one) is equal to the term before it times some constant number, called the 'common ratio'.

Examples: 1, 2, 4, 8, 16, ... has a common ratio of 2 because 2*2 = 4, and 4*2 = 8, and so on.

Also, --> 4, 2, 1, 1/2, 1/4/ 1/8, ... has a common ratio of 1/2 because

4 * 1/2 = the next term 2, and 2 * 1/2 = the next trem 1/4, and son on.

In this case, 3 * 2 = 6

6 * 2 = 12

12 * 2 = 24

The sequence is geometric and the common ratio is 2

6 0

2 years ago

Assume z = x + iy, then find a complex number z satisfying the given equation. d. 2z8 – 2z4 + 1 = 0

kodGreya [7K]

Answer: complex equations has n number of solutions, been n the equation degree. In this case:

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i11,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i101,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i191,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i281,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i78,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i168,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i258,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i348,75°}$

Step-by-step explanation:

I start with a variable substitution:

$Z^{4} = X$

Then:

$2X^{2}-2X+1=0$

Solving the quadratic equation:

$X_{1} =\frac{2+\sqrt{4-4*2*1} }{2*2} \\X_{2} =\frac{2-\sqrt{4-4*2*1} }{2*2}$

$X=\left \{ {{0,5+0,5i} \atop {0,5-0,5i}} \right.$

Replacing for the original variable:

$Z=\sqrt[4]{0,5+0,5i}$

or $Z=\sqrt[4]{0,5-0,5i}$

Remembering that complex numbers can be written as:

$Z=a+ib=|Z|e^{ic}$

Using this:

$Z=\left \{ {{{\frac{\sqrt{2}}{2} e^{i45°} } \atop {{\frac{\sqrt{2}}{2} e^{i-45°} }} \right.$

Solving for the modulus and the angle:

$Z=\left \{ {{\sqrt[4]{\frac{\sqrt{2}}{2} e^{i45}} = \sqrt[4]{\frac{\sqrt{2}}{2} } \sqrt[4]{e^{i45}} } \atop {\sqrt[4]{\frac{\sqrt{2}}{2} e^{i-45}} = \sqrt[4]{\frac{\sqrt{2}}{2} } \sqrt[4]{e^{i-45}} }} \right.$

The possible angle respond to:

$RAng_{12...n} =\frac{Ang +360*(i-1)}{n}$

Been "RAng" the resultant angle, "Ang" the original angle, "n" the degree of the root and "i" a value between 1 and "n"

In this case n=4 with 2 different angles: Ang = 45º and Ang = 315º

Obtaining 8 different angles, therefore 8 different solutions.

3 0

3 years ago

A customer went to a garden shop and bought some potting soil for $11.50 and 9 shrubs. The total bill was $94.75. Write and solv

Vladimir79 [104]

Hey there,

Your question states: A customer went to a garden shop and bought some potting soil for $11.50 and 9 shrubs. The total bill was $94.75. Write and solve an equation to find the price of each shrub.

So, I will do 94.75 minus 11.50 because he bought nice scrubs so that would be 83.25.

I will do 83.25 divided by 9 because that's the number that person bought, each scrub will end up to be 9.25.

Hope this helps.

~Jurgen

6 0

3 years ago

Read 2 more answers

Tom's hair was originally 4 inches long. He asked her hairdresser to cut 1 ⁄3of it off. How many inches did he have cut off?

lord [1]

Answer:

About 3.67

Step-by-step explanation:

1 - 1/3 = 3.66666666667

And 3.66666666667 ≈ 3.67

8 0

2 years ago