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3 years ago

What term denotes the time for one cycle of a periodic process?

Mathematics

2 answers:

ziro4ka [17]3 years ago

3 0

Wavelength denotes the time for one cycle of a periodic process

kobusy [5.1K]3 years ago

3 0

The wave length

I hope this helps you

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If the sum of the zereos of the quadratic polynomial is 3x^2-(3k-2)x-(k-6) is equal to the product of the zereos, then find k?

lys-0071 [83]

Answer:

Step-by-step explanation:

So I'm going to use vieta's formula.

Let u and v the zeros of the given quadratic in ax^2+bx+c form.

By vieta's formula:

1) u+v=-b/a

2) uv=c/a

We are also given not by the formula but by this problem:

3) u+v=uv

If we plug 1) and 2) into 3) we get:

-b/a=c/a

Multiply both sides by a:

-b=c

Here we have:

a=3

b=-(3k-2)

c=-(k-6)

So we are solving

-b=c for k:

3k-2=-(k-6)

Distribute:

3k-2=-k+6

Add k on both sides:

4k-2=6

Add 2 on both side:

4k=8

Divide both sides by 4:

k=2

Let's check:

$3x^2-(3k-2)x-(k-6) \text{ with }k=2$ :

$3x^2-(3\cdot 2-2)x-(2-6)$

$3x^2-4x+4$

I'm going to solve $3x^2-4x+4=0$ for x using the quadratic formula:

$\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\frac{4\pm \sqrt{(-4)^2-4(3)(4)}}{2(3)}$

$\frac{4\pm \sqrt{16-16(3)}}{6}$

$\frac{4\pm \sqrt{16}\sqrt{1-(3)}}{6}$

$\frac{4\pm 4\sqrt{-2}}{6}$

$\frac{2\pm 2\sqrt{-2}}{3}$

$\frac{2\pm 2i\sqrt{2}}{3}$

Let's see if uv=u+v holds.

$uv=\frac{2+2i\sqrt{2}}{3} \cdot \frac{2-2i\sqrt{2}}{3}$

Keep in mind you are multiplying conjugates:

$uv=\frac{1}{9}(4-4i^2(2))$

$uv=\frac{1}{9}(4+4(2))$

$uv=\frac{12}{9}=\frac{4}{3}$

Let's see what u+v is now:

$u+v=\frac{2+2i\sqrt{2}}{3}+\frac{2-2i\sqrt{2}}{3}$

$u+v=\frac{2}{3}+\frac{2}{3}=\frac{4}{3}$

We have confirmed uv=u+v for k=2.

4 0

2 years ago

What is the slope of a line that is parallel to the x-axis? m=

Ludmilka [50]

Parallel to the x-axis and perpendicular to the y-axis: zero
Parallel to the y-axis and perpendicular to the x-axis: undefined
I hope that's right, that's how I remember it

6 0

3 years ago

Two-thirds a number plus 4 is 7

ICE Princess25 [194]

The equation (form) is: $\frac{2}{3}x + 4 = 7$

The solution of the equation is: $x = \frac{9}{2}$

Explanation:

First, let's call the number we are going to solve for "x".

Then two thirds of this number can be written as:

$\frac{2}{3}x$

Then "plus 4" means add 4 we get:

$\frac{2}{3}x + 4$

"is 7" means that the above expression is equal to 7 (as follows):

$\frac{2}{3}x + 4 = 7$

The solution of the above equation is:

$\frac{2}{3}x + 4 = 7 \\ \frac{2}{3}x = 3 \\ x = \frac{9}{2}$

6 0

2 years ago

42/77 in simplest form

svlad2 [7]

The answer is 6/11 :))

8 0

3 years ago

Please help me!!! :(

PSYCHO15rus [73]

Answer:

$15.75x^{10}y^{19}$

Step-by-step explanation:

To find the 5th term in the expansion, we first will need to apply the binomial theorem. I have attached an image of the binomial theorem formula due to not being able to type it.

After applying the binomial theorem and simplifying, you should get:

$512x^{18}y^{27}-576x^{16}y^{25}+288x^{14}y^{23}-84x^{12}y^{21}+\frac{63x^{10}y^{19}}{4}-\frac{63x^8y^{17}}{32}+\frac{21x^6y^{15}}{128}-\frac{9x^4y^{13}}{1024}+\frac{9x^2y^{11}}{32768}-\frac{y^9}{262144}$

Our 5th term here is: $\frac{63x^{10}y^{19}}{4}$ which is equal to $15.75x^{10}y^{19}$

~Hope this helps! Sorry if my answer is confusing at all, it's pretty difficult to explain.~

4 0

2 years ago