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3 years ago

Which graph has an amplitude of 1/2?

Mathematics

1 answer:

Serjik [45]3 years ago

8 0

Answer:

Step-by-step explanation:

The only graph shown in the question doesn't have amplitude 1/2. look for a graph of a periodic wave function that has maximum y-value 1/2 (0.5) and minimum y-value 1/2 (0.5), or if it is not oscillating around the x-axis, verifies that the distance between minimum y-value and maximum y-value is "1" (one). This is because the amplitude is half of the peak-to-peak distance.

Look at the attached image as example.

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hi, i dont undertand number 20 because i was absent in class today and i rerally need help, i will appraciate with the help, and

Mariulka [41]

Given:

The equation is,

$2\log _3x-\log _3(x-2)=2$

Explanation:

Simplify the equation by using logarthimic property.

$\begin{gathered} 2\log _3x-\log _3(x-2)=2 \\ \log _3x^2-\log _3(x-2)=2_{}\text{ \lbrack{}log(a)-log(b) = log(a/b)\rbrack} \\ \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \end{gathered}$

Simplify further.

$\begin{gathered} \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \\ \frac{x^2}{x-2}=3^2 \\ x^2=9(x-2) \\ x^2-9x+18=0 \end{gathered}$

Solve the quadratic equation for x.

$\begin{gathered} x^2-6x-3x+18=0 \\ x(x-6)-3(x-6)=0 \\ (x-6)(x-3)=0 \end{gathered}$

From the above equation (x - 6) = 0 or (x - 3) = 0.

For (x - 6) = 0,

$\begin{gathered} x-6=0 \\ x=6 \end{gathered}$

For (x - 3) = 0,

$\begin{gathered} x-3=0 \\ x=3 \end{gathered}$

The values of x from solving the equations are x = 3 and x = 6.

Substitute the values of x in the equation to check answers are valid or not.

For x = 3,

$\begin{gathered} 2\log _3(3^{})-\log _3(3-2)=2 \\ 2\log _33-\log _31=2 \\ 2\cdot1-0=2 \\ 2=2 \end{gathered}$

Equation satisfy for x = 3. So x = 3 is valid value of x.

For x = 6,

$\begin{gathered} 2\log _36-\log _3(6-2)=2 \\ 2\log _36-\log _34=2 \\ \log _3(6^2)-\log _34=2 \\ \log _3(\frac{36}{4})=2 \\ \log _39=2 \\ \log _3(3^2)=2 \\ 2\log _33=2 \\ 2=2 \end{gathered}$

Equation satifies for x = 6.

Thus values of x for equation are x = 3 and x = 6.

6 0

1 year ago

What is the area of the semicircle?

Serggg [28]

Step-by-step explanation:

$Area (semi-circle)= \frac{r^2\pi }{2}$

$A = \frac{(11)^2\pi }{2}$

$A=\frac{121\pi }{2}$

$A=\frac{379.94}{2}$

$A=189.97$

The area of the semi-circle is 189.97

6 0

2 years ago

The music you hear when listening to a magnetic cassette tape is the result of the magnetic tape passing over magnetic heads, wh

Elden [556K]

Using the given formula T = LS

And given the time is 3 minutes (3 x 60 = 180 seconds)and the speed is 4-1/2 inches per second:

180 = L x 4-1/2

Solve for L by dividing both sides by 4-1/2:

L = 180 / 4-1/2

L = 40

The length should be 40 inches.

7 0

3 years ago

PLEASE HELP ASAP!!!!

Setler [38]

Piecewise Function is like multiple functions with a speific/given domain in one set, or three in one for easier understanding, perhaps.

To evaluate the function, we have to check which value to evalue and which domain is fit or perfect for the three functions.

Since we want to evaluate x = -8 and x = 4. That means x^2 cannot be used because the given domain is less than -8 and 4. For the cube root of x, the domain is given from -8 to 1. That meand we can substitute x = -8 in the cube root function because the cube root contains -8 in domain but can't substitute x = 4 in since it doesn't contain 4 in domain.

Last is the constant function where x ≥ 1. We can substitute x = 4 because it is contained in domain.

Therefore:

$\large{ \begin{cases} f( - 8 ) = \sqrt[3]{ - 8} \\ f(4) = 3 \end{cases}}$

The nth root of a can contain negative number only if n is an odd number.

$\large{ \begin{cases} f( - 8 ) = \sqrt[3]{ - 2 \times - 2 \times - 2} \\ f(4) = 3 \end{cases}} \\ \large{ \begin{cases} f( - 8 ) = - 2\\ f(4) = 3 \end{cases}}$