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Naya [18.7K]
1 year ago
15

What is the midline equation of y = -4sin (2x - 7) + 3?

Mathematics
2 answers:
Georgia [21]1 year ago
4 0

Answer:

y = 3.

Step-by-step explanation:

The minimum and maximum value of \sin(2\, x - 7) over all real x are (-1) and 1, respectively. Hence, the maximum and minimum value of y = -4\, \sin(2\, x - 7) + 3 would be:

  • Maximum: y = (-4)\, (-1) + 3 = 7.
  • Minimum: y = (-4)\, (1)\ + 3 = (-1).

The midline equation of a sine wave is a horizontal line that is right in the middle of maximum and minimum y-values of that sine wave. In the sine wave in this question, the average of the maximum and minimum y\!-values is (1/2) \, (7 + (-1)) = 3. Hence, the midline equation of this sine wave would be y = 3.

AVprozaik [17]1 year ago
4 0

\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}

<h3>Given:</h3>

▪ \longrightarrow \sf{y = -4 \sin (2x - 7) + 3}

This is the equation of the horizontal line equal to the average value of <em>y</em> for the function given.

\leadsto This will correspond to the value where the sine function has a value of 0, which is the average value of the function:

\longrightarrow \sf{Y_{avg } = −4(0) + 3 = 0 + 3 = 3}

\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}

\small\bm{The \: equation\: of \: the \: midline \: is \: \:  y=3.}

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Find the product of (x + 5)(x − 5).
AfilCa [17]

Answer:

x² - 30 + 5x

Step-by-step explanation:

(x + 5)(x − 5)

=x(x − 5)+5(x − 5)

=x² - 5 + 5x - 25

=x² - 30 + 5x

6 0
3 years ago
n a jar of coins, the ratio of nickels to dimes is 5:7. If the jar contains 350 dimes, how many nickels are there?
irina1246 [14]

Answer:

250 nickles

Step-by-step explanation:

Nickles and dimes are coins with different currency values. One nickel(N) is equal to 5 cents while one dime(D) is equal to 10 cents. The ratio of nickel:dime is 5:7, to put into the equation it will be:

N/D= 5/7

7N=5D   ---> 1st equation

There are 350 dimes, the equation will be:

D=350   ----> 2nd equation

We can find out the number of nickels by substitute the 2nd equation into the first. The calculation will be

7N=5D

N= 5D/7

N=5(350)/7

N=  250

4 0
3 years ago
The graph of y=f(x) is shown on the grid​
Ket [755]

Answer:

can't be seen

Step-by-step explanation:

try again by asking a new question

6 0
3 years ago
Alexander deposited money into his retirement account that is compounded annually at an interest rate of 7%.
anzhelika [568]
Tow rates are equivalent if tow initial investments over a the same time, produce the same final value using different interest rates.

For the annually rate we have that:
V_{0} =(1+ i_{a} ) ^{1}
Where
V_{0} = initial investment.
i_{a} = annually interest rate in decimal form.
And the exponent (1) represents the full year.

For the quarterly interest rate we have that:
V_{0} =(1+ i_{q} ) ^{4}
Where
V_{0} = initial investment.
i_{q} = quarterly interest rate in decimal form.
And the exponent (4) the 4 quarters in the full year.

Since the rates are equivalent if tow initial investments over a the same time, produce the same final value, then
(1+ i_{a} )=(1+ i_{q} ) ^{4}
Notice that we are not using the initial investment V_{0} since they are the same.

The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
7%/100 = 0.07
Now, we can replace the value in our equation to get:
(1+0.07)=(1+ i_{q} ) ^{4}
1.07=(1+ i_{q} ) ^{4}
\sqrt[4]{1.07} =1+ i_{q}
 i_{q} = \sqrt[4]{1.07} -1
i_{q} =0.017
Finally, we multiply the quarterly interest rate in decimal form by 100% to get:
(0.017)(100%) = 1.7%
We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.


6 0
3 years ago
What is the common denominator of (5/x^2-4) - (2/x+2) in the complex fraction (2/x-2) - (3/x^2-4)/(5/x^2-4) - (2/x+2)
PIT_PIT [208]

9514 1404 393

Answer:

  • common denominator: (x² -4)
  • simplified complex fraction: (2x +1)/(9 -2x)

Step-by-step explanation:

It is helpful to remember the factoring of the difference of squares:

  a² -b² = (a -b)(a +b)

__

Your denominator of (x² -4) factors as (x -2)(x +2). You will note that one of these factors is the same as the denominator in the other fraction.

It looks like you want to simplify ...

  \dfrac{\left(\dfrac{2}{x-2}-\dfrac{3}{x^2-4}\right)}{\left(\dfrac{5}{x^2-4}-\dfrac{2}{x+2}\right)}=\dfrac{\left(\dfrac{2(x+2)}{(x-2)(x+2)}-\dfrac{3}{(x-2)(x+2)}\right)}{\left(\dfrac{5}{(x-2)(x+2)}-\dfrac{2(x-2)}{(x-2)(x+2)}\right)}\\\\=\dfrac{2(x+2)-3}{5-2(x-2)}=\boxed{\dfrac{2x+1}{9-2x}}

3 0
3 years ago
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