1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Levart [38]
3 years ago
7

Write an equation for the given function given the period, phase shift, and vertical shift.

Mathematics
1 answer:
lbvjy [14]3 years ago
4 0

ANSWER

y = \cot(x  -  \frac{\pi}{3} )  + 2

EXPLANATION

The cotangent function that is fully transformed is of the form

y =a  \cot(bx + c)  + d

where 'a' is the amplitude.

\frac{\pi}{b}  = \pi

is the period.

This implies that b=1

The phase shift is

\frac{c}{b}  =  -  \frac{\pi}{3}

Substitute b=1 to get;

c  =  -  \frac{\pi}{3}

and d=2 is the vertical shift.

We choose a=1 to get the required function as

y = \cot(x  -  \frac{\pi}{3} )  + 2

You might be interested in
Two thirds divided by one quarter
Stells [14]

Answer:

2.66666666667

Step-by-step explanation:

6 0
3 years ago
Find x if a] 5^x=625 root 5 b] 3^2x-1 = 243
katen-ka-za [31]

x=3, you can find this by using finding common bases for equation b because 243=3^5. Because of that you can get rid of three on both sides to get the equation 2x-1=5 and then just solve for x to get x=3. For the first equation 5^3=625 so that also proves x=3.

Sorry if my explanation is a little disorganized if you need more help feel free to ask

6 0
3 years ago
Jack biked to his friend house at a speed of 10 mph. When he was returning home it was raining. So he biked much slower - at 6 m
AVprozaik [17]

Answer:

  7.5

Step-by-step explanation:

The relation between time, speed, and distance is ...

  time = distance/speed

If distance is "1 round trip", then the time going is ...

  going = 0.5/(10 mi/h) . . . . for 1/2 round trip

and the time coming is ...

  coming = 0.5/(6 mi/h)

Then the average speed for the full round trip is ...

  speed = distance/time

  average speed = 1/(going + coming) = 1/(0.5/10 +0.5/6) mi/h

  = 1/((3+5)/60) mi/h

  = 60/8 mi/h = 7.5 mi/h

Jack's average speed for the round trip was 7.5 mph.

7 0
3 years ago
Can you help me on both of this problems
AlekseyPX

Answer:

9. Option D, 2(3x + 5) and 6x + 10

10. 9 + 3 (10÷2) - 5² = -1

Hope this helps!

7 0
3 years ago
Read 2 more answers
Select the procedure that can be used to show the converse of the
Vera_Pavlovna [14]

Answer:

The correct option is C

Step-by-step explanation:

I attached an image that forms the complete question.

The converse Pythagorean theorem states that, "If the square of the longest side of a triangle is equal to the square of the other two sides, then the triangle is a right triangle."

That is if c is the longest side of a triangle and then a and b are the other sides, then if,

c² = a² + b², the triangle is a right triangle.

Looking at all the options, option C fits the theorem well. Because

3² + 4² = 5² implies the triangle is a right triangle and the converse theorem is established.

The option D also looks close, but it's not correct because you can just draw any two sides and put the right angle in between them. The longest is always the part of the triangle that is opposite to the right angle, 90°. If for instance, you draw 3 and 5 then put the right angle in between them, 4 will take the position of the longest side which is wrong.

Therefore, the correct option is c.

7 0
3 years ago
Other questions:
  • Select the correct answer. Which inequality is true? A. |-5| > |-7| B. |-8| < |-5| C. |9| < |7| D. |-9| > |8|
    13·1 answer
  • How to write 6.33x10^2 in standard form​
    10·1 answer
  • Solve the following system of equations algebraically<br>3×-y=0<br>​
    13·1 answer
  • corrine works for 8 hours a day sarting 9 am. in 5 days she makes $720. How much money does corring make in one hour?
    11·2 answers
  • 2x^3-4x+6 turning points , end behavior, zeros
    13·1 answer
  • The solution to an inequality is represented by the number line. A number line going from negative 5 to positive 5. An open circ
    12·1 answer
  • Consider the following recursively defined sequence a1 = 2 an = an-1 – 3 for n &gt;= 2 In this question, we will prove that an =
    14·1 answer
  • Find the rate of change of the line. someone please help​
    15·2 answers
  • I need Help fast Please ​
    10·1 answer
  • Please help me with this again
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!