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
sukhopar [10]
3 years ago
7

An electric current, I, in amps, is given by I=cos(wt)+√8sin(wt), where w≠0 is a constant. What are the maximum and minimum valu

es of I
Mathematics
1 answer:
exis [7]3 years ago
4 0
Take the derivative with respect to t
- w \sin(wt) + \sqrt{8} w cos(wt)
the maximum and minimum values occur when the tangent line is zero so we set the derivative to zero
0 = -w \sin(wt) + \sqrt{8} w cos(wt)
divide by w
0 =- \sin(wt) + \sqrt{8} cos(wt)
we add sin(wt) to both sides

\sin(wt)= \sqrt{8} cos(wt)
divide both sides by cos(wt)
\frac{sin(wt)}{cos(wt)}= \sqrt{8}   \\  \\ arctan(tan(wt))=arctan( \sqrt{8} ) \\  \\ wt=arctan(2 \sqrt{2)} OR\\ wt=arctan( { \frac{1}{ \sqrt{2} } )
(wt)=2(n*pi-arctan(2^0.5))
(wt)=2(n*pi+arctan(2^-0.5))
where n is an integer
the absolute max and min will be

I=cos(2n \pi -2arctan( \sqrt{2} ))
since 2npi is just the period of cos
cos(2arctan( \sqrt{2} ))= \frac{-1}{3} 

substituting our second soultion we get
I=cos(2n \pi +2arctan( \frac{1}{ \sqrt{2} } ))
since 2npi is the period
I=cos(2arctan( \frac{1}{ \sqrt{2}} ))= \frac{1}{3}
so the maximum value =\frac{1}{3}
minimum value =- \frac{1}{3}


You might be interested in
The triangles are similar by the AA similarity postulate find the value of x ?
Natasha_Volkova [10]
4/5 = (4 + 8)/x
4x = 5(12) = 60
x = 60/4 = 15
3 0
3 years ago
What is the answer to number 2 will mark Brainlest!!!!
Nastasia [14]

you have to make a box plot on the data you created in the first question box plots look like this also set up your data in such event based information to make it neat read-able and clear

6 0
3 years ago
Please someone help me! asap!!
kramer

Answer:

Last option= 30 minutes

6 0
3 years ago
#2 is the question<br> convert that number to radians from degrees.
fiasKO [112]
8pi/20 *180/pi
Answer is 72
8 0
3 years ago
What kind of angles are angles 2 and 8?
Ronch [10]
C.Alternate interior....................................

5 0
3 years ago
Other questions:
  • ABC stock sold for $64.50 four days later the same stock sold for $47.10 what is the average change per day?
    12·1 answer
  • The image below shows two dilated figures with lines UV and WX drawn. If the larger figure was dilated using a scale factor of 4
    9·1 answer
  • Find the surface area of the prism
    8·1 answer
  • Ratio of sandwiches white bread to brown bread is 10:3. 2/3 white are vegetarian, half brown are vegetarian. What fraction of th
    14·1 answer
  • WILL GIVE BRAINEST
    11·2 answers
  • Help Please, anyone good at domain values of composite functions.
    13·1 answer
  • Help on my geometry plzzzz
    12·1 answer
  • Laura shades 60 squares on her hundredths grid And Billy shades 50 squares on his hundredths grid. Write the decimal number that
    9·1 answer
  • 5+15 divided by 3 x 4 to the third power
    6·1 answer
  • Kelly Union works as a cashier and earns $12.75 per hour. Kelly worked
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!