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
What’s the output?
4vir4ik [10]

The output would be 81



8 0
3 years ago
Find the slope of the following ponit (5,1) and (7,-3)
MArishka [77]

Answer:

slope=-2

Step-by-step explanation:

First you need to know the slope formula: y2-y1/x2-x1

Then you just plug in and solve:

-3-1/7-5 = -4/2 = -2

5 0
3 years ago
Read 2 more answers
Find an equation to the line tangent to y = 5 + |x – 2| at the coordinate (2, 5) pls answer
myrzilka [38]

Answer:

Step-by-step explanation:

Finding an equation of a tangent line to that function requires that we find the derivative of the function at that point. Since this is an absolute value function with its cusp at (2, 5), the function is not differentiable here.

3 0
3 years ago
The volume of a volleyball is about 288 cubic inches. what is the radius of the volleyball, to the nearest tenth of an inch? use
Len [333]

Answer:

The radius of the volleyball is 8.3 inches

Step-by-step explanation:

Given

r = \sqrt{\frac{3v}{4\pi}}

v = 288

Required

Determine the value of r

To do this, we simply substitute 288 for v and 3.14 for π in the given equation.

This gives

r = \sqrt{\frac{3v}{4\pi}}

r = \sqrt{\frac{3 * 288}{4 * 3.14}}

r = \sqrt{\frac{864}{12.56}}

r = \sqrt{68.7898089172}

r = 8.29396219651

r = 8.3\ inch (Approximated)

Hence;

<em>The radius of the volleyball is 8.3 inches</em>

3 0
3 years ago
Read 2 more answers
-1,2,5,7...with these numbers while using multiplaction, divison, addition, and subtraction, how would u get positive 24
baherus [9]
By adding two positives together, or a big positive number with a small negative number.
4 0
3 years ago
Other questions:
  • Will someone please tell me the values of X and Y ?
    14·1 answer
  • Lin and Jen each thought of a number. Lin thought of a 2-digit number. Jen’s number is 7 times as big as Lin’s. But, if Lin writ
    5·2 answers
  • What two simpler problems can you use to find 9 x 38?
    6·2 answers
  • Edmund makes a cube using eight small cubes.
    6·1 answer
  • I don't understand how to solve this
    15·1 answer
  • Is markup and selling price the same?
    7·2 answers
  • 5/6k+2/3=4/3 <br> What is K? <br> I don't understand how to do these
    5·1 answer
  • Usatestprep Listed in the Item Bank are key terms and expressions, each of which is associated with one of the columns. Some ter
    8·2 answers
  • Please help me solve the answers​
    14·1 answer
  • The foot of a ladder is placed 7 meters from a wall if The top of the ladder rests 9 meters up on the wall how long is the ladde
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!