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
kotykmax [81]
3 years ago
13

If f(x) = sin(x/2), then there exists a number c in the interval pie/2 < x < 3pie/2 that satisfies the conclusion of the m

ean value Theorem. What could be c?
Mathematics
1 answer:
elena-14-01-66 [18.8K]3 years ago
3 0
For the answer to the question above, 
The mean value theorem states the if f is a continuous function on an interval [a,b], then there is a c in [a,b] such that: 
<span>f ' (c) = [f(b) - f(a)] / (b - a) </span>
<span>
So [f(a) - f(b)] ( b - a ) = [sin(3pi/4) - sin(pi/4)]/pi </span>
= [sqrt(2)/2 - sqrt(2)/2]/pi = 0 
So for some c in [pi/2, 3pi/2] we must have f ' (c) = 0 

In general f ' (x) = (1/2) cos (x/2) 
We ask ourselves for what values x in [pi/2, 3pi/2] does the above equation equal 0. 
0 = (1/2) cos (x/2) 
0 = cos (x/2) 
x/2 = ..., -5pi/2, -3pi/2, -pi/2, pi/2, 3pi/2, 5pi/2,... 
x = ..., -5pi, -3pi, -pi, pi. 3pi, 5pi, .... 
and x = pi is the only solution in our interval. 

So c = pi is a solution that satisfies the conclusion of the MVT
You might be interested in
Which of the binomials below is a factor of this trinomial?
8_murik_8 [283]

Answer:

C. x - 4

Step-by-step explanation:

The best way to do this is to first take out GCF

6(x² - x - 12)

Then we factor

6(x - 4)(x + 3)

We can now see our answer.

8 0
3 years ago
Read 2 more answers
Please help on these two​
jeyben [28]

Answer:

For your first problem you want to see what all the sides would equal

You would have to combine them all into one big equation

5x-7+3x+1+4x=30 (now you want to combine like terms)

12x-7+1=30 (combined the x's together)

12x-6=30 (added -7 and 1)

12x=36 (added 6 to each side)

x=3 (divided 12 to each side)

Now you wanna plug 4 in for x for each side to find out the largest to smallest

AB=5(3)-7= 8

BC=3(3)+1= 10

AC=4(3)= 12

So in order from smallest to largest would be angle C, B, A because

Angle C is the smallest angle because the sides AC and BC are the longest so they form the smallest angle

Then it would be angle A being the largest because the smallest sides in length AB and BC make up the biggest angle

The next problem would be that in order for it to have to be a triangle the two smallest sides needs to add up higher than the third side so

11, 11, 24, 11+11=22, which is less than 24 so not this one

18,12,9, 9+12=21 which is greater that 18 so this one would be a triangle

9,10,19, 9+10=19 which 19 isn't greater than 19 so this one is not a triangle

4,7,23, 4+7=11 which is less than 23, so this one is also not a triangle

So your answer would be 18cm,12cm,9cm

8 0
3 years ago
What is the exponent on 10 when you right 5.3 in scientific notation?
salantis [7]
It is zero

the answer is 5.3 x 10^0
because 10^1 would force you to move the decimal place to make it 53

I hope this helps!
8 0
3 years ago
George has two dogs.
Stella [2.4K]
Uhhhhhhhhhhhhhhhhhhhhhhhh
7 0
2 years ago
Read 2 more answers
Please help asap 50 pts
Alexxx [7]
A. The smaller the number, the wider the graph. That equation had the smallest number, so therefore it will produce the widest graph.
6 0
3 years ago
Read 2 more answers
Other questions:
  • Christine Wong has asked Dave and Mike to help her move into a new apartment on Sunday morning. She has asked them both in case
    11·2 answers
  • A store charges 7% sales tax. Which expression can be used to find the total cost of an item with a price of p? 0.07p
    13·1 answer
  • find the slope of the line that has the following intercepts: y-intercept: -15; x-intercept: 3. round your answer to 1 decimal p
    6·1 answer
  • Can someone help me find the answer and explain please??
    12·2 answers
  • A rectangular yard has dimensions 10 meters by 8 meters. In the middle of the yard is a rectangular pond of 8 square meters, lea
    12·1 answer
  • What is |1-8i|?<br><br> A.<br> B.<br> C<br> D
    6·1 answer
  • Rewrite the equation y-31x= 93 as a function of x?<br> Pls answer quick pls.
    7·2 answers
  • Help help help help help plss
    7·2 answers
  • Can someone help me? look at the picture
    7·1 answer
  • Is TAG BAG? IF so, identif th similarity postulate or theorem that applies
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!