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
klasskru [66]
1 year ago
13

The maximum value of 12 sin 0-9 sin²0 is: -​

Mathematics
1 answer:
jeka57 [31]1 year ago
3 0

Answer:

4

Step-by-step explanation:

The question is not clear. You have indicated the original function as 12sin(0) - 9sin²(0)

If so, the solution is trivial. At 0, sin(0) is 0 so the solution is 0

However, I will assume you meant the angle to be \theta rather than 0 which makes sense and proceed accordingly

We can find the maximum or minimum of any function by finding the first derivate and setting it equal to 0

The original function is

f(\theta) = 12sin(\theta) - 9 sin^2(\theta)

Taking the first derivative of this with respect to \theta and setting it equal to 0 lets us solve for the maximum (or minimum) value

The first derivative of f(\theta) w.r.t \theta is

                        12\cos\left(\theta\right)-18\cos\left(\theta\right)\sin\left(\theta\right)

And setting this = 0 gives

12\cos\left(\theta\right)-18\cos\left(\theta\right)\sin\left(\theta\right) = 0

Eliminating cos(\theta) on both sides and solving for sin(\theta) gives us

sin(\theta) = \frac{12}{18} = \frac{2}{3}

Plugging this value of sin(\theta) into the original equation gives us

12(\frac{2}{3}) - 9(\frac{4}{9} ) = 8 - 4 = 4

This is the maximum value that the function can acquire. The attached graph shows this as correct

You might be interested in
During his 2007 MVP season for the New York Yankees, Alex Rodriguez hit 98 singles, 31 doubles, 0 triples, and 54 home runs in a
Pani-rosa [81]
B I think that is the answer. If its not please let me know.
3 0
3 years ago
Read 2 more answers
Use a graphing calculator to solve the system of linear equations. 2.1x+4.2y=14.7 −5.7x−1.9y=−11.4
tia_tia [17]

I used my calculator and got x=1 y=3

solve for y to put them in your calculator

2.1x+4.2y=14.7

y = (14.7 -2.1x)/4.2


−5.7x−1.9y=−11.4

y=(-11.4 +5.7x)/(-1.9)

then using the ploting tool I plotted them and found where they intersected

3 0
3 years ago
The probability a train car will be full is 60%. Which word or words best describes the likelihood the train car will be full?
allsm [11]

Answer:

C-highly likely

Step-by-step explanation:

its bigger than 45 so closer to 100%

5 0
2 years ago
Read 2 more answers
Nickolas practiced his trumpet for 12 hours for ten weeks in a row how many hours did he practice altogether
klemol [59]

Answer:

120 hours

Step-by-step explanation:

If it was 12 hours per week you multiply 12 by 10

8 0
3 years ago
5409/50 simplified<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B5409%7D%7B50%7D%20" id="TexFormula1" title=" \frac{5409}{50
Tatiana [17]
This answer is already in simplest form so the answer is simply 5409/50
6 0
3 years ago
Other questions:
  • Jessica finished a race that was 5 miles long in 30 minutes and 15 seconds. Casey finished a race that was 2 miles log in 11 min
    10·1 answer
  • John Handsmith is one of the football league players
    5·1 answer
  • Your annual salary is $61,061.83 what is your semimonthly salary
    11·1 answer
  • For the given pentagon ABCDE the diagonal
    5·1 answer
  • What does the product of any whole-number factor multiplied by 100 always have ? Explain
    6·1 answer
  • Does anyone know any other good apps for math like Algebra 1.?
    15·2 answers
  • The town park is a rectangular strip of land with a width of 1/2 mile and an area of 1/8 square mile. How long is the town park?
    15·2 answers
  • There were 10 black bears in an area. Some years later, there were 17 black bears in the area. What is the percent gain?
    6·1 answer
  • 5. Explain why each relation is not a function.
    6·2 answers
  • Two trains leave towns 1490 kilometers apart at the same time and travel toward each other. One train travels 20 km/h slower tha
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!