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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

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choose five ordered pairs whose first and second coordinates are equal. plot these points and connect them. what kind of figure
Effectus [21]

Answer:

The figure is a straight line.

The figure lies in the first and the third quadrants.

Step-by-step explanation:

Take five ordered pairs as (1,1),(2,2),(-1,-1),(-2,-2),(3,3)

Here, the first and second coordinates are equal.

Now, plot these points and connect them.

From the graph, it can be observed that the figure is a straight line.

Also, the figure lies in the first and the third quadrants.

Download pptx
5 0
3 years ago
Find the lcd of 2/3 and 1/3
wariber [46]
Hello!

The least common denominator is like the least common multiple. As you can see, these numbers already have the same denominators, and cannot be divided any further as they are prime. 

Therefore, our answer is 3.

I hope this helps!
4 0
3 years ago
Read 2 more answers
Pls I need it for a testI’ll give out 20 points
kompoz [17]

Answer:

It should be D.

Step-by-step explanation:

6 0
2 years ago
Y=2x-2 and 4x+2y=12. solve the equation PLEASE SHOW WORK​
diamong [38]
<h3>The solution as an ordered pair is (x,y) = (2,2)</h3><h3>x = 2 and y = 2 pair up together.</h3>

===============================

Work Shown:

4x+2y = 12

4x+2( y ) = 12

4x+2( 2x-2 ) = 12 ... replace y with 2x-2

4x+2( 2x ) + 2( -2 ) = 12 ... distribution rule

4x+4x-4 = 12

8x-4 = 12

8x-4+4 = 12+4 ... add 4 to both sides

8x = 16

8x/8 = 16/8 ... divide both sides by 8

x = 2 is the first part of the answer

Use x = 2 to find y

y = 2x-2

y = 2(2)-2 ... replace x with 2

y = 4-2

y = 2 is the second part of the answer

8 0
3 years ago
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The net below shows the dimensions of a triangular pyramid with equilateral base. The height of each triangle is 7.2 and the bas
Doss [256]

Answer:

25.98units³

Step-by-step explanation:

Area of the triangular prism = Base Area * Height of the pyramid

A = BH/3

Get the area of the triangle

Area of the triangle = 1/2 Base * height

Base of the triangle = 5

height = √5²-2.5²

h = √25-6.25

h = √18.75

h = 4.33

Area of the triangle = 1/2 * 4.33 * 5

Area of the triangle = 10.82

Base area = 10.82

Get the area of the triangular pyramid

Area of the triangular pyramid = 10.82*7.2/3

Area of the triangular pyramid = 25.98units³

Hence the area triangular pyramid is 25.98units³

6 0
3 years ago
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