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lana66690 [7]
3 years ago
9

Find the greatest maximum y-value of the following equation:

Mathematics
1 answer:
KatRina [158]3 years ago
5 0
A quick way to do this is by recalling the fact that -1\le\cos x\le1, so the largest value that \cos ax alone (for any real value of a) can take on is 1.

This means -3\le3\cos2x\le3, and so 1\le3\cos2x+4\le7.

So the maximum value of this function is 7.
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Factor both quadratic expressions. (x 4 + 5x 2 - 36)(2x 2 + 9x - 5) = 0
Sonbull [250]

So focusing on x^4 + 5x^2 - 36, we will be completing the square. Firstly, what two terms have a product of -36x^4 and a sum of 5x^2? That would be 9x^2 and -4x^2. Replace 5x^2 with 9x^2 - 4x^2: x^4+9x^2-4x^2-36

Next, factor x^4 + 9x^2 and -4x^2 - 36 separately. Make sure that they have the same quantity inside of the parentheses: x^2(x^2+9)-4(x^2+9)

Now you can rewrite this as (x^2-4)(x^2+9) , however this is not completely factored. With (x^2 - 4), we are using the difference of squares, which is a^2-b^2=(a+b)(a-b) . Applying that here, we have (x+2)(x-2)(x^2+9) . x^4 + 5x^2 - 36 is completely factored.

Next, focusing now on 2x^2 + 9x - 5, we will also be completing the square. What two terms have a product of -10x^2 and a sum of 9x? That would be 10x and -x. Replace 9x with 10x - x: 2x^2+10x-x-5

Next, factor 2x^2 + 10x and -x - 5 separately. Make sure that they have the same quantity on the inside: 2x(x+5)-1(x+5)

Now you can rewrite the equation as (2x-1)(x+5) . 2x^2 + 9x - 5 is completely factored.

<h3><u>Putting it all together, your factored expression is (x+2)(x-2)(x^2+9)(2x-1)(x+5)=0</u></h3>
5 0
3 years ago
At First Class Pizza, 12% of the pizzas made yesterday were pepperoni pizzas. If 27 pizzas have pepperoni, how many pizzas were
gogolik [260]

Answer: 225

Step-by-step explanation:

Let the total number of pizza made be represented by x.

Therefore, the situation in the question can be written as:

12% × x = 27

12/100 × x = 27

0.12 × x = 27

0.12x = 27

Divide both side by 0.12

0.12x/0.12 = 27/0.12

x = 225

The total pizza made was 225.

3 0
2 years ago
3 over 32 simplified?
Bess [88]
It is already simplified, three goes into three once but three cant go into 32 without there being a remainder.
7 0
3 years ago
This is the whole picture can someone help??
Maksim231197 [3]

Step-by-step explanation:

I can't see good the picture

3 0
2 years ago
A parallelogram has a base of 7 units. If the height has a corresponding unit of 2/3.
nexus9112 [7]

Answer:

7 x 2/3 = 14/3 = 4 2/3

To find the area of a parallelogram, simply multiply the base times its height.

8 0
3 years ago
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