<span>∫(sinx cosx)^2dx = ∫(1/2sin 2x)^2 dx = 1/4∫sin^2 2x dx = 1/4∫1/2(1 - cos 4x)dx = 1/8∫(1 - cos 4x) dx = 1/8[x - sin 4x / 4] + c = 1/32(4x - sin 4x) + c
</span>
The sign of "b" on the numerator should be negative. So we conclude that the correct option is false.
<h3>Is the equation in the image correct or incorrect?</h3>
For a quadratic equation of the form:

By using the Bhaskara's formula, the solutions of the equation:

Are given by the formula:

Notice that the sign of the first term on the numerator should be negative, while on the image it is positive.
So the equation shown in the image is incorrect.
If you want to learn more about quadratic equations:
brainly.com/question/1214333
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Answer:
20 masks and 100 ventilators
Step-by-step explanation:
I assume the problem ask to maximize the profit of the company.
Let's define the following variables
v: ventilator
m: mask
Restictions:
m + v ≤ 120
10 ≤ m ≤ 50
40 ≤ v ≤ 100
Profit function:
P = 10*m + 65*v
The system of restrictions can be seen in the figure attached. The five points marked are the vertices of the feasible region (the solution is one of these points). Replacing them in the profit function:
point Profit function:
(10, 100) 10*10 + 65*100 = 6600
(20, 100) 10*20 + 65*100 = 6700
(50, 70) 10*50 + 65*70 = 5050
(50, 40) 10*50 + 65*40 = 3100
(10, 40) 10*10 + 65*40 = 2700
Then, the profit maximization is obtained when 20 masks and 100 ventilators are produced.
X = 16y^2 + 1
x - 1 = 16y^2
(x - 1)/16 = y^ 2
( (x-1) / 16 ) ^1/2 = y
( (x-1) ^ 1/2 ) / 4 = y