Answer:
The area of the shaded region is 148.04 cm².
Step-by-step explanation:
It is provided that a 7 cm × 5 cm rectangle is inside a circle with radius 6 cm.
The sides of the rectangle are:
l = 7 cm
b = 6 cm.
The radius of the circle is, r = 6 cm.
Compute the area of the shaded region as follows:
Area of the shaded region = Area of rectangle - Area of circle
Thus, the area of the shaded region is 148.04 cm².
Answer:
t-shirts: 2790
profit: $12209
Step-by-step explanation:
Given the function:
p(x) = -x³ + 4x² + x
we want to maximize it.
The following criteria must be satisfied at the maximum:
dp/dx = 0
d²p/dx² < 0
dp/dx = -3x² + 8x + 1 = 0
Using quadratic formula:
d²p/dx² = -6x + 8
d²p/dx² at x = -0.12: -6(-0.12) + 8 = 8.72 > 0
d²p/dx² at x = 2.79: -6(2.79) + 8 = -8.74 < 0
Then, he should prints 2.79 thousands, that is, 2790 t-shirts to make maximum profits.
Replacing into profit equation:
p(x) = -(2.79)³ + 4(2.79)² + 2.79 = 12.209
that is, $12209
From the above function, it is clear that the value of f is never 0. Hence the statement that is true is (Option E), See explanation of same below.
<h3>What is the explanation for the above function?</h3>Note that the function is related to Euler's number which is depicted as:
e ≈ 2.7182. The function is given as:
f(x) = 100 *
Assuming x = -2, we'd have:
100 * 2.7182
= 271.82
= 0.00001353354
Hence, even when x tends < 0 the function f(x) thus, is never 0. See the attached graph for confirmation.
Learn more about functions at:
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