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Dominik [7]
3 years ago
6

Angles of a triangle

Mathematics
1 answer:
mina [271]3 years ago
5 0
Answer: A= 1/2bh

The b is for base and the h is for height
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2 years ago
Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total
Katarina [22]

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:

x = \frac{-b \pm \sqrt{b^2 -4(a)(c)}}{2(a)}

x = \frac{-8 \pm \sqrt{8^2 -4(-3)(1)}}{2(-3)}

x = \frac{-8 \pm 8.72}{-6}

x_1 = \frac{-8 + 8.72}{-6}

x_1 = -0.12

x_2 = \frac{-8 - 8.72}{-6}

x_2 = 2.79

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

3 0
3 years ago
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