6. Write the equation of the line in slope-intercept form that has the following points: (1, -3) (0, -5)
1 answer:
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Answer:
Step-by-step explanation:
a = 3
b = 3
c = 1
Discriminate = sqrt(b^2 - 4ac)
Discriminate = sqrt(9 - 4*3*1)
Discriminate = sqrt(9 - 12)
Discriminate = sqrt(-3)
What negative value means that there are no real roots and the y intercept = 1. You should always graph this kind of question, which I am doing for you. I use Desmos which is a very handy program.
You should notice that the minimum is above the x axis. That means there are no real roots, just as the discriminate tells you.
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