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34kurt
3 years ago
15

Prove, using the second derivative, that the general quadratic y= ax^2+bx+c, is:

Mathematics
1 answer:
Nonamiya [84]3 years ago
7 0

Answer:

dy/dx = 2ax + b

d²y/dx² = 2a

2a < 0

When a < 0

(So concave)

2a > 0

When a > 0

(So convex)

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Answer:1

1. x = 30

2. ∠ABC = 120°, ∠BCD = 90°, ∠CDA = 60°, ∠DAB = 90°

Step-by-step explanation:

It's important to note here that the measure of all interior angles in a quadrilateral will add up to 360°

We know this using the formula(n-2)\cdot 180, a 4 sided figures angles will add up to

(4-2)\cdot 180\\\\2\cdot 180\\\\360

This means that all of the angles (4x, 3x, 2x, 3x) will add up to 360.

4x + 3x + 2x + 3x = 360

Combine like terms:

12x = 360

Divide both sides by 12:

x = 30

We know now substitute x for 30 in for all of the side lengths.

∠ABC = 4x = 4\cdot 30 = 120°

∠BCD = 3x = 3\cdot 30 = 90°

∠CDA = 2x = 2\cdot 30 = 60°

∠DAB = 3x = 3\cdot 30 = 90°

Hope this helped!

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