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3 years ago

F(x) = x2 + 10 What is the average rate of chan hange of f over the interval [-2, -1]?

Mathematics

1 answer:

Readme [11.4K]3 years ago

5 0

The average rate of change is given by [f(b) - f(a)]/(b - a), where a and b represent the interval [a, b].

Let a = -2

Let b = -1

[(-1)^2 + 10 - ((-2)^2 + 10)]/(-1 -(-2))

[1 + 10 - (4 + 10)]/(-1 + 2)

[1 + 10 -4 -10]/(1)

[1 - 4]/(1)

-3/1

Answer: -3

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for v= 4i - 5j, find unit vector u in the direction of v, and write your answer as a linear combination of the standard unit vec

umka21 [38]

Answer:

a. $u=\frac{4\sqrt{41}i }{41}-\frac{5\sqrt{41}j}{41}$

Step-by-step explanation:

The given vector is v= 4i - 5j

The magnitude of this vector is;

$|v|=\sqrt{(-4)^2+(-5)^2}$

$|v|=\sqrt{16+25}$

$|v|=\sqrt{41}$

The unit vector u in the direction of v is;

$u=\frac{v}{|v|}$

$u=\frac{4i - 5j}{\sqrt{41}}$

$u=\frac{4i }{\sqrt{41}}-\frac{5j}{\sqrt{41}}$

We rationalize to get

$u=\frac{4\sqrt{41}i }{41}-\frac{5\sqrt{41}j}{41}$

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3 years ago

Read 2 more answers

Please help me

kirza4 [7]

This is a hexagonal prism: Volume = Area of Base (hexagon) x Height:
There are 6 equal equilateral triangles in a hexagone.
The apothem (or altitude of each triangle) = side x (√3)/2 =12(√3)/2 = 6√3
Area of ONE equilateral triangle = (side x altitude)/2:
Area of ONE equilateral triangle = (12 x 6√3)/2 = 36√3 ft²
Area of the SIX equilateral triangles = 36√3 x 6 = 216√3 ft²
VOLUME = BASE X HEIGHT = 216√3 x 15 = 3240√3 ft³

OR VOLUME = 5612 ft³

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