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Free_Kalibri [48]
3 years ago
9

What is the average rate of change for the function f(x)=x^2+4 for the domain of -2 to 4

Mathematics
1 answer:
Neko [114]3 years ago
5 0

Answer:

  2

Step-by-step explanation:

For a quadratic function the average rate of change on an interval is the rate of change at the midpoint of the interval. The rate of change of a function is given by its derivative.

The derivative of f(x) = x^2 is f'(x) = 2x. The midpoint of the interval is (4+(-2))/2 = 1. Then the average rate of change is ...

  f'(1) = 2(1) = 2

The average rate of change of f(x) on [-2, 4] is 2.

__

<em>Alternate solution</em>

The average rate of change is the slope of the line between the end points of the interval:

  m = (y2 -y1)/(x2 -x1)

  m = (f(4) -f(-2))/(4 -(-2)) = (20 -8)/(6) = 2

The average rate of change on [-2, 4] is 2.

_____

The attached graph shows the points on the curve and a line with slope 2 between them. It also shows the various slope calculations.

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Which equation is a solution to (x-3)(x+9)=27?
Shtirlitz [24]

Answer:

x = ± 3\sqrt{7} - 3

Explanation:

I'm assuming you want the solutions to that equation, so here goes! (If not, please comment.)

(x-3)(x+9)=27

Let's FOIL this all out and expand. (Remember: First, Outer, Inner, Last.)

x^2 +   9x    -    3x    -  27

(first+ inner + outer + last)

x^2 + 9x - 3x - 27 = 27

Combine like terms, and add 27 to both sides.

x^2 + 6x - 27 + 27 = 27 + 27

x^2 + 6x = 54

Let's complete the square, because factoring doesn't work, and because it's good practice.

x^2 + 6x + ___ = 54 + ____

In the blank we will put b/2 ^2 = 6/2 ^2 = 3^2 = 9 to complete the square.

x^2 + 6x + 9 = 54 + 9

Now we've got a perfect square factor:

(x + 3)^2 = 63

sqrt(x+3)^2 = \sqrt{63}

x + 3 = ± 3\sqrt{7}

x = ± 3\sqrt{7} - 3

7 0
3 years ago
The room is a cube with edge length 11 feet including the ceiling in the floor how much surface area must be painted
Xelga [282]
Answer: 726cm squared

Surface area is the area of all the faces added together.

If the area of one face is 11x11=121

Because it is a cube and it has six faces with the same surface area we do 121x6=726 to give us the total surface area.

6 0
2 years ago
What is a Unit Rate please give an example, and then how do you use the unit rate in the real world?
slava [35]

Answer:

It's when rates are expressed as quantities.

Step-by-step explanation:

An example would be miles per hour (mph). People use these to determine the distance they will go in an amount of time and to judge safe speed.

8 0
3 years ago
A field is to be fertilized at a cost of $0.08 per square yard. the rectangular part of the field is 95 yd long and the diameter
Alekssandra [29.7K]
Assuming that this field is rectangular with 2 semi-circles (one on both ends of the field), we must first calculate the total area of the field. this is done by adding the area of the rectangular portion and the circular portion. This is done below:

Given:

Rectangular length = 95 yards
Rectangular width = semi-circle diameter = 49 yards

Area of rectangle = length * width = 95 * 49
Area of rectangle = 4655 yd^2

The area of the 2 semi-circles can be obtained by treating both as one circle.
Area of circle = pi * (d/2)^2 = 3.1416 * (49/2)^2
Area of circle = 1885.74 yd^2

Total area = 1885.74 + 4655 = 6540.74

We multiply the area by the cost of fertilizing:
Total cost = cost per sq. yd * total area 
Total cost = 0.08 * 6540.74
Total cost = $523.26
8 0
3 years ago
What can baby lizards do that baby snakes can't
Lostsunrise [7]

Answer:

We know that both snakes and lizards are species of reptiles.

the things that baby lizards can do but baby snakes can't are : Walking and Leaping , they both had a very different body structure. Since snakes can only move by slithering their muscle and scale, they had no abilities to walk and leaping as lizards have legs so they move around by using them while snakes don't have one. Snakes are elongated, legless, carnivorous reptiles of the suborder Serpentes.



7 0
3 years ago
Read 2 more answers
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