MATHEMATICS HIGH SCHOOL

Consider f(x)=2|x|What is the rate of change over the interval 0≤x≤4?

How is the rate of change over this interval related to the form of the function?

Answers

Answer 1

Answer:

Answer:

Please check the explanation.

Step-by-step explanation:

As we know that the average rate of change of f(x) in the closed

interval [a, b] is

$(f\left(b\right)-f\left(a\right))/(b-a)$

Given the interval [a, b] = [0, 4]

$f(x)=2|x|$

$f(b)=f(2)=2\cdot \:4$ ∵ $\mathrm{Apply\:absolute\:rule}:\quad \left|a\right|=a,\:a\ge 0$

$= 8$

$f(x)=2|x|$

$f(a)=f(0)=2\cdot \:0$ ∵ $\mathrm{Apply\:absolute\:rule}:\quad \left|a\right|=a,\:a\ge 0$

$= 0$

so the average rate of change :

$(f\left(b\right)-f\left(a\right))/(b-a)=(8-0)/(4-0)$

$=(8)/(4)$

$= 2$

We know that a rate of change basically indicates how an output quantity changes relative to the change in the input quantity. Here, it is clear the value of y increase with the increase of input.

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Simplify.i^68

A. -i

B. 1 (I think it's B, please tell me if it's right or not. Thank you.)

C. -1

D. i

Answers

Answer:

B. 1

Step-by-step explanation:

Isolate i on one side of the equation.

First, use exponent rule.

$\displaystyle \mathsf{A^B^C=(A^B)^C}}$

$\displaystyle \mathsf{(I^2)^3^4=I^6^8}}$

$\displaystyle \mathsf{(I^2)^3^4}}$

Solve. (by imaginary number rule.)

i²=-1

(-1)³⁴

=1³⁴

1³⁴=1

$\Large\boxed{\mathsf{\Rightarrow 1}}}$

In conclusion, the final answer is (B.) 1.

Solve for the positive value of x: 6x2 – 54 = 0

Answers

If you would like to solve for the positive value of x, you can do this using the following steps:

6 * x^2 - 54 = 0 /6
x^2 - 9 = 0
(x - 3) * (x + 3) = 0
1. x = 3
2. x = - 3

The correct result would be x = 3.

For each quadratic function, find the axis of symmetry of its graph. Y=x^2+ 4x-7 Y=2x^2+3x-4

Answers

first find the vertex
the x coordinate of the vertex is the axis of symmetry

the vertex of an equation in form
y=ax^2+bx+c is
-b/2a=x coordinate

y=1x^2+4x-7
vertex=-4/2=-2
axis of symmetry is x=-2

y=2x^2+3x-4
ertex=-3/(2*2)=-3/4
axis of symmetry is x=-3/4

Add. Write your answer in simplest form.

3/8 + 2/5