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3 years ago

Find the average rate of change of f(x) = 1x + 6 on [4,9). Round your answer to the nearest hundredth.

Mathematics

1 answer:

olga2289 [7]3 years ago

6 0

Answer:

The average rate of change of f(x) = x + 6 on [4,9) is 1.

Step-by-step explanation:

Given a function y, the average rate of change S of $y=f(x)$ in an interval $(x_{s}, x_{f})$ will be given by the following equation:

$S = \frac{f(x_{f}) - f(x_{s})}{x_{f} - x_{s}}$

In this problem, we have that:

$f(x) = x + 6$

Interval [4,9]

Continuous function(no denominator or even root), this is why i can consider 9 a part of the interval for the calculation. So

$x_{s} = 4, x_{f} = 9, f(x_{s}) = f(4) = 10, f(x_{f}}) = f(9) = 15$ .

$S = \frac{f(x_{f}) - f(x_{s})}{x_{f} - x_{s}} = \frac{15 - 10}{9 - 4} = 1$

The average rate of change of f(x) = x + 6 on [4,9) is 1.

You might be interested in

How much of a radioactive kind of thorium will be left after 14,680 years if you start with

babymother [125]

Answer:

8978 grams

Step-by-step explanation:

The equation to find the half-life is:

$N(t)= N_{0}e^{-kt}$

N(t) = amount after the time <em>t</em>

$N_{0}$ = initial amount of substance

t = time

It is known that after a half-life there will be twice less of a substance than what it intially was. So, we can get a simplified equation that looks like this, in terms of half-lives.

$N(t)= N_{0}e^{-\frac{ln(\frac{1}{2}) }{t_{h} } t}$ or more simply $N(t)= N_{0}(\frac{1}{2})^{\frac{1}{t_{h} } }$

$t_{h}$ = time of the half-life

We know that $N_{0}$ = 35,912, t = 14,680, and $t_{h}$ =7,340

Plug these into the equation:

$N(t) = 35912(\frac{1}{2})^{\frac{14680}{7340} }$

Using a calculator we get:

N(t) = 8978

Therefore, after 14,680 years 8,978 grams of thorium will be left.

Hope this helps!! Ask questions if you need!!

8 0

2 years ago

HELPPPPP ASAP!!!! Thx!! and NOOO FILESSSS!!

tiny-mole [99]

Answer:

$x=32$ °

Step-by-step explanation:

The law of sines is a property of all triangles that relates the sides and angles of a triangle. This property states the following:

$\frac{sin(a)}{A}=\frac{sin(b)}{B}=\frac{sin(c)}{C}$

Where side (A) is the side opposite angle (<a), side (B) is the side opposite angle (<b), and side (C) is the property opposite angle (<c).

Substitute each of the sides and respective angles into the formula, and solve for the unknown angle (<x). Please note that a triangle with two congruent sides (referred to as an isosceles triangle) has a property called the base angles theorem. This states that the angles opposite the congruent sides in an isosceles triangle are congruent. Therefore, there can be two (<x)'s in this triangle.

$\frac{sin(a)}{A}=\frac{sin(b)}{B}=\frac{sin(c)}{C}$

$\frac{sin(x)}{10}=\frac{sin(116)}{17}=\frac{sin(x)}{10}$