All categories

3 years ago

What is the average rate of change of the function on the interval from x = 0 to x = 5?

Mathematics

1 answer:

crimeas [40]3 years ago

4 0

Answer:

Average rate of change $=\frac{1}{8}$

Step-by-step explanation:

Given interval are from $x=0\ to\ x=5$

Also, $=\frac{1}{2^3}x=\frac{1}{8}x$

Average rate of change $=\frac{f(b)-f(a)}{b-a}\ for\ given\ interval\ [a,b]$

Here given intervals are $a=0\ and\ b=5$

Plugging these value in formula, we get.

Average rate of change $=\frac{\frac{1}{8}(5)-\frac{1}{8}(0)}{5-0}\\\\=\frac{\frac{1}{8}(5)-0}{5-0}\\ \\=\frac{\frac{1}{8}(5)}{5}\\\\=\frac{1}{8}$

You might be interested in

Which of the following is equivalent to the radical expression below? 5^8*13

Bezzdna [24]

Answer:

$(d)$ $5^{8.13} = 5^{8} * 5^{\frac{1}{10}} * 5^{\frac{3}{100}}$

Step-by-step explanation:

Given

$5^{8.13}$

Required

Select an equivalent expression

$5^{8.13}$

Simplify the power

$5^{8.13} = 5^{8 + 0.1 + 0.03}$

Apply law of indices:

$5^{8.13} = 5^{8} * 5^{0.1} * 5^{0.03}$

Express decimal as fractions

$5^{8.13} = 5^{8} * 5^{\frac{1}{10}} * 5^{\frac{3}{100}}$

5 0

3 years ago

I need help asap....................

docker41 [41]

Based on the given points, the point that is located on the y-axis is (0,7).

<h3>Which point is on the y axis?</h3>

The point that is on the y-axis should have a coordinate such that x is equal to 0.

This leads to the point being on the y-axis because the nonzero coordinate of the y axis would then have to be placed on the same axis.

The only point with a 0 coordinate is (0, 7) so this is the point that is located on the y-axis.

Find out more on points on the y-axis at brainly.com/question/4656315

#SPJ1

7 0

2 years ago

A series of three? separate, adjacent tunnels is constructed through a mountain. Its length is approximately 25 kilometers. Each

Nadya [2.5K]

Answer:

$312.5\pi \text{ km}^3\approx 981.75\text{ km}^3$

Step-by-step explanation:

We have been given that a series of 3 separate, adjacent tunnels is constructed through a mountain. Its length is approximately 25 kilometers.

Each of the three tunnels is shaped like a half-cylinder with a radius of 5 meters.

Since we know that volume of a semicircular or a half cylinder is half the volume of a circular cylinder.

$\text{Volume of a semicircular cylinder}=\frac{\pi r^2h}{2}$ , where,

r = Radius of cylinder,

h = height of the cylinder.

Upon substituting our given values in volume formula we will get,

$\text{Volume of a semicircular cylinder}=\frac{\pi (5\text{ km})^2*25\text{ km}}{2}$

$\text{Volume of a semicircular cylinder}=\frac{\pi*25\text{ km}^2*25\text{ km}}{2}$

$\text{Volume of a semicircular cylinder}=\frac{\pi*625\text{ km}^3}{2}$

$\text{Volume of a semicircular cylinder}=\pi*312.5\text{ km}^3$

$\text{Volume of a semicircular cylinder}=981.74770\text{ km}^3$

Therefore, the volume of earth removed to build the three tunnels is $312.5\pi \text{ km}^3\approx 981.75\text{ km}^3$ .

4 0

3 years ago

How many different 5-digit pins are there where none of the digits are repeated?

vazorg [7]

<span>With no digit being repeated: 10*9*8*7*6= 30,240</span>

7 0

3 years ago

Which sequence of transformations maps pre-image ABC to

matrenka [14]

Triangle ABC was reflected over the y-axis and then translated 2 units up and 2 units to the right

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Translation is the movement of a point up, down, left or right. If a point A(x, y) is translated b units up and a units to the right, the new point is A'(x + a, y + b).

Reflection is the flipping of a figure. If a point A(x, y) is reflected along the y axis the new point is A'(-x, y).

Triangle ABC is at A(1, 2), B(4, 6) and C(7, 3). If it is reflected over the y-axis, the new point is A*(-1, 2), B*(-4, 6) and C*(-7, 3). If it is then translated 2 units up and 2 units to the right, the new image is:

A'(1, 4), B'(-2, 8) and C'(-5, 5)

Hence, Triangle ABC was reflected over the y-axis and then translated 2 units up and 2 units to the right

Find out more at: brainly.com/question/11707700

3 0

3 years ago