What are the next three terms of the sequence 3, 6, 9, 12,

The diagram shows the curve y=(1/2x-2)^6+5. Find the area of the shaded region.

Zepler [3.9K]

So the line that is the limit is where the equation crosses the y axis or where x=0

so
y=(1/2(0)-2)^2+5
y=(-2)^2+5
y=4+5
y=9
at y=9

the upper bound is y=9

alrighty

we will do
let's call the curve that is 6th degree f(x)
and the y=9, g(x)

f(x)=(1/2x-2)^6+5
g(x)=9

find where they intersect

9=(1/2x-2)^6+5
4=(1/2x-2)^6
fancy math
x=8

so the area under the curve will be
$\int\limits^8_0 {g(x)-f(x)} \, dx$ because g(x) is above f(x)
so

$\int\limits^8_0 {g(x)-f(x)} \, dx= \int\limits^8_0 {9-((\frac{1}{2}x-2)^6+5)} \, dx=$
using our calculator because I can't figure out what $\int\limits (\frac{1}{2}x-2)^6} \, dx$ is
$\int\limits^8_0 {9-((\frac{1}{2}x-2)^6+5)} \, dx=$ $\frac{64}{3}$ or about 21.33333333

3 0

3 years ago

HELPPP i need to find standard form and general form, please help

Rudiy27

The equation in slope-intercept form is y = 13/8x -17/8 and the equation in standard form is 13x -8y = 17

<h3>Equation of a line</h3>

A line is the shortest distance between two points. The equation of a line in slope-intercept form is y = mx + b while as a standard notation is Ax+By = C

Given the coordinate points (-3, -7) and (5, 6)

<u>Determine the slope</u>

Slope = 6-(-7)/5-(-3)

Slope = 13/8

<u>For the y-intercept</u>

6 = 13/8(5) + b

6 = 65/8 + b

b = 6 - 65/8

b = -17/8

The equation in slope-intercept form is y = 13/8x -17/8

Write in standard form

Recall y = 13/8x - 17/8

<em>Multiply through by 8</em>

8y = 13x - 17

-13x + 8y = -17

13x -8y = 17

Hence the equation in standard form is 13x -8y = 17

Learn more on equation of a line here: brainly.com/question/13763238

#SPJ1

3 0

2 years ago

The image shows a geometric representation of the function f(x) = x^2 + 2x + 3 written in standard form. What is this function w

AlekseyPX

Answer:

f(x) = (x + 1)² + 2 in vertex form ⇒ 3rd answer

Step-by-step explanation:

* Lets revise how to find the vertex form the standard form

- Standard form ⇒ x² + bx + c, where a , b , c are constant

- Vertex form ⇒(x - h)² + k, where h , k are constant and (h , k) is the

vertex point (minimum or maximum) of the function

- At first we must find h and k

- By equating the two forms we can find the value of h and k

* Lets solve the problem

∵ f(x) = x² + 2x + 3 ⇒ standard form

∵ f(x) = (x - h)² + k ⇒ vertex form

- Put them equal each other

∴ x² + 2x + 3 = (x - h)² + k ⇒ open the bracket power 2

∴ x² + 2x + 3 = x² - 2hx + h² + k

- Now compare the like terms in both sides

∵ 2x = -2hx ⇒ cancel x from both sides

∴ 2 = -2h ⇒ divide both sides by -2

∴ -1 = h

∴ The value of h is -1

∵ 3 = h² + k

- Substitute the value of h

∴ 3 = (-1)² + k

∴ 3 = 1 + k ⇒ subtract 1 from both sides

∴ 2 = k

∴ The value of k = 2

- Lets substitute the value of h and k in the vertex form

∴ f(x) = (x - -1)² + 2

∴ f(x) = (x + 1)² + 2

* f(x) = (x + 1)² + 2 in vertex form

5 0

4 years ago

What is the slope of y=0.50x+5 and write a sentence to describe the meaning

castortr0y [4]

Answer:

5.5

Step-by-step explanation:

y = 0.5x + 5

Use the slope-intercept form to find the slope and y-intercept.

Slope: 0.5

y-intercept: 5

Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding values.

To find the y intercept using the equation of the line, plug in 0 for the x variable and solve for y.

y = 0.5(0) + 5

y = 5

To graph the y intercept using the equation of the line, plug in 1 for the x variable and solve for y.

y = 0.5(1) + 5

y = 5.5

Which means when x is 0, y intercept at 5 and when x is 1 y intercept at 5.5. Graph the line using the slope and the y-intercept, or the points.

This tells us, in practical terms, that, for every one unit that the x-variable increases (that is, moves over to the right), the y-variable increases (that is, goes up) by 50% of a unit.

6 0

4 years ago

2. f is a differentiable function on the interval [0, 1] and g(x) = f(3x). The table below gives values of f '(x). What is the v

Nataliya [291]

Chain rule:

$g(x)=f(3x)\implies g'(x)=3f'(3x)$

so

$g'(0.1)=3f'(0.3)=3(3)=9$

8 0

3 years ago

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