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2 years ago

What is the domain and derivative of f(x)=ln(2xsqrt(2+x))?

Mathematics

1 answer:

wolverine [178]2 years ago

5 0

For domain 2x sqrt(2+x)>0
x>0,2+x>0,x>-2 combining
we get x>2
f'(x)=[1/{2x sqrt(2+x)}][{2x/(2 sqrt(2+x))}+2 sqrt(2+x)]

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I have been asking for assistance for an hour and a half now, I will greaty appreciate anyone that can help with this..Find the

blagie [28]

Answer:

1st graph: m = -1/2. (m is the slope)

2nd graph: m = 3/2.

3rd graph: Midpoint = (1/2, 1/2)

Step-by-step explanation:

1st graph:

Find the slope by looking for two points on the line. Use the formula $m = \frac{y_{2}-y_{1} }{x_{2}-x_{1}}$

We can derive the points (-3, 0) and (1, -2). Plug these into the equation above.

$m= \frac{-2-0}{1-(-3)}$

Simplify this, giving you: m = -1/2.

2nd graph:

Use the same formula as stated above. From this graph, you can plug in the points (-1, 1) and (1, 4)

$m = \frac{4-1}{1-(-1)}$

Simplifying gets you: m = 3/2.

3rd graph:

To find the midpoint, use the formula: $(\frac{x_{1}+x_{2} }{2} , \frac{y_{1} +y_{2} }{2} )$

Plug in the end-points of the graph, or (-3, 2) and (4, -1).

You get:

$(\frac{-3+4}{2}, \frac{2-1}{2})$

Simplify:

Midpoint = (1/2, 1/2)

3 0

3 years ago

Help!!!which of the following best describes the algebraic expression 10x+2

padilas [110]

I believe the correct answer is C) Ten times the quantity of a number plus two. Hope this helps! =)

4 0

3 years ago

Read 2 more answers

X² - 36= x² - y²= 100 - a²= c² - 9/49=

bixtya [17]

Answer:

Step-by-step explanation:

i am using my sisters account hehe thats what u get for taking a shortcut boyyyyyyyyyy

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3 years ago

Write and equati9n of a l8ne that passes through (1,-2) and is perpendicular to -4x+7y=21

yarga [219]

Given:

A line passes through (1,-2) and is perpendicular to $-4x+7y=21$ .

To find:

The equation of that line.

Solution:

We have, equation of perpendicular line.

$-4x+7y=21$

Slope of this line is

$m_1=-\dfrac{\text{Coefficient of x}}{\text{Coefficient of y}}$

$m_1=-\dfrac{-4}{7}$

$m_1=\dfrac{4}{7}$

Product of slope of two perpendicular lines is -1.

$m_1\times m_2=-1$

$\dfrac{4}{7}\times m_2=-1$

$m_2=-\dfrac{7}{4}$

Now, slope of required line is $-\dfrac{7}{4}$ and it passes through (1,-2). So, the equation of line is

$y-y_1=m(x-x_1)$

where, m is slope.

$y-(-2)=-\dfrac{7}{4}(x-1)$

$4(y+2)=-7(x-1)$

$4y+8=-7x+7$

$4y+7x=7-8$

$7x+4y=-1$

Therefore, the equation of required line is $7x+4y=-1$ .

7 0

2 years ago

Which triangles are similar by the angle-angle criterion for similarity of triangles ?

Alex Ar [27]

Answer:

Option D is correct.

$\triangle ADE \sim \triangle ABC$

Step-by-step explanation:

In triangle ADE and triangle ABC

From the figure:

$\angle ADE = \angle ABE$ [Angle] [Given]

$\angle DAE = \angle BAC$ [Angle]

AA(Angle-Angle) similarity criterion states that in two triangles if two pairs of corresponding angles are equal, then these triangle Similar.

By AA similarity:

⇒ $\triangle ADE \sim \triangle ABC$

5 0

3 years ago