1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
alukav5142 [94]
3 years ago
12

Which expression is equivalent to (1/4ab)^-2? Assume a is not equal to 0,b is not equal to 0

Mathematics
2 answers:
Ede4ka [16]3 years ago
8 0

Answer:

d. 16a^2b^2

Step-by-step explanation:

Given expression,

(\frac{1}{4ab})^{-2}

=((4ab)^{-1})^{-2}     \because \frac{1}{a^m}=a^{-m}

=(4ab)^{-1\times -2}    \because (a^m)^n=a^{mn}

=(4ab)^2

=(4)^2(a)^2(b)^2        \because (ab)^m=a^mb^m

=16a^2b^2

Hence, option d is correct.

Pie3 years ago
7 0
The answer would be D. 
You might be interested in
PLEASE HELP ME
Kitty [74]

Answer:

C.

hope it help^_^(♡˙︶˙♡)

5 0
3 years ago
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 ln(x) (a) Find the interval on which f is incre
Ainat [17]

Answer: (a) Interval where f is increasing: (0.78,+∞);

Interval where f is decreasing: (0,0.78);

(b) Local minimum: (0.78, - 0.09)

(c) Inflection point: (0.56,-0.06)

Interval concave up: (0.56,+∞)

Interval concave down: (0,0.56)

Step-by-step explanation:

(a) To determine the interval where function f is increasing or decreasing, first derive the function:

f'(x) = \frac{d}{dx}[x^{4}ln(x)]

Using the product rule of derivative, which is: [u(x).v(x)]' = u'(x)v(x) + u(x).v'(x),

you have:

f'(x) = 4x^{3}ln(x) + x_{4}.\frac{1}{x}

f'(x) = 4x^{3}ln(x) + x^{3}

f'(x) = x^{3}[4ln(x) + 1]

Now, find the critical points: f'(x) = 0

x^{3}[4ln(x) + 1] = 0

x^{3} = 0

x = 0

and

4ln(x) + 1 = 0

ln(x) = \frac{-1}{4}

x = e^{\frac{-1}{4} }

x = 0.78

To determine the interval where f(x) is positive (increasing) or negative (decreasing), evaluate the function at each interval:

interval                 x-value                      f'(x)                       result

0<x<0.78                 0.5                 f'(0.5) = -0.22            decreasing

x>0.78                       1                         f'(1) = 1                  increasing

With the table, it can be concluded that in the interval (0,0.78) the function is decreasing while in the interval (0.78, +∞), f is increasing.

Note: As it is a natural logarithm function, there are no negative x-values.

(b) A extremum point (maximum or minimum) is found where f is defined and f' changes signs. In this case:

  • Between 0 and 0.78, the function decreases and at point and it is defined at point 0.78;
  • After 0.78, it increase (has a change of sign) and f is also defined;

Then, x=0.78 is a point of minimum and its y-value is:

f(x) = x^{4}ln(x)

f(0.78) = 0.78^{4}ln(0.78)

f(0.78) = - 0.092

The point of <u>minimum</u> is (0.78, - 0.092)

(c) To determine the inflection point (IP), calculate the second derivative of the function and solve for x:

f"(x) = \frac{d^{2}}{dx^{2}} [x^{3}[4ln(x) + 1]]

f"(x) = 3x^{2}[4ln(x) + 1] + 4x^{2}

f"(x) = x^{2}[12ln(x) + 7]

x^{2}[12ln(x) + 7] = 0

x^{2} = 0\\x = 0

and

12ln(x) + 7 = 0\\ln(x) = \frac{-7}{12} \\x = e^{\frac{-7}{12} }\\x = 0.56

Substituing x in the function:

f(x) = x^{4}ln(x)

f(0.56) = 0.56^{4} ln(0.56)

f(0.56) = - 0.06

The <u>inflection point</u> will be: (0.56, - 0.06)

In a function, the concave is down when f"(x) < 0 and up when f"(x) > 0, adn knowing that the critical points for that derivative are 0 and 0.56:

f"(x) =  x^{2}[12ln(x) + 7]

f"(0.1) = 0.1^{2}[12ln(0.1)+7]

f"(0.1) = - 0.21, i.e. <u>Concave</u> is <u>DOWN.</u>

f"(0.7) = 0.7^{2}[12ln(0.7)+7]

f"(0.7) = + 1.33, i.e. <u>Concave</u> is <u>UP.</u>

4 0
3 years ago
if serena invested the 2500 in the cd that she yields at 4% interest, what will the cdbe worthafte 2 years?
Naya [18.7K]

Your answer would be <u>2700</u>

Using I=P*r*t

P= 2500

R= 4% (substitue to 0.04)

T= 2 Years

I= 2500* 0.04 * 2

I= 100* 2

I= 200

2500+200=

2700

6 0
3 years ago
Read 2 more answers
What type of function is y=x^2+6x+5
nata0808 [166]

Hello.

\mathrm{y=x^{2} +6x+5} is a quadratic function, because it has an \mathrm{x^{2} } (x squared, or x times x) term.

Here's what linear functions look like:

\mathrm{y=mx+b}

A graph of a linear function is a line.

Quadratic functions look like so:

\mathrm{y=ax^{2} +bx+c}

A graph of a quadratic function is a parabola.

Therefore, the given function is a quadratic function.

I hope this helps.

Have a nice day.

\boxed{imperturbability}

3 0
2 years ago
Write the multiple of the first even number from 11 to 20​
andrew-mc [135]

Answer:

Multiples [10] - 10, 20, 30, 40, 50

Multiples [11] - 11, 22, 33, 44, and 55

<u><em>Find the Even numbers of these multiples</em></u>

Multiples [10]

  • - 10 = Even
  • - 20 = Even
  • - 30 = Not Even
  • - 40 = Even
  • - 50 = Not Even

  1. <u><em>10 × 1 = 10</em></u>
  2. <u><em>10 × 2 = 20</em></u>
  3. <u><em>10 × 3 = 30</em></u>
  4. <u><em>10 × 4 = 40</em></u>
  5. <u><em>10 × 5 = 50</em></u>

Multiples [11]

  • - 11 = Not Even
  • - 22 = Even
  • - 33 = Not Even
  • - 44 = Even
  • - 55 =  Not Even

  1. <u><em>    11 × 1 = 11</em></u>
  2. <u><em>    11 × 2 = 22</em></u>
  3. <u><em>    11 × 3 = 33</em></u>
  4. <u><em>    11 × 4 = 44</em></u>
  5. <u><em>    11 × 5 = 55</em></u>
  6. <u><em>    11 × 6 = 66</em></u>
  7. <u><em>    11 × 7 = 77</em></u>
  8. <u><em>    11 × 8 = 88</em></u>
  9. <u><em>    11 × 9 = 99</em></u>

Step-by-step explanation:

.... I messed up, sorry. I thought that 20 said 11

8 0
2 years ago
Other questions:
  • Describe a transformation of the graph of f(x)=x that results in the graph of g(x)=4x
    9·1 answer
  • Please help me with 25-29!!
    12·1 answer
  • A carriage on a carnival ride can hold up to 4 people. How many carriages are needed for a group of 22 people to ride?
    15·1 answer
  • Need this question answered correctly and FAST! PLEASE!
    5·1 answer
  • A square has a side of 3x - 4 what is the area of the Square in terms of x?
    10·1 answer
  • Two destinations A and B are located on an east-west line 152 miles apart. From A to the starting point, S, bearing is N62 ° E,
    11·1 answer
  • Mr. Allen needs to store his boat for winter. He needs to fill the gas tank and put fuel preserver in the tank. The fuel tank ho
    6·1 answer
  • HELP ME I NEED YOUR HELP PEALSE will give brainliest
    13·1 answer
  • Which is the net for this rectangular prism?
    13·1 answer
  • In a triangle where side a = 15 inches, side b = 11 inches, and angle A = 30 degrees, what is angle C?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!