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
Ilia_Sergeevich [38]
3 years ago
14

If the interval (a, infinity) describes all values of x for which the graph of f(x)=4/x^2-6x+9 is decreasing, what is the value

of a
Mathematics
2 answers:
Afina-wow [57]3 years ago
7 0

Answer:

The answer is "3".

Step-by-step explanation:

\texttt{Given graph equation: } \\\\\bold{\Rightarrow f(x)=\frac{4}{x^2-6x+9} }

\bold{\ interval:  (a,\infty)}

differentiate the function f(x):

\Rightarrow f'(x) = \frac{d }{dx}(\frac{4}{x^2-6x+9})\\\\

Formula:

\bold{\frac{d}{dx} \frac{v}{u}= \frac{u \frac{d}{dx} v- v\frac{d}{dx}u }{u^2}}

\Rightarrow f'(x) = \frac{d }{dx}(\frac{4}{x^2-6x+9})\\\\\\\Rightarrow f'(x) = \frac{d }{dx}(\frac{(x^2-6x+9) \frac{d}{dx} 4- 4\frac{d}{dx}(x^2-6x+9) }{(x^2-6x+9)^2})\\\\\\\Rightarrow f'(x) = \frac{d }{dx}(\frac{(x^2-6x+9) \times 0 - 4(2x-6) }{(x^2-6x+9)^2})\\\\\\\Rightarrow f'(x) =  \frac{- 4(2x-6)}{(x^2-6x+9)^2}\\\\\\\Rightarrow  \frac{- 4(2x-6)}{(x^2-6x+9)^2}=0\\\\\Rightarrow - 4(2x-6)=0\\\\\Rightarrow  8x-24=0\\\\\Rightarrow  8x=24\\\\\Rightarrow  x=\frac{24}{8}\\\\\Rightarrow  x=3\\\\

since the value of x in: (-3 ,\infty) \ \  and  \ \ (3, \infty) and f'(x). So, the value of a is 3

wariber [46]3 years ago
6 0

Answer:

3

Step-by-step explanation:

You might be interested in
Aleksandra started studying how the number of branches in her tree grows over time. Every 1.5 years, the number of branches incr
vova2212 [387]

Answer:

N = 52 * (9/7)^(t/1.5)

Step-by-step explanation:

This problem can be modelated as an exponencial problem, using the formula:

N = Po * (1+r)^(t/1.5)

Where P is the final value, Po is the inicial value, r is the rate and t is the amount of time.

In our case, we have that N is the final number of branches after t years, Po = 52 branches, r = 2/7 and t is the number of years since the beginning (in the formula we divide by 1.5 because the rate is defined for 1.5 years)

Then, we have that:

N = 52 * (1 + 2/7)^(t/1.5)

N = 52 * (9/7)^(t/1.5)

7 0
3 years ago
Write 5 consecutive integers of which x is the middle one
stich3 [128]
X-2, x-1, x, x+1, x+2
3 0
3 years ago
Which set of numbers is correctly ordered from greatest to least?
Nina [5.8K]

Answer:

It's D.

Step-by-step explanation:

Convert each number to decimal format.

It is option D , if we convert as above we get

7.36799, 7.36666.., 7.363636.., 7.33333..

4 0
3 years ago
Read 2 more answers
Benjamin bought 12 goldfish. Each goldfish cost $0.98. How much did Benjamin spend?
almond37 [142]
11.76 dollars. just multiply the numbers together

5 0
3 years ago
Read 2 more answers
1. Which would be a more helpful for solving the system: adding the two equations or subtracting
ira [324]

Answer:

1) Subtracting one from the other

2) x = 0.375 and y = 0.125

Step-by-step explanation:

Equation 1 :

\frac{2x+1}{2y}=7\\\\

Equation 2:

\frac{6x-1}{2y}=5

To solve these equations by the Elimination method we multiply equation 1 with 6 and multiply equation 2 with 2 so now,

\frac{2x+1}{2y} =7\\\\2x+1=14y\\\\Multiplying\ Equation\ 1\  with\ 6\\\\12x+6=84y

Now for the second equation:

\frac{6x-1}{2y}=5\\\\6x-1=10y\\\\Multiplying\ equation\ 2\ with\ 2 \\\\12x-2=20y

Now subtracting equation 2 from equation 1

12x+6=84y\\\\12x-2=20y\\\\Subtracting\ leads\ to\\12x-12x+6-(-2)=84y-20y\\0+8=64y\\8=64y\\8/64=y\\0.125=y

now insert this value of y into any equation

lets insert it into equation 1

\frac{2x+1}{2y} =7\\\\2x+1=14y\\2x+1=14(0.125)\\2x+1=1.75\\2x=1.75-1\\2x=0.75\\x=0.75/2\\x-0.375

5 0
3 years ago
Other questions:
  • A recipe for cookies requires 2/3 cup of butter. Raheim wants to make 3/4 of the recipe. How many cups of butter should Raheim u
    11·2 answers
  • Jonathan is making his favorite pasta dish his mom ate 2/7 of the pasta his brother ate 1/6 of the pasta how much did they eat i
    7·2 answers
  • If r(x) = 3x – 1 and s(x) = 2x + 1, which expression is equivalent to
    14·2 answers
  • Find the area of an equilateral triangle (regular 3-gon) with the given measurement.
    5·1 answer
  • Help me please !!!!!!!
    9·2 answers
  • I DONT KNOW HELP PLEASE !!!
    11·1 answer
  • F(x)=x2+1 g(x)=5-1
    6·1 answer
  • Use your calculator to find when the car will be worth $9885
    11·1 answer
  • The perimeter of a rectangle is 304 cm. The length is 40 cm longer than the
    11·1 answer
  • Select the three equations that have the same solution.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!