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
pychu [463]
2 years ago
11

Prove 2√(x) + 1/√(x + 1) <= 2√(x+1) for all x in [0,inf)

Mathematics
1 answer:
EleoNora [17]2 years ago
3 0
Start by multiplying each side of the inequality by \sqrt{x + 1} and simplifying:

2 \sqrt x + \frac{1}{\sqrt{x+1}}  \leq  2 \sqrt{x + 1}
(2 \sqrt x + \frac{1}{\sqrt{x+1}})(\sqrt{x + 1}) \leq (2 \sqrt{x + 1})(\sqrt{x + 1})
2 \sqrt{x(x + 1)} + 1 \leq 2(x + 1)
2 \sqrt{x^2 + x} + 1 \leq 2x + 2
2 \sqrt{x^2 + x} \leq 2x + 1
\sqrt{x^2 + x} \leq x + \frac{1}{2}

From here, we can square both sides to get

x^2 + x \leq (x + \frac{1}{2})^2
x^2 + x \leq x^2 + x + \frac{1}{4}
0  \leq \frac{1}{4}, which is always true.
You might be interested in
10.
Kay [80]

Answer:

\frac{(82)(2.4)^2}{104.139} \leq \sigma^2 \leq \frac{(82)(2.4)^2}{62.132}

4.535 \leq \sigma^2 \leq 7.602

Now we just take square root on both sides of the interval and we got:

2.2 \leq \sigma \leq 2.8

And the best option would be:

A.  2.2 < σ < 2.8

Step-by-step explanation:

Information provided

\bar X=32.1 represent the sample mean

\mu population mean  

s=2.4 represent the sample standard deviation

n=83 represent the sample size  

Confidence interval

The confidence interval for the population variance is given by the following formula:

\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}

The degrees of freedom are given by:

df=n-1=83-1=82

The Confidence is given by 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, the critical values for this case are:

\chi^2_{\alpha/2}=62.132

\chi^2_{1- \alpha/2}=104.139

And replacing into the formula for the interval we got:

\frac{(82)(2.4)^2}{104.139} \leq \sigma^2 \leq \frac{(82)(2.4)^2}{62.132}

4.535 \leq \sigma^2 \leq 7.602

Now we just take square root on both sides of the interval and we got:

2.2 \leq \sigma \leq 2.8

And the best option would be:

A.  2.2 < σ < 2.8

3 0
3 years ago
PLEASE HELP ASAP 25 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
Alex777 [14]

Answer:

Its D

Step-by-step explanation:

x = 1

x = -1

 x=  0.0000 - 3.0000 i

 x=  0.0000 + 3.0000 i

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".  4 more similar replacement(s).

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((((((x6)-(2•(x5)))+(9•(x4)))-24x3)-x2)+18x)-9  = 0

Step  2  :

Equation at the end of step  2  :

 (x6)-(2•(x5)+(32x4)-24x3)-x2)+18x)-9  = 0

Step  3  :

Equation at the end of step  3  :

 (x6)-2x5)+32x4)-24x3)-x2)+18x)-9  = 0

4 0
3 years ago
A triangle has an area of 24 square cm and a base of 4 cm. Which is the
devlian [24]
The answer is C. So if u plug it in the equation should look something like this: 4*12 / 2
3 0
3 years ago
What does the perimeter of this figure consist of?
Alexandra [31]
We have on the top of the figure one semircle, on the bottom of the figure another semicircle, to the left of the figure a line segment, and to the right of the figure another line segment, then we have a total of two semicircles and two line segments.

Answer: Fourth option: two semicircles and two line segments
8 0
3 years ago
Read 2 more answers
Graph a line with a slope of -2/5 that contains the point (-3, 5)
ValentinkaMS [17]
Picture so I am able to solve problem please
8 0
3 years ago
Other questions:
  • Need help one step equations multiplication and Division
    9·1 answer
  • What is the sample mean of the data set? Round to the
    10·1 answer
  • What is the solution to the equation below?<br> log 4x2 - log6x = 2
    15·1 answer
  • write an equation for this situation then Solve it. employee A gets paid $13 an hour .he got paid $591.50 this month. how many h
    9·1 answer
  • The perpendicular bisector of side AB of triangle ABC intersects the extension of side AC at D. Find the measure of angle ABC if
    6·1 answer
  • 9-(7-3x) = 4+x-(3-x) solve for x
    10·1 answer
  • Sean wants to buy a DVD that sells for $12. An advertisement says that next week that DVD will be on sale for $9. How much money
    15·2 answers
  • Identify h (x) = [x] + 4
    10·1 answer
  • PLZZ HELP?
    14·2 answers
  • Altogether in a school there are 240 people.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!