[tex]\frac{1}{1+\sqrt{2} } +\frac{1}{\sqrt{2} +\sqrt{3} } +...+\frac{1}{\sqrt{99} +\sqrt{100} }[/tex]

Answers

Answer 1

Answer:

9

Step-by-step explanation:

the given expression can be re-written:

[tex]\frac{\sqrt{2} -1}{(\sqrt{2}-1)(\sqrt{2}+1)} +\frac{\sqrt{3} -\sqrt{2}}{(\sqrt{3} +\sqrt{2})(\sqrt{3} -\sqrt{2})} + ...+\frac{\sqrt{100} -\sqrt{99}}{(\sqrt{100} -\sqrt{99})(\sqrt{100} +\sqrt{99})};[/tex]

then

[tex]\sqrt{2} -1+\sqrt{3} -\sqrt{2} +\sqrt{4} -\sqrt{3}+\sqrt{5} -\sqrt{4}+...+\sqrt{100}-\sqrt{99}= -1+\sqrt{100}=9.[/tex]


Related Questions

a cheetah ran 300ft in 2.92 sec what was the average speed in mph

Answers

Answer:

70.05 mph

Step-by-step explanation:

A cheetah ran 300 feet in 2.92 seconds. What is the cheetah's average speed in miles per hour

--------------------------------------

(300 ft/2.92 sec)(1 mi/ 5280 ft)(3600 sec/1 hour)

= {300*1*3600 miles)/(2.92*5280*1 hour)

 

= 91080000 miles/15417.6 hours

= 70.05 mph

The following relation is a function: {(-1,0), (1,3), (-2,0), (0,4)}.
True
False

Answers

Answer:

My answer is true hope this'll help

simplify the problem 4 . 3 + 1 . 6 + 8 . 4 − 0 . 9

Answers

Answer:

13.4

Step-by-step explanation:

4.3+1.6=5.9

5.9+8.4=14.3

14.3-0.9=13.4

The Wilsons have triplets and another child who is ten years old. The sum of the ages of their children is 37. How old are the triplets

Answers

Hope this helps have a nice day!!!!

9 years old because u do 37-10= 27 and 27/3= 9

Claire ate dinner at her favorite restaurant. When she received her bill, she wanted to
leave a 15% tip. What is the correct amount for Claire to tip, if the bill was $9.00?

Answers

Answer:

$1.35

Step-by-step explanation:

you multiply $9.00 (9) by 15% (.15). Which gives you 1.35.

The answer is $1.35.

Pablo's father is 4 years older than his mother. Pablo's mother is 42 years old. How old is his father? Pablo's father's age is:

Answers

Answer:

46

Step-by-step explanation:

1 sum  42+4

30 POINTS, WILL GIVE BRAINLIEST IF ONLY RIGHT
Which of these expressions is equivalent to log 200?

A) 2 + log 2
B) 2 + log 20
C) log 50 + log 150
D) log 250 – log 50

Answers

Answer:

ITS A ITS A ITS A

ANSWER = A

Step-by-step explanation:

There are 4 times as many dogs as cats if the total number of dogs and cats is 20

how many dogs are there

Answers

Answer:5

Step-by-step explanation: 4*5=20

Solve 4(x−5)=6x. You must SHOW EACH STEP for full credit.

Answers

Answer:

x = − 10

Step-by-step explanation:

Let's solve your equation step-by-step.

4 ( x − 5 ) = 6x

Step 1: Simplify both sides of the equation.

4 ( x − 5 ) = 6x

( 4 ) ( x ) + ( 4 ) ( − 5 ) = 6x ( Distribute )

4x + − 20 = 6x

4x − 20 = 6x

Step 2: Subtract 6x from both sides.

4x − 20 − 6x = 6x − 6x

− 2x − 20 = 0

Step 3: Add 20 to both sides.

− 2x − 20 + 20 = 0 + 20 − 2x = 20

Step 4: Divide both sides by -2.

− 2x / − 2 = 20 / − 2

x = − 10

at sunrise,the temperature outside was 5 below zero . by noon the temperature dropped 27. what was the temprature at noon

Answers

Answer:

-32

Step-by-step explanation:

hope this helps you with the question

Can someone help me please ?

Answers

Answer:

=

Step-by-step explanation:

1. The square root of 4 is 2 because [tex]2^2[/tex] = 4.

2. The cube root of 8 is 2 because [tex]2^3 = 2* 2 * 2[/tex] = 8.

3. 2 and 2 are equal.

Therefore, the correct symbol is =.

PLEASE HELP HELPPPPPPPPP

Answers

Answer:

(1,-4)

Step-by-step explanation:

2x+4y=-14

x-2y=9

2x+4y=-14

2(x-2y)=(9)2

2x+4y=-14

2x-4y=18

Add X

4x=4

X=1

Substitute x into any equation

(1)-2y=9

-2y=8

y=-4

The magnitude of an earthquake measured on the Richter scale is given by:
R(L) = log (l/l0), where l = amplitude.
Find the Richter scale rating of an earthquake with amplitude 1. 80 X 10 l0.
HELP ME PLEASEEEEEEEEEEE

Answers

Answer:

1.26

Step-by-step explanation:

R(L)=log((1.8 ×10)=log(18)=1.26

Someone pls help me I will make you brain

Answers

The answer is the 2nd choice, number of sales.

The function described f(x) = B + Cx

3.5m/min = how manny miles/hour

Answers

Answer:

[tex]\sf\longmapsto0.13 miles/hour[/tex]

Step-by-step explanation:

Firstly we have to use the formula to find the miles/hour

[tex]\sf\longmapsto \: Formula:Divide \: the \: speed \: value \: by \: 26.822.[/tex]

[tex]\sf\longmapsto \: 3.5 \div 26.822[/tex]

[tex]\sf\longmapsto \: 0.13 miles/hour[/tex]

|2i+3j| is equal to:

Answers

Answer:

Step-by-step explanation:

|2i+3j|=√(2²+3²)=√(4+9)=√13

Please answer these and find the slope intercept form for each one.
Best answer gets brainliest!

Answers

1. 5/y=2/3x +3
2. y= 7/1-4
3. y=2/5x8
4. y=-3/4 +1 I could be wrong but I think this is right

Eight identical pens cost $10.80.
a. Write an equation in the given box that represents the total cost, y, in dollars for a pens.

Answers

answer 10.80 x Y = X

Ricardo invests $8650 in an account that earns 3.9% interest compounded weekly. What is the total amount of his investment after 9 years? Round your answer to the nearest dollar.

Answers

Based on the amount he invested and the period of his investment, Ricardo's investment worth in 9 years will be $12,286.

The period of compounding is weekly so you first need to convert the interest rate to a weekly rate as well as the period of investment:

= 3.9% / 52 = 3.9/52%

= 9 years x 52 weeks per year = 468

Value of the investment after 9 years is:

= Amount x ( 1 + rate) ^ no. of periods

= 8,650 x (1 + 3.9/52%)⁴⁶⁸

= 12,285.599

= $12,286

In conclusion, the investment would be worth $12,286.

Find out more at https://brainly.com/question/10582389.

why did lil uzi vert get a diamond in his head

Answers

because he think he cool or whateva

Answer:

Because he thought it would make him stand out.

What is the square root of 111.2

Answers

Answer:

Well that whole thing is to the power of 2, so whatever the square root is, it gets multiplied by itself again just to get 111.2, so the solution to that question is 111.2.

Solve the problem based on the picture

Answers

Step-by-step explanation:

those are the x values in the graph above

now the slope

first, find the derivative = (-2*x)/(9+(6*x^2)+x^4)+(50*Cos(x))/(3+x^2)+((-100*x)*Sin(x))/(9+(6*x^2)+x^4)

then substitute the X values

the slope at first point=0.00214262528

the slope at secondpoint=0.29521512101

the slope at the third point=0.29521512101

Show 2 + 5 in number line.

Answers

To mark 2/5; move two parts on the right-side of zero. To mark 11/5; move eleven parts on the right-side of zero. To mark -8/5; move eight parts on the left-side of zero. To mark -3/5; move three parts on the left-side of zero

Write 3/6/7 in an improper fraction in the lowest term

Answers

Answer:

27/7

the mixed number 3 6/7 can be written as 27/7.

The value of an improper fraction in the lowest term is,

⇒ 27/7

We have to give that,

A mixed fraction is,

⇒ 3 6/7

Now, We can change the fraction into an improper fraction as,

⇒ 3 6/7

⇒ (3×7 + 6)/7

⇒ (21 + 6)/7

⇒ 27/7

Therefore, an improper fraction in the lowest term is,

⇒ 27/7

To learn more about the fraction visit:

https://brainly.com/question/5454147

#SPJ6

Which of the ordered pairs is a solution to
4x - y = 8?
a. (0, -8).
b. (0,8).
c. (8,0).
(-3.0

Answers

Answer:

a(0,-8)

Step-by-step explanation:

4x0=0

0--8= 8

What is the volume of this rectangular prism

Answers

Answer:

Do 7 x 4 = 28 and the bottom is 28

do answer is 56 enjoy brainliest

URGENT PLEASE HELP, respond to c, d, e, and f please !!

Answers

Answer:

Step-by-step explanation:

c. (18.5-17)/.9= 1.66666666667= 1.6667

d. .7107

e. .2185

f.  0.675=(x-17)/.9 x= 17.6075

please actually help me

Answers

Answer:

A.) 6:51

B.)The train at 6:42

C.)34 minutes

Can someone help me, please?

Answers

Answer:

112

Step-by-step explanation:

Y=5x+b

how do i solve for B?

Answers

Answer:

Y=5x+b

y-5x=b

B= y-5x

hope this helps

Answer:

b = y-5x

Step-by-step explanation:

y =5x+b  

Step 1- Cancelation minus or add the numeric first both side then variable numbers, then variables then exponents ^2 last.

In this case if we were asked to find x we would divide both sides by 5. But we are not asked that and instead asked to find b so we just apply and keep 5x together through add or subtraction.

For exponents we sqrt both sides. But this equation doesnt show any exponents so we stop at -5 each side.

y-5x=b

Step 2 - keep doing to isolate b we have no more to change other than reverse to show b first.

b = y-5x

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