[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

The expression - 250 + 16z represents a submarine that began at a depth of 250 feet below sea level
and ascended at a rate of 16 feet per minute. What was the depth of the submarine after 9 minutes?

Answers

= -250 + 16z
= -250 + 16(9)
= -250 + 144
= -106 feet

An insect's head accounts for approximately 60% of its total mass. If the insect weighs 40 g, what is the mass
of its head?

Answers

Answer:

24 g

Step-by-step explanation:

60/100x40

2400/100

24

A water tank has two valves, one for inlet pipe and the other is outlet pipe. If the tank is empty the inlet valve is

opened, the tank will be full of water after 5 hours. If the tank is full and the outlet valved is opened, the tank

will be emptied in 8 hours. Suppose the tank is empty and both valves are opened, in how many hours will the

tank be full?

Answers

Let V be the volume of the tank. The inlet pipe fills the tank at a rate of

V / (5 hours) = 0.2V / hour

and the outlet pipe drains it at a rate of

V / (8 hours) = 0.125V / hour

With both valves open, the net rate of water entering the tank is

(0.2V - 0.125V ) / hour = 0.075V / hour

If t is the time it takes for the tank to be full, then

(0.075V ) / hour • t = V

Solve for t :

t = V / ((0.075V ) / hour)

t = 1/0.075 hour

t ≈ 13.333 hours

Ken bought a new car and had to borrow $6,500 from the bank. The bank charged
Ken 3.7% in simple interest for the 5 years Ken had the bank loan. What's the total
amount Ken will have to repay the bank?

Answers

Answer: 65005.037

Step-by-step explanation:

I=?

P=6,500

R=037

T=5 years

 I=  6,500+037+5= 65005.037

9. The repair order is a legal document because

People say it’s B or C, which one is correct.

Correct gets brainliest!!!

Answers

Answer:

C is the correct answer cos it is paid by the customer

Write 6^7 + 6^5 + 11 in base six. Use the digits 0, 1, 2, 3, 4, 5

Answers

Answer:

Sorry I don't remember the answer

Help help help help help help help​

Answers

I) Degree Yes No m b

6) 1 √ 1 10

7) 1 √ 5 -1

8) 2 √

II)

9) x = 1,y = 3, 3x

x = 2,y = 6, 3x

x = 3,y = 9, 3x

It's a linear equation because it has 1 degree of function.

f(x) = 3x + 0.

10) x = -2,y = 4,x²

x = -1,y = 1,x²

x = 0,y = 0,x²

It's not linear a linear equation because it has 2 degree of function.

A)

1. m = -2/3 , b = 4

y = mx + b

y = -2/3x + 4

Values;

x= 0,y = 4 (0, 4)

x=1,y=10/3 (1,10/3)

x=2, y= 8/3 (2, 8/3)

x=3, y=2 (3, 2)

x=4, y=4/3 (4, 4/3)

The graph is the 1st one above.

2. a = -2 , b = 3

y = mx + b

at y = 0, x = -2

0 = m(-2) + 3

-3 = -2m

m = 3/2

y = 3/2x + 3

Values;

x = -2, y=0, (-2, 0)

x = -1, y = 3/2, (-1, 3/2)

x = 0,y = 3, (0, 3)

x = 1,y = 9/2, (1, 9/2)

x = 2, y = 6, (2, 6)

The graph is the 2nd one above.

mr. tyler has a total of $5,000 in savings account and in a mutual fund. If he has x dollars in the savings account, how much dollars does he have in the mutusl fund?

Answers

5000-x is the number of dollars in the mutual fund

Mr. Tyler has $(5000 - x) in the mutual fund, where is amount in the saving account.

If Mr. Tyler has $5,000 in total, and x dollars in the savings account.

The amount he has in the mutual fund can be calculated by subtracting the amount in the savings account from the total amount.

Amount in the mutual fund = Total amount - Amount in the savings account

Here, Total amount = $5000 and Amount in the savings account = x

Substituting the values back to the formula as

Amount in the mutual fund = $5,000 - x

So, Mr. Tyler has $(5000 - x) in the mutual fund.

Learn more about Mutual Fund here:

https://brainly.com/question/22525531

#SPJ3

CAN SOMEONE HELP ME ASAP: Write 0.0000000642 in scientific notation.

Answers

Answer:

6.42 × 10-8.

Step-by-step explanation:

vububTodyksyk

Answer:

6.42 x [tex]10^{-8}[/tex]

Step-by-step explanation:

0.0000000642 in scientific notation = 6.42 x [tex]10^{-8}[/tex]

The sum of the real numbers x and y is 11. Their difference is 5. What is the value of xy?

Answers

Answer:8

Step-by-step explanation:

Answer:

xy=24

Step-by-step explanation:

x+y=11

x-y=5

x=y+5

y+5+y=11

2y=6

y=3

x=8

xy=24

can somebody please just help me do not answer if you do not know

Answers

Answer:

it could be 34 , 34 and 82

or 34 , 73 and 37

Step-by-step explanation:

angles in a triangle add up to 180. in and isosceles triangle two angles are always the same so there will be 2 possible outcomes.

pls mark brainalist

Brainlest Evaluate (-2-2-1/2)³​

Answers

Decimal form -91.125

Exact form -729/8

Answer:

[tex]\sf\longmapsto \: \frac{ - 792}{8} [/tex]

Step-by-step explanation:

[tex]\sf\longmapsto \: (−4− \frac{1}{2} ) {}^{3} [/tex]

[tex]\sf\longmapsto \: (− \frac{9}{2} ) {}^{3} [/tex]

[tex]\sf\longmapsto \: \frac{ - 729}{8} [/tex]

[tex]\sf\longmapsto \: Decimal: -91.125[/tex]

a line containing the points (4, y) and (-3, 2) has a slope of 3/2.

Answers

Answer:

y=14.5

Step-by-step explanation:

A slope of 3/2 means that for every unit it moves to the right, it will move 1.5 units up. The x of 4 is 7 more than the -3 of our other point. 7*1.5=12.5, and 12.5+2=14.5.

guys pls help me!!!!!!

Answers

Answer:

X would also be 59° due to the Corresponding property.

Express the values below I’m scientific notation 52,800g, 255.6m, 0.04109cm!?

Answers

Answer:

1) 5.28 x 10^4 g

2)2.556 x 10^2 m

3)4.109 × 10^-2cm

Have a nice day!!!!!

Answer:

52,800 in scientific notation is [tex]5.28[/tex] × [tex]10^4[/tex].

255.6 in scientific notation is [tex]2.556[/tex] × [tex]10^2[/tex].

0.04109 in scientific notation is [tex]4.109[/tex] × [tex]10^{-2}[/tex].

the average age of teacher at school is 36 years.mr Smith age is 11/9 of the average. how old is Mr Smith?​

Answers

Answer: 44

Step-by-step explanation:

I'm positive this is right! Have a good day! Hope this helps! Please give brainliest, i would help a lot if you did, but its fine if you don't Just have a good rest of the day!

HELP RN PLEASE!!!!!!!!​

Answers

What is the question

Step-by-step explanation:

this is the answer

hopes it helps

which is colder -3°c or -2°c

Answers

-3°C is the coldest temperature

Answer:

-2 is colder

Step-by-step explanation:

Becuase when you get to the negative the Closest number to 0 is greater which means -2 is closer to 0 which makes it colder.

(Hope this helps can I pls have brainlist (crown)☺️)

4 cm
15 cm

-
Find volume

Answers

Answer:

The answer is 753.98224.

V=πr^2h, so v=pie4^2*15

Therefore, V=πr2h=π·42·15=753.98224

Step-by-step explanation:

The volume = [tex](\frac{22}{7} )(4^{2} )(15)[/tex]

= 754.285714

please give me a brainliest answer

a man earned $180 for working 14 hours. How many hours must he work to earn 300

Answers

Answer:

it would be roughly 24 hours

Step-by-step explanation:

180÷14

12.8571428571

simplify to 12.85

12.85× X = 300

X=24

Evaluate. 2 > 8 - 4/3h

Answers

Answer: h>9/2

Step-by-step explanation:

Which expression is equivalent to 5 to the power of 6

5^6

Answers

Answer:

5^6

5^6 is the same thing as

5^6=5×5×5×5×5×5

=5×5=25×5=125×5=625×5=3125×5=15625

5^6= 15625

Answer:

125 * 125

Step-by-step explanation:

do 125 x 125 = 15625

LY!
Fill in the missing numbers to complete the pattern:
2.6, 3.1,
4.6, 5.1

Answers

The pattern is adding 0.5 each time. So the missing values are:
3.6 and 4.1

plz help me help me help me

Answers

The answer is this :) hope I helped

Answer:

Step-by-step explanation: 16 is for the apple juice for when the orange juice is 8 since orange juice is half of the apple juice. For the last one the apple juice is 32 and the orange juice is 16

Will give 5 points for answer

Answers

Answer:

1and 3 are not a function 2 and 4 are a function 6 not enough

Step-by-step explanation:

helpppppppppppppppppppppppppppppp meeeeeeeeeeeeeeeeeee plsssssssssssssssssssssss there is more but plss help mee​

Answers

Answer: The attachment is a bit difficult to read, and long.  I'll make some suggestions and add some detail to a few of the problems, but would ask that these suggestions be applied to other problems to find the answers.

Step-by-step explanation:

9.   Coinciding lines line on top of each other.  I.e., they are the same equation.  If we take A, for example, we can reduce the second expression by dividing by 2:  (2x+4y=6)/2 = (x + 2y = 3).  This matches the first expression (x + 2y = 3).  !   Whoa, that went fast.

10.   (x+8)(x-8) = x² +8x -8x - 64 = x² - 64

11.  I don't have the time to explain how one can factor, but practice is important.  And I don't know if this is completely factored, but it matches one of the options.  Try (n-2)(n²+2n + 4)  [n³ +2n² +4n - 2n² -4n -8 = n³ - 8.  It works.

12.  The denominators are the same, so add the numerators and keep the denominator.  (7x+4y)/x²y

13.  The slope is the "Rise" over the "Run."  (3,4), (8,-1)  Rise = (-1 - 4) = -5.  Run = (8-3) = 5  Slope = -(5/5) = -1

14.  A line with a positive slope will move upwards as x increases.  We can eliminate options C and D immediately.  That leaves A and B.  The line we are looking for is y = 5x + b.  We are not given b, the y-intercept, so determine the slopes of both lines:  I get 4 for A and 5 for B.  To confirm B is correct, we could calculate b for y=5x+b by using given point, (2,3).  3 = 5*2 + b, b = -7.  We can't see this point (0,-7) on the graph, but it appears correct.  B is the best answer.

15.  The line will have the form of y=mx+b.  Calculate m, the slope, from the two points (3,1) and (4,7).  Rise = 6, Run = 1  Slope = 6.  y=6x+b.  Find b by using either of the given poins and solving for b.  I'll choose (3,1).  y=6x+b;  1 = 18 + b; b = -17.  The equation is y=6x-17.  Rearrange option A (y =6x - 17).

16.  The second value in each factor must, when multiplied together, equal the final term of the original expression, -9y².  I see only one option for which that is true, C.  Multiply the two factors in C to be certain, and you'll find they result in the correct expression.

What is a correct congruence statement for the triangles shown?
Enter your answer in the box.
ΔQDJ=Δ____

Answers

Answer:

GAP but if not that AGP

Step-by-step explanation:

Answer:

ΔQDJ ≅ GAP

Step-by-step explanation:

Use the order of corresponding vertices.

Q and G, D and A, J and P are corresponding considering the marks on the lines.

ΔQDJ ≅ GAP

What is the equation of a line that passes through the point (8, -2) and is parallel to the line whose equation is 3x + 4y = 15?

Answers

Answer:

y = -3/4x + 4 or 3x + 4y = 16

Step-by-step explanation:

Step 1

Find the slope of the given line

we have

3x + 4y = 15

Isolate the variable y

Subtract 3x from both sides

3x + 4y -3x = 15-3x

Divide by 4 both sides

y = -3/4x + 15/4

the slope of the given line is

m = -3/4

Step 2

Find the equation of the line that passes through  the point  and is parallel to the given line

we know that

if two lines are parallel, then their slopes are equal

The equation of the line into point-slope form is equal to

y - y₁ = m(x-x₁)

we have

m= -3/4

(x1,y1) = (8,-2)

substitute in the equation

y + 2= -3/4(x-8)

y = -3/4x + 6 - 2

y = -3/4x + 4 or 3x + 4y = 16

therefore

the answer is

y = -3/4x + 4

or

3x + 4y = 16

Simplify to create an equivalent expression
-5(3p+3) + 9(-7+p)
The answers are:
A)-5p-78
B)-6p-78
C)-6p-48
D)-6p+78

Answers

The answer is B. -6p-78. Pls mark brainliest.

THANK YOU TO WHOEVER DOES THIS <3

Answers

Answer:

2436 cubic centimeters

Step-by-step explanation:

11 * 14 = 154

14 * 7 / 2 = 49

154 + 49 = 203

203 * 12 = 2436

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