2/4.7+2/7.10+2/10.13+2/13.16+.....+2/49.52

tính giá trị biểu thức

Answers

Answer 1

It looks like you're trying to evaluate the sum,

[tex]\displaystyle \frac2{4\times7} + \frac2{7\times10} + \frac2{10\times13}+\cdots+\frac2{49\times52}[/tex]

which can be written as

[tex]\displaystyle \sum_{n=1}^{16} \frac2{(3n+1)(3n+4)}[/tex]

Split up the summand into partial fractions:

[tex]\displaystyle \frac2{(3n+1)(3n+4)} = \frac a{3n+1} + \frac b{3n+4} \\\\ \implies 2 = a(3n+4)+b(3n+1) \\\\ \implies 2 = (3a+3b)n+4a+b[/tex]

so that

3a + 3b = 0, or a = -b

4a + b = 2

Solve for a and b :

4a + (-a) = 3a = 2   ==>   a = 2/3   ==>   b = -2/3

So the sum is

[tex]\displaystyle \frac23 \sum_{n=1}^{16} \left(\frac1{3n+1} - \frac1{3n+4}\right)[/tex]

Write out the first terms and observe that several terms cancel with each other:

2/3 (1/4 - 1/7)

+ 2/3 (1/7 - 1/10)

+ 2/3 (1/10 - 1/13)

+ …

+ 2/3 (1/43 - 1/46)

+ 2/3 (1/46 - 1/49)

+ 2/3 (1/49 - 1/52)

So the sum collapses and simplifies to

[tex]\displaystyle \sum_{n=1}^{16} \frac2{(3n+1)(3n+4)} = \frac23 \left(\frac14 - \frac1{52}\right) = \boxed{\frac2{13}}[/tex]


Related Questions

Help please…

If (tan^30-1/tan0-1)-sec^20+1=0, find cot0

Answers

Answer:

dl5fgtrrfhrruf ofender fkufgj jjgglr

Fill the empty slots by dragging tiles from the left to show the next step for sloving the equation solve the two step equation negative nine and a mumber plus zero point four equals to four

Answers

Step-by-step explanation:

gjlhcohuguo

y.krgkyfjfhcxhhhxhhxfucuchhcjvgjjgvjvkvkx

simplify: 5 (6 - ab) + 2 (-7 + 3ab)

Answers

Answer:

30-5ab-14+6ab

16-ab ans

Answer:

[tex] \boxed{ab + 16} [/tex]

Step-by-step explanation:

5 (6 – ab) + 2 (-7 + 3ab)

[distribution property]

(6)(5) – (ab)(5) + (-7)(2) + (3ab)(2)

30 – 5ab – 14 + 6ab

[group like terms]

(6ab – 5ab) + (30 – 14)

ab + 16


There is a bag filled with 4 blue, 3 red and 5 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is
replaced.
Another marble is taken at random.
What is the probability of exactly 1 red?

Answers

Answer:

25%

Step-by-step explanation:

4+3+5=12

3/12 ×100=25

Determine whether the equation represents direct, inverse, joint, or combined variation.
y = 4x^3z^3

Answers

Answer: The retort to the peculiar proposed interrogate is definitively identified as ‘Joint Variation’, interchangeably acknowledged as ‘Combined Variation’.

Step-by-Step Explanation:

Given the mathematical statement,
Y = 4x^3z^3

Such coherently demonstrates the principle of a foreign variable, ‘y’, which whom varies directly as the product of at least two distinct or distinguishable quantities occur.

The mentioned is the precise definition of Joint Variation, where ‘y’ is jointly proportional to the product of the minimum agglomerate of two quantities, whilst a presence of a nonzero constant, k.


*I hope this helps.

can someone help me with the question?​

Answers

Corndogs broo likeee everyone knows this

state the dimensions of the matrix. identify the indicated element​

Answers

Answer:

D; 2 * 3; -4

Step-by-step explanation:

The dimension of the matrix refers to the number of elements in a row multiplied by the number of elements is a column

In a row, we have 2 elements, in a column , we have 3 elements

So the matrix is of 2 * 3 dimension

a21, refers to the element in the matrix that is in the row 2 column 1 and that is -4

Can someone help me with this math homework please!

Answers

Answer:

Below

Step-by-step explanation:

From the graph the first local minimum is -16.18

The local maximum is 3.75

The second local minimum is -3.

Answer:

Over the interval (-3,0), the local minimum is -16.18Over the interval  [0,3], the local maximum is -3.75Over the interval [0,3], the minimum is -3

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

Hope it helps..

Have a great day!!

please me in the math
Find the H.C.F
[tex] {x}^{2} - 4 \\ {x}^{3} + 8 \\ {x}^{2} + 5x + 6[/tex]
​it so simple

Answers

Step-by-step explanation:

Solution

First equation x ² - 4

= (x+2) (x-2)

Second equation = x ³ +8 + = x³+2^3

= (x-2) (x² + x₁2 +2²) = (x-2) (x² + 2x+4)

3 Third equation = x ² + 5x + 6

= x² + 6x= x +6 = x(x+6)-1(x+6)

(x-1) (x+6)

H.C. F= x-2

Question 6 of 10
How much would $500 invested at 6% interest compounded monthly be
worth after 5 years? Round your answer to the nearest cen
(0) - P(144
A $674,43
B. $886,41
C, 5669.11
D. $512,68

Answers

9514 1404 393

Answer:

  A.  $674.43

Step-by-step explanation:

The account balance is given by ...

  A = P(1 +r/12)^(12t) . . . . . principal P invested at annual rate r for t years

  A = $500(1 +0.06/12)^(12·5) = $500(1.005^60)

  A ≈ $674.43

Choose the inequality that could be used to solve the following problem.

Three times a number is at most negative six.

A. 3x ≥ -6
B. 3x < -6
C. 3x > -6
D. 3x ≤ -6

Answers

D. Which is basically saying that three times a number is less than or equal to negative 6, so six or less
D Is correct answer. Great job above

What is the perimeter of the rectangular narrow on the aircraft carrier HMS Queen Elizabeth

Answers

Answer:

dddjshsbs zhzusushwbsgzyzhsbssbs s hsbd d dhd ssbshebebs shyshs s sbshss s s

Step-by-step explanation:

shshshsnsnsjzj shsjs s sjsn s s snsnsbzbznnz ssjs s snsnsmkzkxnz

There is meters on the end right over here in the picture I marked could you tell me what the number is there so I could do the problem (comment on this answer and I will reply back) or you could also do it your self I wrote down how to do it on the picture. Let me know if it helps!

If triangle LMQ is similar to triangle LNP, calculate the length of segment LP.

Answers

Answer:

LP = 15

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{LM}{LN}[/tex] = [tex]\frac{LQ}{LP}[/tex] , substitute values

[tex]\frac{4}{10}[/tex] = [tex]\frac{LQ}{LQ+QP}[/tex]

[tex]\frac{2}{5}[/tex] = [tex]\frac{LQ}{LQ+9 }[/tex] ( cross- multiply )

5LQ = 2(LQ + 9) = 2LQ + 18 ( subtract 2LQ from both sides )

3LQ = 18 ( divide both sides by 3 )

LQ = 6

Then

LP = LQ + QP = 6 + 9 = 15

hi these are geometry questions, :)

Answers

Answer:  80

========================================================

Explanation:

For any inscribed quadrilateral like this, the opposite angles are always supplementary. This means the angles add to 180

B+D = 180

(2x-1) + (3x-59) = 180

(2x+3x) + (-1-59) = 180

5x-60 = 180

5x = 180+60

5x = 240

x = 240/5

x = 48

Use this x value to find angle A

A = 2x+4

A = 2*48+4

A = 96+4

A = 100

This then means,

A+C = 180

C = 180-A

C = 180-100

C = 80 degrees

Side note: The term "cyclic quadrilateral" is the same as "inscribed quadrilateral".

Given m||n, find the value of x.
+
mm
(6x+4)
(4x-14)
Answer:
Submit Answer
attempt out of 2

Answers

Answer:

x = 19

Step-by-step explanation:

6x+4 + 4x - 14 = 180

10x    - 10 = 180

10 X = 190

x = 19

x=19 would be your final answer

Solve for ppp. 16-3p=\dfrac23p+516−3p= 3 2 ​ p+516, minus, 3, p, equals, start fraction, 2, divided by, 3, end fraction, p, plus, 5 p=p=p, equals

Answers

Given:

The given equation is:

[tex]16-3p=\dfrac{2}{3}p+5[/tex]

To find:

The value of p.

Solution:

We have,

[tex]16-3p=\dfrac{2}{3}p+5[/tex]

Multiply both sides by 3.

[tex]3(16-3p)=3\left(\dfrac{2}{3}p+5\right)[/tex]

[tex]48-9p=2p+15[/tex]

Isolating the variable terms, we get

[tex]48-15=2p+9p[/tex]

[tex]33=11p[/tex]

Divide both sides by 11, we get

[tex]\dfrac{33}{11}=p[/tex]

[tex]3=p[/tex]

Therefore, the required solution is [tex]p=3[/tex].

Answer:

p=3

Step-by-step explanation:

i got it right on khan

May someone explain to me how to do this?

Answers

Answer:

All you gotta do is go to "desmos" and type in all of the 4 solutions. A, B, C, and D. and see which answer matches the graph

Step-by-step explanation:

HELP ASAP ILL GIVE BRAINLIST





Imagine that your best friend missed the lesson on how to solve a system of equations using the substitution method. You want to help him or her catch up in their math class, so you decide to write an e-mail describing what they missed. Write an email to your friend including:
An explanation of what a system of equations is

A general description of how to use the substitution method

An example of a system of equations

Your solution steps and explanations including the substitution method

Your final answer for the system

Answers

I'm just going to start writing the email XD (btw, bold = non-email parts/me talking)

Hey (Friend name),

You kinda missed math the other day, and being the nice friend I am, I decided to catch you up on what we learned.

We learned how to solve a system of equations using the substitution method.

A system of equations is a set of two or more equations with common variables. We use those two equations to solve for the variables.

One example might be:

3x+y=3

4x+3y=10

Solving each of these two equations by themselves would be impossible, so this is where the substitution method comes in.

Solving by substitution means that you first solve one equation for a variable, and then you substitute the value of that variable into the other equation. You might understand better if you see how I use this method to solve the previous system.

Step 1: Solve for y.

 3x+y=3

 Subtract 3x from each side.

 y=3-3x

Step 2: Use the substitution method (plug in the y value).

 4x+3y=10

 4x+3(3-3x)=10

 See how we plugged in the right side of the equation that is equal to y? Now       only the x variable is left and we can easily solve it!

Step 3: Simplify to get x.

 4x+9-9x=10

 -5x=1

 x=-1/5

Step 4: Use the substitution method AGAIN (for the y).

 Now we plug in the x value into the equation for y.

 y=3-3x

 y=3-3(-1/5)

 y=3-(-3/5)

 y=18/5

The final answer is x=-1/5, y=18/5.

As you can see, using the substitution method to solve two impossible equations is how we can get the values of the variables they share! It's simple, quick, and easy!

Sincerely,

(your name)

I hope this helped! :D

tanA × cosecA = secA​

Answers

Step-by-step explanation:

L.H.S

tanA * cosecA

=sinA/cosA * 1/sinA

now cancel sinA and sinA

then,

1/cosA

= secA

= RHS

hence proved

What makes a trapezoid an isosceles trapezoid

Answers

Answer:

A trapezoid is a quadrilateral with exactly one pair of parallel sides. A pair of angles that share a base as a common side are called a pair of base angles. A trapezoid with the two non-parallel sides the same length is called an isosceles trapezoid.

what is 3^-8 x 3^-4 x 3^-2

Answers

Answer:

Value of given expression is 3⁻¹⁴

Step-by-step explanation:

Given expression:

3⁻⁸ x 3⁻⁴ x 3⁻²

Find:

Value of given expression

Computation:

⇒ 3⁻⁸ x 3⁻⁴ x 3⁻²

⇒ 3[⁻⁸⁻⁴⁻²]

⇒ 3⁻¹⁴

Value of given expression is 3⁻¹⁴

1. What is the sum of 3/4 and 4/5?

Answers

3/4 + 4/5 =
15/20 + 16/20 = 31/20
= 1 and 11/20

Given that $x < 5$, rewrite $5x - |x - 5|$ without using absolute value signs. WILL GIVE BRAINLIEST

Answers

Answer:

6x-5 if x<5

Step-by-step explanation:

If x<5, then x-5<0.

If x-5 is negative, then |x-5)=-(x-5) or -x+5.

5x - |x - 5|

5x-(-x+5) provided x<5

5x+x-5 by distributive property

6x-5 combined liked terms

The cost price of a box and a pen is Rs 120. The box is sold at 10% profita the pen is sold at 10% loss. If the selling price of the box is Rs 52 more than of the pen, calculate the profit or loss percent in the whole.​

Answers

Answer:

3.803% Profit

Step-by-step explanation:

First let us calculate total sales, then calculate the total cost, and then divide the two.

Sale: 120*1.1=132 and 52*.9=46.8

Cost: 120 and 52

Profit equation:

[tex]\frac{Net sales-COGS}{Net Sales} =Profit[/tex]

[tex]\frac{(132+46.8)-(120+52)}{(132+46.8)}[/tex]

Simplify:

[tex]\frac{6.8}{178.8} =.03803[/tex] or 3.803% Profit

Suppose f(x)=x^3 what is the graph of f(x+3)

Answers

Answer:

[tex]f(x + 3) = {(x + 3)}^{3} [/tex]

Shifted left with x-intercept at (-3,0) and the y-intercept at (0,27)

Explain this to me I don't understand

Answers

Answer:

26.124

Step-by-step explanation:

SOH CAH TOA

tan 43 = about 0.933

than times it by 28 and get

26.124

Pedro signed up for a streaming music service that costs $13 per month. The service
allows Pedro to listen to unlimited music, but if he wants to download songs for
offline listening, the service charges $0.75 per song. How much total money would
Pedro have to pay in a month in which he downloaded 45 songs? How much would he
have to pay if he downloaded s songs?
Cost with 45 songs:
Cost with s songs:

Answers

Answer:

Cost with 45 songs: $46.75

Cost with s songs: $13 + (s * $0.75)

Step-by-step explanation:

First multiply the number of songs by the cost per song (45 * $0.75 = $33.75), then add the monthly service cost to that number ($13 + $33.75 = $46.75) to get the total monthly cost to Pedro.

A block is being dragged along a horizontal surface by a constant horizontal force of size 45 N. It covers 8 m in the first 2 s and 8.5 m in the next 1 s. Find the mass of the block.

Answer: 15kg

Can anyone please explain this sum with proper working? ​

Answers

Answer:

Solution: To determine mass of the block we can use second Newton' law \vec F=m\vec a

F

=m

a

. The force and acceleration according the problem is directed along a horizontal surface, and we can omit the vector sign in Newton's law. The force we know F=45NF=45N, thus we should deduce the acceleration. The problem does not specify the initial speed at which time began to count, so for the first time interval, we may write the kinematics equation in the form

(1) S_1=v_1\cdot t_1+a\frac {t_1^2}{2}S

1

=v

1

⋅t

1

+a

2

t

1

2

, where S_1=8m, t_1=2s S

1

=8m,t

1

=2s , other quantities we don't know. The similar equation we can write for next time interval

(2) S_2=v_2\cdot t_2+ a\frac{t_2^2}{2}S

2

=v

2

⋅t

2

+a

2

t

2

2

. where S_2=8.5m, t_2=1s S

2

=8.5m,t

2

=1s

Note that during the first time interval, the speed of the block increased in accordance with the law of equidistant motion and it became the initial speed of the second interval, i.e.

(3) v_2=v_1+a\cdot t_1v

2

=v

1

+a⋅t

1

Substitute (3) to (2) we get

(4) S_2=(v_1+a\cdot t_1)\cdot t_2+ a\frac{t_2^2}{2}=v_1\cdot t_2+a\cdot t_1\cdot t_2+a\frac{t_2^2}{2}S

2

=(v

1

+a⋅t

1

)⋅t

2

+a

2

t

2

2

=v

1

⋅t

2

+a⋅t

1

⋅t

2

+a

2

t

2

2

From equation (1) and (4) we can exclude unknown quantity v_1v

1

, then remain only one unknown aa. For determine aa we dived (1) by t_1t

1

, (4) by t_2t

2

to find the average speed at time intervals and subtract (1) from (4).

(5) \frac {S_2}{t_2}-\frac {S_1}{t_1}=v_1+a\cdot t_1 +a\frac {t_2}{2}-(v_1+a\frac{t_1}{2})=a\frac{t_1+t_2}{2}-

t

2

S

2

t

1

S

1

=v

1

+a⋅t

1

+a

2

t

2

−(v

1

+a

2

t

1

)=a

2

t

1

+t

2

− For acceleration we get

(6) a=2\cdot ( {\frac{S_2}{t_2}-\frac{S_1}{t_1})/(t_1+t_2)}=2\cdot \frac{(8.5m/s-4m/s)}{3s}=3ms^{-2}a=2⋅(

t

2

S

2

t

1

S

1

)/(t

1

+t

2

)=2⋅

3s

(8.5m/s−4m/s)

=3ms

−2

For mass from second Newton's law we get

(7) m=\frac{F}{a}=\frac{45N}{3ms^{-2}}=15kgm=

a

F

=

3ms

−2

45N

=15kg

Answer: The mass of the block is 15 kg

Complete table of values

Answers

Step-by-step explanation:

here's the answer to your question

Find the measure of the missing angle using the triangle angle sum theorm.

Answers

Answer:

65°

Step-by-step explanation:

The sum of angles in a triangle =180

53°+62°+?°=180°

115°+?°=180°

?°=180°-115°

Rate the answer If you love everything I did n explanation

Answer:

65 degrees

Step-by-step explanation:

Angles in a triangle add up to 180, so 180 - 53 - 62 = 65.

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