Find the 7th term in the following binomial expansion(4f+t/3)8 in ascending powers of t

Answers

Answer 1

Answer:

[tex]\displaystyle T_6=\frac{448}{729} f^2t^6[/tex]

Step-by-step explanation:

Binomial Theorem

Any power of x + y can be expanded into a sum of the form:

[tex]\displaystyle (x+y)^{n}={n \choose 0}x^{n}y^{0}+{n \choose 1}x^{n-1}y^{1}+{n \choose 2}x^{n-2}y^{2}+\cdots +{n \choose n-1}x^{1}y^{n-1}+{n \choose n}x^{0}y^{n}[/tex]

For any given term k, counted from 0 to n:

[tex]\displaystyle T_k={n \choose k}x^{n-k}y^{k}[/tex]

Note if we have to find the 7th term, we have to use k=6. The expression is:

[tex]\displaystyle \left(4f+\frac{t}{3}\right)^8[/tex]

For n=8, x=4f, y=t/3, k=6:

[tex]\displaystyle T_6={8 \choose 6}(4f)^{8-6}\left (\frac{t}{3} \right )^{6}[/tex]

[tex]\displaystyle T_6={8 \choose 6}(4f)^{2}\left (\frac{t}{3} \right )^{6}[/tex]

[tex]\displaystyle T_6={8 \choose 6}16f^2\frac{t^6}{3^6}[/tex]

Calculate:

[tex]\displaystyle {8 \choose 6}=\frac{8!}{2!\cdot 6!}=28[/tex]

Thus:

[tex]\displaystyle T_6=28\cdot 16f^2\frac{t^6}{729}[/tex]

Simplifying, the 7th term is:

[tex]\mathbf{\displaystyle T_6=\frac{448}{729} f^2t^6}[/tex]


Related Questions

1. Suppose y varies directly with and y= 14 when x = -4. What is the value ofy when x= -6? (1 point)
0-21
O 10
O 18
O21

Answers

y=kx

14=k×-4

k=14÷-4

k=-3.5

y=-3.5×-6

y=21.




Which steps can be used to solve StartFraction 6 Over 7 EndFraction x + one-half = StartFraction 7 Over 8 EndFraction for x? Check all that apply.
Divide both sides of the equation by StartFraction 7 Over 8 EndFraction.
Subtract One-half from both sides of the equation.
Use the LCD of 2 to combine like terms.
Divide both sides by StartFraction 6 Over 7 EndFraction.
Multiply both sides by StartFraction 7 Over 8 EndFraction.

Answers

Answer: the answer is 2,4,5

Step-by-step explanation:

Answer:

B, D, E

Step-by-step explanation:

Took the test

Twenty percent of the town's population is over the age of 65. If there are 320 residents over the age of 65, what is the town's total population?

Answers

Answer:

65

Step-by-step explanation:

I think. hope this hepls

Answer:

There are 1600 residents.

Step-by-step explanation:

0.2 times x = 320  divide by 0.2

x = 1600

5*Please answer this correctly very urgent!

Answers

Answer:

1  3/15 - 5/15

Step-by-step explanation:

Hope this helps. PS the / sign is supposed to be for the fraction.

Step-by-step explanation:

1 1/5 - 1/3 = 0.86

Hope I helped. The only way I know how to dot this is in decimal form sorry.

Find the values of a and b such that x² - 2x + 2 = ( x - a )² + b

Answers

Answer:

a = b = 1

Step-by-step explanation:

x² - 2x + 2 = ( x - a )² + b

x² - 2x + 2 = ( x² - 2x + 1) - 1 + 2 = (x - 1)² + 1

a = b = 1  

first to answer correct gets brainliest

Answers

Answer:

64-6=x

Step-by-step explanation:

What is the measure of /__B? Type the number only

Answers

Answer: I believe it would be 30

Step-by-step explanation:

A=X

B=Y

C=Z

Which cannot be the angle measurements of triangle ABC? OmZA = 55°, mZB = 65°, mZC = 60°
OmZA = 60°, mZB = 60°, mC = 60°
MZA= 57°, MZB = 58°, mZC = 65°
MZA = 61°, mZB = 57°, mZC = 61°​

Answers

Answer:

D. m<A = 61°, m<B = 57°, m<C = 61°

Step-by-step explanation:

The sum of all interior angles of a triangle is always equal to 180°.

Therefore, any set of given angle measurement of a triangle should sum up to 180°.

From the options given, the following angle measurements given in option D,

,m<A = 61°, m<B = 57°, m<C = 61° cannot be angle measurements of ∆ABC. This is because they sum up to give 179° instead of 180°.

Answer:

The answer is D

Credits to the person above me.

; )

Step-by-step explanation:

EDGE 2021

I kind of don’t get this could someone explain and answer this question I would really appreciate :)

Answers

Answer:

its the fourth one

sts3ps oe

Answer:

the first picture A.

Step-by-step explanation:

Vertical angles are just two angles that lie across from each other. The other 3 pictures are referring to adjacent angles which are two angles that lie directly next to each other.

A small deck of 5 cards consists of 3 red Jards and 2 green cards.
Draw 7 times with replacement.
Find the probability that a red card is drawn exactly 3 times.

Answers

Answer:

Approximately [tex]0.19[/tex].

Step-by-step explanation:

The cards were drawn with replacement. Therefore, the probability of drawing a red card will be [tex](3 / 5)[/tex] at every one of the seven draws. The probability of not drawing a red card would be [tex](1 - (3/5)) = (2/5)[/tex].

One way to get three red cards out of the seven draws would be [tex]\verb!red!\; \verb!red!\; \verb!red!\; \verb!green!\; \verb!green!\; \verb!green!\; \verb!green![/tex]. That corresponds to a probability of [tex](3/5)^3\, (2/5)^{7-3}[/tex].

However, there are many other ways to get three red cards during the seven draws. For example:

[tex]\verb!red!\; \verb!red!\; \verb!green!\; \verb!red!\; \verb!green!\; \verb!green!\; \verb!green![/tex], [tex]\verb!red!\; \verb!red!\; \verb!green!\; \verb!green!\; \verb!red!\; \verb!green!\; \verb!green![/tex].[tex]\cdots[/tex].[tex]\verb!green!\; \verb!green!\; \verb!green!\; \verb!green!\; \verb!red!\; \verb!red!\; \verb!red![/tex].

There are [tex]\displaystyle {\genfrac{(}{)}{0}{0}{7}{3}} = 35[/tex] such ways in total to choose three draws out of seven draws.

These ways are mutually-exclusive. Each of these ways has a probability of [tex](3/5)^3\, (2/5)^{7-3}[/tex]. The probability for getting a red card on exactly three out of the seven draws would be:

[tex]\displaystyle {\genfrac{(}{)}{0}{0}{7}{3}} \, (3/5)^3\, (1 - (3/5))^{7-3} \approx 0.19[/tex].

How can you tell if an element has been oxidized?
A. Its oxidation state has not changed in the reaction.

B. Its oxidation state is higher in the product than in the reactant

C. Its oxidation state is lower in the product than in the reactant.

D. It has a negative oxidation state in the product.​

Answers

Step-by-step explanation:

B. Its oxidation state is higher in the product than in the reactant

Y=8x+9
Give slope(m)
Parallel slope
Perpendicular slope

Answers

Answer:

the slope is 8

Step-by-step explanation:

the slope is x not sure if its parallel of perpendicular but is i had to gues id guess parallel

Answer:

the slope is 8

the parallel slope is 8

the perpendicular slope is -1/8

What partial products can be used to find the product 3x219

Answers

Answer:

You can do (3x200)+(3x10)+(3x9) Hope it helps!

The product is 657 if you need it!

Step-by-step explanation:

What is 3,350,000 in scientific notation?

Answers

Answer:

10^4 or 3.5

Step-by-step explanation:

A Toyota Prius can drive 70 miles on two gallons of gas. At this rate, how far can the Prius travel on 13 gallons of gas? Include your units.

Answers

Answer:

460 miles

Step-by-step explanation:

Since it is a ratio problem, you see that the prius drives 70 miles on 2 gallons of gas which gives you 70:2 or 70/2.

You also set up the other ratio as a fraction with the unknown value as x --> x/13.

now, you cross multiply

70/2=x/13

70*13=910

910/2=460

460 miles

Answer:

455 miles

Step-by-step explanation:

Distance Prius can travel with one gallon of gas:

70/2

= 35 miles

Distance Prius can travel with 13 gallons of gas:

35*13

= 455 miles

Hope this helped!

How many elements are in this equation:Mg2N3? ​

Answers

Answer:

there are 2 Magnesium and Nitrogen

Step-by-step explanation:

can you help me out​

Answers

Answer:

$36

Step-by-step explanation:

Answer:

$36.

Step-by-step explanation:

(Hot dog) 2 for 5: Unit price is 5/2 = 2.5

(Soda) 3 for 3 so unit price is 1 for 1.

6 sodas = 6 dollars

12 Hot dogs = 12. x 2.5 = 30 dollars.

Price for both = 30 + 6 = 36.

The diagram compares the ratio of girls in the chorus to boys in the chorus. What is the ratio of girls to boys? If there are 30 students in the chorus, how many are girls and how many are boys.

girls 3 parts
boys 2 parts

Answers

Answer:

it should be girls 12 to 18

Step-by-step explanation:

i just messed around with a calculator and found it.

Determine the domain of the function graphed above.

Answers

Answer:

Domain: (-∞, ∞)

General Formulas and Concepts:

Algebra I

Domain is the set of x-values that can be inputted into function f(x)

Step-by-step explanation:

According the the graph, we see that our x-values are spanning forever in both directions. Therefore our domain is:

(-∞, ∞) or -∞ < x < ∞

Use the figure on the right to find the length of DC.

Answers

Answer:

this is the figure btw

Step-by-step explanation:

Question 1 The number of books Annie reads in a month increased from 8 books to 16 books. By what percentage did the number of books she reads increase ?

Answers

Answer:

Very easy Bud

Step-by-step explanation:

Nope

A cat walks 3 meters toward a laser, then jumps 5 meters due south of the laser when it

sees a thing. What is the displacement of the cat (to the nearest tenth)?

Answers

Answer:

Displacement is 5.8 meters

Step-by-step explanation:

Here, we want to calculate the displacement of the cat

When we talk of displacement, we mean distance traveled in a specified direction

To find the displacement of the cat, we calculate the distance between where the cat is now from where it started off

So to calculate this, we shall have a right angled triangle where the displacement we want to calculate will be the hypotenuse

We proceed to use Pythagoras’ theorem which states that the square of the hypotenuse equals the sum of the squares of the two other sides

Mathematically, we have ;

D^2 = 3^2 + 5^2

D^2 = 9 + 25

D^2 = 34

D = √34

D = 5.8309

To the nearest tenth, the displacement is 5.8 meters

In quadrilateral ABCD, \angle A=5x+20,\angle B=3x-30,\angle C=2x+10,and\angle D=8x.∠A=5x+20,∠B=3x−30,∠C=2x+10,and∠D=8x. Find the value of Angle B.

Equation:
x=
angle b=

Answers

Answer:

Equation: (5x + 20) + (3x - 30) + (2x + 10) + 8x = 360

x = 20

Angle B = 30°

Step-by-step explanation:

Given:

<A = 5x + 20

<B = 3x - 30

<C = 2x + 10

<D = 8x

Sum of interior angles of a quadrilateral = 360°

Therefore:

<A + <B + <C + <D = 360°

(5x + 20) + (3x - 30) + (2x + 10) + 8x = 360

Solve for x

5x + 20 + 3x - 30 + 2x + 10 + 8x = 360

Collect like terms

5x + 3x + 2x + 8x + 20 - 30 + 10 = 360

18x = 360

Divide both sides by 18

x = 360/18

x = 20

<B = 3x - 30

Plug in the value of x

<B = 3(20) - 30 = 60 - 30

<B = 30°

If (x2 – 4) ÷ (x + 2) = x – 2, which polynomial should fill in the blank below?
(x + 2) ´ ______ = x2 – 4
x2 – 4
x – 2
x + 2
x2 – 2
what the answer to this question

Answers

Answer:

(x+2)(x-2)=x^2-4

Step-by-step explanation:

(X+2)(x-2)= x^2-2x+2x-4

=x^2-4

30/90 del número de plantas en un cultivo de caña está contaminada. De estas, el 1/2 ha sido tratada. ¿Cual es la fracción del número de plantas del cultivo que no ha sido tratada?

Answers

Answer:

1/6

Step-by-step explanation:

De la pregunta, sabemos:

30/90 del número de plantas de un cultivo de caña está contaminado.

30/90, simplificamos aún más

30/90 => 3/9 => 1/3

De estos, la mitad han sido tratados.

La fracción de los cultivos tratados son:

1/2 de 3/9 = 1/2 × 1/3

= 1/6

La fracción del número de plantas del cultivo que no ha sido tratada se calcula como:

1/3 - 1/6

El mínimo común denominador es 6

= (2 × 1) - (1 × 1) / 6

= 2 - 1/6

= 1/6

Usando proporciones, se encuentra que la fracción del número de plantas del cultivo que no ha sido tratada es [tex]\mathbf{\frac{5}{6}}[/tex]

Las plantas que no han sido tratadas son:

Las que non estan contamidas(6/9 de el total).1/2 de las contaminadas(1/2 de 3/9).

Por eso, la proporción total es dada por:

[tex]\frac{6}{9} + \frac{1}{2}\frac{3}{9} = \frac{6}{9} + \frac{3}{18} = \frac{12}{18} + \frac{3}{18} = \frac{15}{18} = \frac{5}{6}[/tex]

La fracción del número de plantas del cultivo que no ha sido tratada es [tex]\mathbf{\frac{5}{6}}[/tex]

Un problema similar es dado en https://brainly.com/question/25377229

si me dan 200 pesos a la semana y quiero comprar algo de 15000 pesos cuantas semanas tengo que ahorrar

Answers

Answer:

75 semanas

Step-by-step explanation:

15,000 = 200s

15,000/200 = s

75 = s

Solve the equation . Show your work

Answers

Answer:

x = -1

Step-by-step explanation:

First you multiply by crossover and you get 3(5-x)=18

Then divide the two wings and you'll get 5-x=6

Then you need to separate the x from the numbers

so you move 5 to the right side and you get -x=6-5

Then you calculate it and you get -x=1

and x= -1

hope it helped <3

Answer:

[tex]x=-1[/tex]

Step-by-step explanation:

Given the equation

[tex]\frac{5-x}{9}=\frac{2}{3}[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}9[/tex]

[tex]\frac{9\left(5-x\right)}{9}=\frac{2\cdot \:9}{3}[/tex]

[tex]5-x=6[/tex]

[tex]\mathrm{Subtract\:}5\mathrm{\:from\:both\:sides}[/tex]

[tex]5-x-5=6-5[/tex]

[tex]-x=1[/tex]

[tex]x=-1[/tex]

3 is 10% of what number?
I

Answers

Answer:

30

Step-by-step explanation:

3 multiplied by 10 would equal 30. 3 is 10% of 30

i need help with math

Answers

I believe that is a corresponding angle. Hope this helps!

Mattie Evan's drove 100 miles in the same amount of time that it took a turbo turbopropeller plane to travel 500 miles. The speed of the plane was 200 mph faster than the speed of the car. Find the speed of the plane.

Answers

200 :) hehehehehehheh

Answer:250

Step-by-step explanation:Answer:


100/r=500/r+200=50

50+200 =250

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