Determine the most efficient way to use the Binomial Theorem to show the following. (11)^4= 14641A)Write 11=5+6 and expand.
B) Write 11= 10+1 and expand.
C) Write 11= 3+3+2 and expand.
D)Write 11= 4+4+3 and expand.

Answers

Answer 1

Answer:

The formula for binomial theorem is

$(a+b)^n=( \left \ {{n} \atop {0}} \right.)a^(n)+( \left \ {{n} \atop {1}} \right.)a^(n-1)b+( \left \ {{n} \atop {0}} \right.)a^(n-2)b^2+...+( \left \ {{n} \atop {n}} \right.)b^n$

Now this shall be very easy if the value of a = 1

The formula shall become

$(1+b)^n=( \left \ {{n} \atop {0}} \right.)1^(n)+( \left \ {{n} \atop {1}} \right.)1^(n-1)b+( \left \ {{n} \atop {0}} \right.)1^(n-2)b^2+...+( \left \ {{n} \atop {n}} \right.)b^n$

Which shall be

$(1+b)^n=( \left \ {{n} \atop {0}} \right.)+( \left \ {{n} \atop {1}} \right.)b+( \left \ {{n} \atop {0}} \right.)b^2+...+( \left \ {{n} \atop {n}} \right.)b^n$

So to find 11^4

We must break it as 1 + 10.

Option B) is the right answer.

Answer 2

Answer: Write (1+10) and expand. As you will have nCr *(10)^(n-r)
Where r index n count ( less terms)

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168 newspaper per week equal newspaper per hour ?

Answers

Final answer:

To calculate the number of newspapers per hour, divide the total number of newspapers in a week by the number of hours in a week.

Explanation:

To calculate the number of newspapers per hour, we need to know the number of hours in a week. There are 24 hours in a day and 7 days in a week, so there are 24 x 7 = 168 hours in a week. To find the number of newspapers per hour, we divide the total number of newspapers in a week by the number of hours in a week. In this case, 168 newspapers divided by 168 hours will give us 1 newspaper per hour.

Learn more about Newspapers per hour here:

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Due tomorrow please help!!!

Answers

Associative i think, if not then sry it’s probably distributive then

When using the Internet to conduct research, it is most important to:a. get the most current information.
b. not spend too much time shopping online while researching.
c. evaluate carefully that the sources are reliable and credible.
d. realize it is the most time-saving method.

Answers

C. evaluate carefully that the sources are reliable and credible

Please help me with this (and my other questions) thanks

Answers

Answer:

Correct answer: V = 486 π ft³

Step-by-step explanation:

Given:

Diameter of the sphere d = 18 ft

d = 2 · r where r is radius

r = d / 2 = 18 / 2 = 9 ft

r = 9 ft

V = (2/3) · r³· π

V = (2/3) · 9³ · π = (2/3) · 729 · π = 486 π ft³

V = 486 π ft³

God is with you!!!

What is the greatest common factor of 36x3 and 8x?
A. 4x
B. 4x3
C. 8x
D. 8x3

Answers

The greatest common factor of two variables or numbers can be determined by listing all of the factors of the two numbers and then determining which is the greatest among all. In this case, the answer should be A. 4x since the least power of x is 1 and 36 and 8 has a GCF of 4.

36x^3 = 4*9*x*x^2
and
8x = 4*2*x

so the gcf. will be 4x so choice A. is right sure

hope helped

The quadratic equation y=-0.5x+4x+10 models the path of a heavy ball through the air, where y represents the height in feet and x represents time in seconds. When will the ball hit the ground?

Answers

We have been given that the quadratic equation $y=-0.5x^2+4x+10$ models the path of a heavy ball through the air, where y represents the height in feet and x represents time in seconds. We are asked to find the time when ball will hit the ground.