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3 years ago

Use the binomial theorem to show that 7^n + 2 is divisible by 3, where n is a positive integer.

Mathematics

1 answer:

masha68 [24]3 years ago

7 0

By the binomial theorem,

$7^n=(6+1)^n=6^n+n6^{n-1}+\dbinom n26^{n-2}+\cdots+\dbinom n{n-2}6^2+n6^1+1$

Each term containing a factor 6 is divisible by 3, since 3 divides 6. The remaining 1 and 2 sum to 3, which is also divisible by 3.

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Simplify t^12/t^6 help!

meriva

$t^{12}/t^6=t^{12-6}=t^6$

4 0

3 years ago

Justin Verlander of the Astros threw a pitch 100 miles per hour. How many seconds did it take to get to home plate. The plate is

castortr0y [4]

It will take 0.4 seconds to get to the home plate.

Given:

The speed of the pitch thrown by Justin is 100 miles per hour

The distance of home plate from the pitching rubber is 60.5 feet

To find:

The time taken by a pitch to reach the home plate

Solution:

The distance home plate from the pitching rubber = d = 60.5 feet

$1 mile = 5280 feet\\1 foot=\frac{1}{5280} mile\\60.5 feet=60.5 \times \frac{1}{5280} mile=\frac{60.5}{5280}miles$

The speed of pitch thrown by Justin = s = 100 miles/hr

The time taken by a pitch to reach the home plate = t =?

The speed of the moving object is given by dividing the distance covered from the time taken to cover that distance.

$Speed=\frac{Distance}{Time}\\s=\frac{d}{t}\\100 miles/hr=\frac{\frac{60.5}{5280}miles}{t}\\t=\frac{60.5}{5280}miles\times \frac{1}{100 miles/hr}\\= 0.000114583 hr$

In an hour there are 3600 seconds, then in 0.000114583 hours will be:

$1 hour=3600 seconds\\=0.000114583 \times 3600=0.4124988 s\approx 0.4 s$

It will take 0.4 seconds to get to the home plate.

Learn more about conversions here:

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5 0

2 years ago

A phone company worker needs to know the height of a cell tower, so he decides to use a 2 m pole and shadows cast by the sun, as

olganol [36]

I always found it easiest to draw out the picture

6 0

3 years ago

Salomon tracks the weight of his new puppy every 2 weeks. She weighs 10 lbs the

Gekata [30.6K]

Equation (B) "y = 3x + 10" represents the growth of the puppy.

<h3>What are equations?</h3>

An equation is a mathematical formula where the "equal to" sign appears between two expressions having the same value.
Like 3x plus 5 equals 15, for example.
Different types of equations exist, such as linear, quadratic, cubic, and others.
The three primary forms of linear equations are the slope-intercept form, standard form, and point-slope form.

So, the equation that represents the situation:

The weight increase is: (10, 13, 16, 19, 22, 25)
We can observe that every time, there is a rise of 3lbs of weight.
Now, let 10 be a constant as the weight is starting from 10 lbs.
And 'x' be the number of time Salomon tracks the weight.

Then:

y = 3x + 10

For example, Salomon checks the weight for the 6th time then:

y = 3x + 10
y = 3(5) + 10
y = 15 + 10
y = 25

So, the equation is correct.

Therefore, equation (B) "y = 3x + 10" represents the growth of the puppy.

Know more about equations here:

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#SPJ13

The correct question is given below:
Salomon tracks the weight of his new puppy every 2 weeks. She weighs 10 lbs the day he brings her home. His list for her first 6 "weighs" is as follows: (10, 13, 16, 19, 22, 25}

Which equation represents the growth of the puppy? Select one:

A. y = x + 3

B. y = 3x + 10

C. y = 10x + 3

D. y = x + 10

8 0

11 months ago

Which of the following are invloved in graphs or linear functions?

olga_2 [115]

Answer:

I dont know you never explain properly

Step-by-step explanation:

8 0

3 years ago