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11 months ago

The 3rd term of (a-b)4 is

Mathematics

1 answer:

fgiga [73]11 months ago

4 0

The third term of the expansion is 6a^2b^2

<h3>How to determine the third term of the expansion?</h3>

The binomial term is given as

(a - b)^4

The r-th term of the expansion is calculated using

r-th term = C(n, r - 1) * x^(n - r + 1) * y^(r - 1)

So, we have

3rd term = C(4, 3 - 1) * (a)^(4 - 3 + 1) * (-b)^(3-1)

Evaluate the sum and the difference

3rd term = C(4, 2) * (a)^2 * (-b)^2

Evaluate the exponents

3rd term = C(4, 2) * a^2b^2

Evaluate the combination expression

3rd term = 6 * a^2b^2

Evaluate the product

3rd term = 6a^2b^2

Hence, the third term of the expansion is 6a^2b^2

Read more about binomial expansion at

brainly.com/question/13602562

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If $48,000 is invested in an account earning 3.1% interest compounded continuously, determine how long it will

Bas_tet [7]

Answer:

It will take about 35.439 years to triple.

Step-by-step explanation:

Recall the formula for continuously compounded interest:

$A=P\,e^{r*t}$

where "A" is the total (accrued or future) accumulated value, "r" is the rate (in our case 0.031 which is the decimal form of 3.1%), "P" is the principal, and "t" is the time in years (our unknown).

Notice also that even that the final amount we want to get is three times $48,000. So our formula becomes:

$3\,*\,48,000=\,48,000\,\,e^{0.031\,*t}\\\frac{3\,*\,48,000}{48,000} =e^{0.031*t}\\3=e^{0.031*t}$

Now,in order to solve for "t" (which is in the exponent, we use logarithms:

$ln(3)=0.031\,*\,t\\t=\frac{ln(3)}{0.031} \\t=35.439 \,\,years$

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3 years ago

Let n be equal to 156% of 70. Which of the following proportions is true?

aniked [119]

Well all u have to do is 156%*70= 109.2 so N= 109.2

6 0

2 years ago

X = ?????????????????

Evgen [1.6K]

Answer:

Step-by-step explanation:

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2 years ago

In how many ways can 6 competitors finish a race assuming there are no ties?In how many ways can we sit n people on r < n cha

VLD [36.1K]

Answer: a) 720, b) $^nC_r=\dfrac{n!}{(n-r)!r!}$ c) 336, d) 30240 e) 120.

Step-by-step explanation:

Since we have given that

a) Number of competitors = 6

We need to find the number of ways that 6 competitors can finish a race and there are no ties.

So, Number of ways would be

$6!=720$

b) number of people = n

Number of chairs = r (r<n)

so, the number of ways we can sit n people on r<n chairs is given by

$^nC_r=\dfrac{n!}{(n-r)!r!}$

c) If there are three awards :

Gold, silver, bronze.

We need to find the number of ways that these medals can be awarded.

Number of ways is given by

$^8P_3\\\\=336$

d) Number of 5-digit zip codes are possible is given by

$^{10}P_5=30240$

e) Number of poeple = 10

Number of people required in committee = 3

Number of different 3 person committee that are selected from 10 people is given by

$^{10}C_3=120$

Hence, a) 720, b) $^nC_r=\dfrac{n!}{(n-r)!r!}$ c) 336, d) 30240 e) 120.

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3 years ago

The slope of a line passing through H (-2,5) is -3/4. Which ordered pair represents a point on this line?

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3 years ago