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trapecia [35]
2 years ago
13

Find the third term in the expansion of (a+b)^9 in the simplest form

Mathematics
1 answer:
forsale [732]2 years ago
6 0

Answer:

The\ third\ term\ is\ \boxed{36a^7b^2}\\

Step-by-step explanation:

\left(\begin{array}{c}9\\ 1\end{array}\right)=\dfrac{9}{1} =9\\\\\left(\begin{array}{c}9\\ 2\end{array}\right)=\dfrac{9*8}{2*1} =36\\\\\\(a+b)^9=a^9+\left(\begin{array}{c}9\\ 1\end{array}\right)a^8b+\left(\begin{array}{c}9\\ 2\end{array}\right)a^7b^2+....+b^9\\\\\\The\ third\ term\ is\ \boxed{36a^7b^2}\\

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Fill in the numbers to find a Sum
Alekssandra [29.7K]

Answer:

The numbers are -15 and 100

\frac{2}{10} +\frac{-15}{100} =\frac{5}{100}

Step-by-step explanation:

we have

\frac{2}{10} +\frac{x}{100} =\frac{5}{y}

Solve the left side

\frac{2}{10} +\frac{x}{100} =\frac{20+x}{100}

so

\frac{20+x}{100}=\frac{5}{y}

equate the numerators and the denominators

20+x=5 ------> x=5-20=-15

100=y -------> y=5

therefore

The numbers are -15 and 100

\frac{2}{10} +\frac{-15}{100} =\frac{5}{100}

4 0
3 years ago
Please help me. This is real confusing. ​
katrin2010 [14]

Answer:

1st problem: b) A=2500(1.01)^{12t}

2nd problem:  c) A=2500e^{.12t}

Step-by-step explanation:

1st problem:

The formula/equation you want to use is:

A=P(1+\frac{r}{n})^{nt}

where

t=number of years

A=amount he will owe in t years

P=principal (initial amount)

r=rate

n=number of times the interest is compounded per year t.

We are given:

P=2500

r=12%=.12

n=12 (since there are 12 months in a year and the interest is being compounded per month)

A=2500(1+\frac{.12}{12})^{12t}

Time to clean up the inside of the ( ).

A=2500(1+.01)^{12t}

A=2500(1.01)^{12t}

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

2nd Problem:

Compounded continuously problems use base as e.

A=Pe^{rt}

P is still the principal

r is still the rate

t is still the number of years

A is still the amount.

You are given:

P=2500

r=12%=.12

Let's plug that information in:

A=2500e^{.12t}.

6 0
3 years ago
With what radius will a circle with a central angle
Vinil7 [7]

Answer:

no

Step-by-step explanation:

3 0
3 years ago
Does anyone know matrices?
Sunny_sXe [5.5K]

Answer:

this is Geometry right?

Step-by-step explanation:

3 0
3 years ago
Hamish and Harry work as plumbers. Harry earns a dollar more than the amount Hamish earns per hour. The amount Harry earns per h
natulia [17]

Answer:

Hamish and Harry work as plumbers. Harry earns a dollar an hour more than 5/4 the amount hamish earns per hour. harry earns per hour is 2$ less than 7/5 the amount hamish earns per hour. how much do each of them make an hour

Step-by-step explanation:

Let

x is the  amount Harry earns 

y is the amount Hamish earns 

x=(5/4)y+1 ⇒ (x-1)*4/5 = y-------- equation 1

x=(7/5)y-2⇒ (x+2)*5/7 = y-------- equation 2

equals 1 and 2

(x-1)*4/5 = (x+2)*5/7

(4x-4)/5 = (5x+10)/7

(4x-4)*7 = (5x+10)*5

28x-28 = 25x+50

28x-25x = 50+28

3x = 78

x = 26

substitute x = 26 for y=(x-1)*4/5

y = (x-1)*4/5

y =  (26-1)*4/5

y = 20

the answer is

<h3>Harry earns $26 an hour</h3><h3>Hamish earns  $20 an hour</h3>
7 0
3 years ago
Read 2 more answers
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