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2 years ago

What is the coefficient of x^4y^4 in the expansion (x+y)^8?

Mathematics

1 answer:

Ivanshal [37]2 years ago

3 0

Answer:

C. 70

Step-by-step explanation:

In the expansion of (a + b)^n, the k-th term is ...

nCk·a^(n-k)b^k . . . . . k = 0 to n; nCk = n!/(k!(n-k)!)

Here, we have n=8, k=4, so the term of interest is ...

8C4·x^4y^4 = (8·7·6·5)/(4·3·2·1)x^4y^4 = 70x^4y^4

The coefficient of the term is 70.

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The given two-parameter family is a solution of the indicated differential equation on the interval

mr_godi [17]

Answer:

I do 1 option for you as an example, you need to check the leftover by yourself.

Step-by-step explanation:

for d) y(0) = 0 and y'(pi) =0

$y(0) = C_1e^0cos(0)+ C_2 e^0 sin(0) = 0 \longrightarrow C_1 = 0$

$y(x) ' = C_1e^x cos(x) - C_1e^x sin (x) + C_2e^x sin(x) + C_2e^x cos(x)$

$y(\pi)'=C_1e^\pi cos(\pi)- C_1e^\pi sin(\pi)+ C_2e^\pi sin(\pi) + C_2e^\pi cos (\pi)$

Replace $C_1 = 0$ we have

$y'(\pi) = -C_2e^\pi = 0$

if and only if $C_2 =0$

Hence the given solution does not work.

then, d is NOT the correct answer.

3 0

2 years ago

7. Which set of ordered pairs represents a function?

Likurg_2 [28]

Answer:

Step-by-step explanation:

to be a function, every x has to have exactly one y, so there can't be the same number x twice wirh different y's

5 0

2 years ago

Sheila, janice, and katen, working together at the same rate, can complete a job in 3 1/3 days. Working at the same rate, how mu

pychu [463]

Answer:

Janice and Karen could do in 1 day:

20% of the job.

Step-by-step explanation:

To identify how much of the job could janice and caren do in 1 day, first, we must find how much of the job make just 1 person at the same rate:

If three persons make a job in 3 1/3 days, 1 person make the job in x:

3 persons ⇒ 3 1/3 days or 10/3 days
1 person ⇒ x

Then:

$x=\frac{1 person*\frac{10}{3}days }{3 persons}$ (we cancel the unit "persons")
$x=\frac{\frac{10}{3}days }{3}$
x = 10 days

Just a person would need 10 days to complete a job, now, we're gonna divide this value in 2 to obtain the time that need two persons to complete a job:

Time to complete a job between 2 persons = $\frac{10}{2}days$
Time to complete a job between 2 persons = 5 days

How two persons need 5 days to complete a job (in this case, the two persons are Janice and Karen), we can make a simple rule of three to obtain the percentage made in 1 day:

5 days ⇒ 100% of a job
1 day ⇒ x

Then:

$x=\frac{1*100}{5}$ (you can use the % if you want, the result is the same)
$x=\frac{100}{5}$
$x=20$

As you can see, Janice and Karen just in a day could do 20% of the job.

3 0

2 years ago

HELP I need to fine the slope-intercept form. Please it’s a timed assignment I only have two try’s and I already used one

barxatty [35]

Answer:

5. y = -1/2x + 6

6. y = 1/2x + 150

7. y = 10x + 20

8. y = 25x

Step-by-step explanation:

Look at the y-intercept and eliminate the answers you dont need.

Then find the slope of each.

8 0

2 years ago

Kendra is participating in a fundraiser walk-a-thon she walks 4 miles in 60 minutes how many minutes will it take to walk 7 mile

Lemur [1.5K]

Answer:

105 min

Step-by-step explanation:

60 minutes ÷ 4 miles= 15 minutes per mile

15min per mile x 7 miles = 105 minutes

8 0

2 years ago