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taurus [48]
3 years ago
12

Find the term indecent of x in the expansion of (x^2-1/x)^6

Mathematics
1 answer:
Mars2501 [29]3 years ago
3 0

By the binomial theorem,

\displaystyle \left(x^2-\frac1x\right)^6 = \sum_{k=0}^6 \binom 6k (x^2)^{6-k} \left(-\frac1x\right)^k = \sum_{k=0}^6 \binom 6k (-1)^k x^{12-3k}

I assume you meant to say "independent", not "indecent", meaning we're looking for the constant term in the expansion. This happens for k such that

12 - 3k = 0   ===>   3k = 12   ===>   k = 4

which corresponds to the constant coefficient

\dbinom 64 (-1)^4 = \dfrac{6!}{4!(6-4)!} = \boxed{15}

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To get the right shade of paint, the paint store mixes 1 part yellow with
Sever21 [200]

Answer:

6 parts yellow

Step-by-step explanation:

6 0
3 years ago
triangle QRS is an equilateral triangle. If QR is seventeen more than twice x, RS is 19 less than six times x, and QS is one les
koban [17]

Value of x is 9 and measure of each side is 35 units.

<u>SOLUTION: </u>

Given, Triangle QRS is an equilateral triangle.  

QR is seventeen more than twice x, \rightarrow QR = 17 + 2x

RS is 19 less than six times x, \rightarrow RS = 6x-19

And QS is one less four times x, \rightarrow QS = 4x-1

We have to find x and measure of each side.

Now, we know that, sides of equilateral triangle are equal,  

Then QR = QS \rightarrow 17 + 2x = 4x-1 \rightarrow 4x-2x = 17 + 1 \rightarrow 2x = 18 \rightarrow x = 9

So, value of x is 9.

\begin{array}{l}{\text { Now, } \mathrm{QR}=17+2(9)=17+18=35} \\\\ {\mathrm{RS}=6(9)-19=54-19=35} \\\\ {\mathrm{QS}=4(9)-1=36-1=35}\end{array}

Hence, value of x is 9 and measure of each side is 35.

5 0
4 years ago
I need help pleaseeee
bekas [8.4K]

Answer:

20cm

Step-by-step explanation:

pythagorean theorem

15^2 + b^2 = 25^2

225 + b^2 = 625

b^2 = 400

b = 20

6 0
4 years ago
Read 2 more answers
Plz help<br><br> Simplify 6(x + 4)
saw5 [17]

Final Answer: 6x + 24

Steps/Reasons:

Question: Simplify 6(x + 4)

<u>Step 1</u>: Expand by distributing the terms.

6x+ 6 × 4

<u>Step 2</u>: Simplify 6 × 4 to 24.

6x + 24

~I hope I helped you :)~

8 0
3 years ago
Read 2 more answers
The price of an item has been reduced by 20%. the origianal price was 76
mafiozo [28]

Answer:

$60.8

Step-by-step explanation:

Twenty percent of 76 is,

→ 20% of 76

→ (20/100) × 76

→ 1520/100

→ [ $15.2 ]

The reduced price of the item is,

→ 76 - 15.2

→ [ $60.8 ]

Hence, the price is $60.8.

4 0
3 years ago
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