Find the 6th term in the expanded form of the equation (2x+y)^9

Answers

Answer 1

Answer: $T_r={n \choose r-1}a^(n-(r-1))b^(r-1)\n T_6={9 \choose 6-1}(2x)^(9-(6-1))y^(6-1)\n T_6={9 \choose 5}(2x)^4y^(5)\n T_6=(9!)/(5!4!)16x^4y^(5)\n T_6=(6\cdot7\cdot8\cdot9)/(2\cdot3\cdot4)16x^4y^(5)\n T_6=7\cdot2\cdot9\cdot16x^4y^(5)\n T_6=2016x^4y^5$

Answer 2

Answer: $Use\ the\ Pascal's\ Triangle\ (look\ at\ the\ picture)\n\n6-th\ term\ of\ (2x+y)^9\ is\n\n 126(2x)^4y^5=126*16x^4y^5=2016x^4y^5$

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Answers

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The portion of a student’s ballpoint pen that contains the ink is a cylinder with a diameter of 0.400 cm and a height of 11.5 cm. If the ink lasts 7 weeks, what is the volume of ink that the student uses each week?

Answers

Volume of all of the ink is (0.2^{2})* \pi * 11,5 = 0.46 cm^{3} . When we divide the volume by 7, we get 0.0657142857 cm^{3} of ink

Solve the equation
1/2log(x-2) = 3log2-3/2log(x-2)
all logs are in base 5

Answers

no clue sorry i tried my best

Factor the expression 28x + 49

Answers

Answer:

7(4x+7)

Step-by-step explanation:

28x+49

Rewriting

4*7*x + 7*7

Factor out a 7

7(4x+7)

Answer:

7(4x+7)

Step-by-step explanation:

Just divide both numbers by the common factor,7.

What are the real and imaginary parts of the complex number?

9+7i

Answers

Answer:

9 is the real part and 7i is the imaginary part

Step-by-step explanation:

A complex number is written in the form a+bi where a is the real part and bi is the imaginary part

9 = real part

7i is the imaginary part

Convert 10.6 to fraction

Answers

10.6 = 10.6 / 1

Numerator = 10.6 × 10 = 106
Denominator = 1 × 10 = 10

Numerator / Denominator = 106 / 10

The simplified fraction:

= 106/10

= 53/5

= 10 3/5

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