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2 years ago

Consider the expansion of (x + 2y)^10. Determine the coefficients for the terms with the powers of x and y shown.

Mathematics

2 answers:

julsineya [31]2 years ago

7 0

Answer with Step-by-step explanation:

We are given that an expression

$(x+2y)^{10}$

Binomial expansion o f $(x+y)^n$ is given by

= $nC_0 x^n+nC_1x^{n-1}y^1+nC_2x^{n-2}y^2+nC_3x^{n-3}y^3+... nC_n y^n$

a. We have to find the coefficient of $x^2y^8$

$(x+2y)^{10}=10C_0x^{10}+10C_1x^9(2y)+10C_2x^8(2y)^2+10C_3x^7(2y)^3+...+10C_{10}(2y)^{10}$

Term is $10C_8x^(2y)^8$

Coefficient = $10C_8\cdot 2^8$

b.Term in which $x^4y^6$ is $10C_6x^4(2y)^6$

Coefficient = $10C_4\cdot 2^6$

c.We have to find the coefficient of $x^5y^5$

Term is $10C_5x^5(2y)^5$

Coefficient = $10C_5\cdot 2^5$

kifflom [539]2 years ago

3 0

Answer:

Step-by-step explanation:

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sdas [7]

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\\ \quad \\
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\\ \quad \\
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-----------------------------\\\\
log_b(xy^2z^{-6}\implies log_b(x)+log_b(y^2)+log_b(z^{-6})
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2 years ago

The original price of a video game is $32.99 before tax. When Mario bought the video game it rang up as $26.39 before tax. He th

mihalych1998 [28]

Answer:

Part A: The percent discount on game is 20%.

Part B: Mario paid a total of $28.50 including sales tax.

Step-by-step explanation:

Given that:

Part A:

Original price of video game = $32.99

Discounted price = $26.39

Amount of discount = 32.99 - 26.39 = $6.60

Discount percent = $\frac{Amount\ of\ discount}{Original\ price}*100$

Discount percent = $\frac{6.60}{32.99}*100 = 0.20*100$

Discount percent = 20%

Part B:

Sales tax = 8% of discounted price

Amount of sales tax = $\frac{8}{100}*26.39 = 0.08*26.39$

Amount of sales tax = $2.11

Total amount = $26.39 + $ 2.11 = $28.50

Hence,

Part A: The percent discount on game is 20%.

Part B: Mario paid a total of $28.50 including sales tax.

5 0

2 years ago

Let p = x2 + 6.<br> Which equation is equivalent to (22 + 6)2 – 21 = 4x2 + 24 in terms of p?

Alona [7]

Answer:

$\frac{35}{4} =p$

Step-by-step explanation:

p= $x^{2} +6$ ,

(22+6)2-21= $4x^{2} +24$

44+12-21= $4x^{2} +24$

35= $4x^{2} +24$ ,

If you factor out the equation, you get that 35=4p(if you factor it out)

Therefore, $\frac{35}{4} =p$

4 0

2 years ago

A hot air balloon holds 1,592 cubic meters of helium. The density of helium is 0.1785 kilograms per cubic

yuradex [85]

Answer: 285.2 kg

Step-by-step explanation:

Given

The volume of helium in the balloon is $V=1592\ m^3$

The density of the helium is $\rho =0.1785\ kg/m^3$

Mass of the helium gas is given by the product of density and volume

$\Rightarrow M=\rho \cdot V\\\Rightarrow M=0.1785\times 1592\\\Rightarrow M=285.2\ kg$

Thus, the mass of gas is 285.2 kg

3 0

2 years ago

Which point is the incenter of △JKL ?

allsm [11]

Answer: In-center of the triangle is point N.

Step-by-step explanation:

We are given a triangle △JKL.

In triangle △JKL, they drew perpendicular bisectors of each side of the triangle.

Also we are given angle bisectors of the each of angles in given triangle.

Note: Perpendicular bisector is a line that intersect a segment into two equal parts and also perpendicular to it.

<em>Also note that the in-center is the point forming the origin of a circle inscribed inside the triangle. It is constructed by taking the intersection of the angle bisectors of the three vertices of the triangle.</em>

<h3>We can see that angle bisectors are intersecting at a point N. </h3><h3>Therefore, in-center of the triangle is point N.</h3>

3 0

3 years ago

Read 2 more answers