All categories

2 years ago

What is the coefficient of the x9y-term in the binomial expansion of (2y + 4x3)4? 4 32 128 512

Mathematics

2 answers:

sasho [114]2 years ago

7 0

Answer:- 512

Explanation:-

We know that $(m+1)^{th},\ (T_{m+1})$ in the binomial expansion $(p+q)^n$ is given by

$T_{m+1}=^nC_m\ p^{n-m}q^m$

Assume that $x^9y$ occurs in the $(m+1)^{th}$ term of the expansion of $(2y+4x^3)^4=(4x^3+2y)^4$

$T_{m+1}=^4C_m\ (4x^3)^{4-m}(2y)^m$

Comparing power of x and y in $x^9y$ we get m=1

Thus term for m=1 $=\ ^4C_1\ (4x^3)^{3}(2y)^1=^4C_1=\frac{4!}{(4-1)!1!}(64x^9)(2y)=4(128x^9y)=512x^9y$

Thus the coefficient of $x^9y$ is 512.

Nesterboy [21]2 years ago

5 0

512 is the coefficient of the x9y-term

You might be interested in

The parent cosecant function is shifted 4 units right and 3 units up. Which of the following is the graph of the transformed fun

snow_lady [41]

We have that

using a graph tool--------------> graph the <span> cosecant function
</span>see the attached figure

the answer is the option B

4 0

2 years ago

Read 2 more answers

the table shows different ways that cameron can display his 12 model cars on shelves. How many shelves will display 2 cars if 8

Lera25 [3.4K]

Answer:

4 shelves

Step-by-step explanation:

if there is 8 shelves that display 1 car then that means there is 8 cars total.

so if you need a total of 12 cars then you would do (total of cars needed - total of cars you have).

(12-8) which would equal 4.

you need 4 cars left but on each shelf going forward needs to have 2 cars on it.

now since you have 4 cars you would divide that by the amount of cars on each shelf going forward.

4/2) which equals 2.

you need 2 more shelfs for the 4 cars needed.

3 0

2 years ago

Water is poured into a conical paper cup at the rate of 3/2 in3/sec (similar to Example 4 in Section 3.7). If the cup is 6 inche

aliya0001 [1]

Answer:

The water level rising when the water is 4 inches deep is $\frac{3}{8\times \pi} inch/s$ .

Step-by-step explanation:

Rate of water pouring out in the cone = R= $\frac{3}{2} inch^3/s$

Height of the cup = h = 6 inches

Radius of the cup = r = 3 inches

$\frac{r}{h}=\frac{3 inch}{6 inch}=\frac{1}{2}$

r = h/2

Volume of the cone = $V=\frac{1}{3}\pi r^2h$

$V=\frac{1}{3}\pi r^2h$

$\frac{dV}{dt}=\frac{d(\frac{1}{3}\pi r^2h)}{dt}$

$\frac{dV}{dt}=\frac{d(\frac{1}{3}\pi (\frac{h}{2})^2h)}{dt}$

$\frac{dV}{dt}=\frac{1}{3\times 4}\pi \times \frac{d(h^3)}{dt}$

$\frac{dV}{dt}=\frac{1\pi }{12}\times 3h^2\times \frac{dh}{dt}$

$\frac{3}{2} inch^3/s=\frac{1\pi }{12}\times 3h^2\times \frac{dh}{dt}$

h = 4 inches

$\frac{3}{2} inch^3/s=\frac{1\pi }{12}\times 3\times (4inches )^2\times \frac{dh}{dt}$

$\frac{3}{2} inch^3/s=\pi\times 4\times \frac{dh}{dt} inches^2$

$\frac{dh}{dt}=\frac{3}{8\times \pi} inch/s$

The water level rising when the water is 4 inches deep is $\frac{3}{8\times \pi} inch/s$ .

6 0

2 years ago

Which expression is equivalent to StartFraction 3 x Superscript negative 6 Baseline y Superscript negative 3 Baseline Over 15 x

arsen [322]

Answer:

<h3>The correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline EndFraction</h3>

Step-by-step explanation:

Given the expression $\frac{3x^{-6}y^{-3} }{15x^{2}y^{10} }$ for x ≠ 0, y ≠ 0 to get the equivalent expression we will have to simplify the given expression.

$\frac{3x^{-6}y^{-3} }{15x^{2}y^{10} }\\= \frac{3}{15} x^{-6-2}y^{-3-10}\\ = \frac{3}{15}x^{-8}y^{-13} \\ =\frac{1}{5}x^{-8}y^{-13} \\$

The correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline EndFraction

6 0

2 years ago

There were 340,000 cattle placed on feed. Write an equivalent ratio that could be used to find how many of these cattle were bet

lutik1710 [3]

There were 340,000 cattle placed on feed

How many of the 340,000 cattle placed on feed were between 700 and 799 pounds?

Given the fraction of total cattle for 700 - 799 pounds is 2/5

Let x be the number of cattle between 700 - 799 pounds

We make a proportion using the fraction

$\frac{2}{5} = \frac{x}{340,000}$

Cross multiply it and solve for x

340000* 2 = 5x

680000 = 5x

Divide by 5 on both sides

So x= 136,000

There were 136,000 cattle between 700 and 799 pounds

3 0

2 years ago

Read 2 more answers