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2 years ago

The tThe term 10x3y2 is a term in which binomial expansion?

Mathematics

1 answer:

MAXImum [283]2 years ago

6 0

Answer:

(x + y)^5.

Step-by-step explanation:

The (r+1)th term of (x + y)^n = nCr x^n-r y^r

Compare this with 10x^3 y^2 we get

nCr = 10 , n-r = 3 and r = 2 giving n = 3+2 = 5

5C2 = 10.

So the answer is (x + y)^5.

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Find the solution of the initial value problem<br><br> dy/dx=(-2x+y)^2-7 ,y(0)=0

Leokris [45]

Substitute $v(x)=-2x+y(x)$ , so that $\dfrac{\mathrm dv}{\mathrm dx}=-2+\dfrac{\mathrm dy}{\mathrm dx}$ . Then the ODE is equivalent to

$\dfrac{\mathrm dv}{\mathrm dx}+2=v^2-7$

which is separable as

$\dfrac{\mathrm dv}{v^2-9}=\mathrm dx$

Split the left side into partial fractions,

$\dfrac1{v^2-9}=\dfrac16\left(\dfrac1{v-3}-\dfrac1{v+3}\right)$

so that integrating both sides is trivial and we get

$\dfrac{\ln|v-3|-\ln|v+3|}6=x+C$

$\ln\left|\dfrac{v-3}{v+3}\right|=6x+C$

$\dfrac{v-3}{v+3}=Ce^{6x}$

$\dfrac{v+3-6}{v+3}=1-\dfrac6{v+3}=Ce^{6x}$

$\dfrac6{v+3}=1-Ce^{6x}$

$v=\dfrac6{1-Ce^{6x}}-3$

$-2x+y=\dfrac6{1-Ce^{6x}}-3$

$y=2x+\dfrac6{1-Ce^{6x}}-3$

Given the initial condition $y(0)=0$ , we find

$0=\dfrac6{1-C}-3\implies C=-1$

so that the ODE has the particular solution,

$\boxed{y=2x+\dfrac6{1+e^{6x}}-3}$

5 0

2 years ago

A store sells cheese in half a pound package a recipe calls fpr 1.72 pound of cheese how many packages does the chef need

Sedbober [7]

Answer:

4 packages

Step-by-step explanation:

Since the store sells by 1/2 packages, we have to round 1.72 UP to 2.00. Then we multiply 1/2pound by 4= 2.00 pounds

4 0

2 years ago

Can you please help me answer this picture

Nana76 [90]

Answer:

Step-by-step explanation:

b + 2 = b + 2

8 0

2 years ago

Read 2 more answers

A show owner offers a 20% discount off the regular price of a mirror. The amount of the discount is $3 what is the regular price

hram777 [196]

Answer:

$15

Step-by-step explanation:

The original price of the mirror is unknown, so let's call it x.

The discount on the original price is a 20% discount, so it is 20% of x, or 0.2x.

We are told the discount is $3, so 0.2x = 3. Now we solve the equation for x.

0.2x = 3

Divide both sides by 0.2.

x = 3/0.2

x = 15

The regular price is $15.

5 0

2 years ago

What is the slope ? M=

frez [133]

Answer:

-3/2

Step-by-step explanation:

The slope is found by

m = ( y2-y1)/(x2-x1)

Using the points (-4,11) and ( 0,5)

m = ( 11-5)/( -4-0)

= 6/-4

= -3/2

4 0

2 years ago