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3 years ago

Can anyone please help with this question?

Mathematics

1 answer:

vitfil [10]3 years ago

6 0

The middle section is n(n+1)

The top row is n+2

The bottom row is 2n+1

So the rule for the total number of tiles will be the sum of the above rules...

s(n)=n(n+1)+n+2+2n+1

s(n)=n^2+n+n+2+2n+1

s(n)=n^2+4n+3

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The indicated function y1(x is a solution of the given differential equation. use reduction of order or formula (5 in section 4.

Taya2010 [7]

Given a solution $y_1(x)=\ln x$ , we can attempt to find a solution of the form $y_2(x)=v(x)y_1(x)$ . We have derivatives

$y_2=v\ln x$
${y_2}'=v'\ln x+\dfrac vx$
${y_2}''=v''\ln x+\dfrac{v'}x+\dfrac{v'x-v}{x^2}=v''\ln x+\dfrac{2v'}x-\dfrac v{x^2}$

Substituting into the ODE, we get

$v''x\ln x+2v'-\dfrac vx+v'\ln x+\dfrac vx=0$
$v''x\ln x+(2+\ln x)v'=0$

Setting $w=v'$ , we end up with the linear ODE

$w'x\ln x+(2+\ln x)w=0$

Multiplying both sides by $\ln x$ , we have

$w' x(\ln x)^2+(2\ln x+(\ln x)^2)w=0$

and noting that

$\dfrac{\mathrm d}{\mathrm dx}\left[x(\ln x)^2\right]=(\ln x)^2+\dfrac{2x\ln x}x=(\ln x)^2+2\ln x$

we can write the ODE as

$\dfrac{\mathrm d}{\mathrm dx}\left[wx(\ln x)^2\right]=0$

Integrating both sides with respect to $x$ , we get

$wx(\ln x)^2=C_1$
$w=\dfrac{C_1}{x(\ln x)^2}$

Now solve for $v$ :

$v'=\dfrac{C_1}{x(\ln x)^2}$
$v=-\dfrac{C_1}{\ln x}+C_2$

So you have

$y_2=v\ln x=-C_1+C_2\ln x$

and given that $y_1=\ln x$ , the second term in $y_2$ is already taken into account in the solution set, which means that $y_2=1$ , i.e. any constant solution is in the solution set.

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2 years ago

An ore ship is traveling west toward Duluth on Lake Superior at 18 miles per hour. The bearing of Split Rock Lighthouse is 285de

Luda [366]

<span>You are given an ore ship that is traveling west toward Duluth on Lake Superior at 18 miles per hour with a bearing of 285deg Split Rock Lighthouse. Also, after 1 hour the bearing of the lighthouse is 340deg. The distance between the ship and the lighthouse when the second bearing is determined is 35 miles.</span>

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3 years ago

Flagpole to the ground using a piece of rope that is 10 feet long. He is going to tie the rope to the top of the flagpole and th

Flauer [41]

Answer:

Step-by-step explanation

Using the pythagoras theorem;

Given

The length of the flag pole = 8 feet = opposite side

Length of the rope = 10 feet = hypotenuse

To determine how far out on the ground he need to secure the rope from the flagpole so that the rope is tight, we need to look for the adjacent. Using the equation

hyp² = opp² + adj²

10² = 8² + adj²

adj² = 100-64

adj² = 36

adj = √36

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Hence the rope should be placed 6feet out of the ground

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2 years ago

Is 6^-2 positive or negative?

serious [3.7K]

The 6 is a positive and the 2 is a negative. Basically the answer to the equation would be a negative

6 x -6 = -36

Hope this helps you

-AaronWiseIsBae

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3 years ago

Square MNPQ has an area of 9 square units. The vertex M is located at (2,3). What is a possible coordinate pair for vertex N?

almond37 [142]

Answer:

(2,0)

Step-by-step explanation:

7 0

2 years ago