Solution to the linear inequality below <br> X-4y<-12

CALLING ON K12 STUDENTS... I'm in Honors Geometry and am so stuck on the end of the year Trig in Baseball assignment... Anybody

Katyanochek1 [597]

RIP, i finished my geometry hon. EOC today, i'm in 8th :P

7 0

3 years ago

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.

4 0

3 years ago

I WILL GIVE U A CROWN.......

steposvetlana [31]

<h3>Answer: Likely it's choice D) </h3>

See below for the explanation why

========================================================

down payment = 22% of home value

down payment = 22% of $426,000

down payment = 0.22*426,000

down payment = 93,720 dollars

The remaining amount mortgaged (i.e. loaned out) is

home value - (down payment) = 426,000 - 93,720 = 332,280

----------------

The monthly payment formula is

P = (L*i)/(1 - (1+i)^(-n))

where,

P = monthly payment
L = amount loaned
i = monthly interest rate in decimal form
n = number of months

In this case,

L = 332,280 dollars
i = 0.0525/12 = 0.004375 which is exact without any rounding
n = 20*12 = 240 months (equivalent to 20 years)

Plugging those three values into the formula mentioned gets us the following:

P = (L*i)/(1 - (1+i)^(-n))

P = (332,280*0.004375)/(1 - (1+0.004375)^(-240))

P = 2,239.0493959316

P = 2,239.05

Multiply this monthly payment by the 240 months mentioned.

2,239.05*240 = 537,372

This is the total amount paid back (principal + interest)

Add on the down payment to find out how much money total is handed over: 537,372 + 93,720 = 631,092

Unfortunately $631,092 is not listed as one of the answer choices. The closest would be D) $631,057

I'm not sure if I made a rounding error somewhere, or perhaps your teacher is using an amortization table. It's also possible your teacher made a typo somewhere. I'd ask them for clarification.

5 0

2 years ago

2x/3 + 2/3 + 1x/5 = x

lubasha [3.4K]

Answer:

your answer will be x = 5

Step-by-step explanation:

5 0

3 years ago

Could some please help me with this math question

umka21 [38]

Y = 3x - 1

Slope intercept form is written in this format:
y=mx+b

m represents the slope
b represents the y intercept

You can clearly see that line intercepts the y axis at -1 so if you substitute that in:

y = mx - 1

You can easily find the slope by following this simple formula: rise/run

If you start at (0, -1) and try to get to (1, 2) then you go up 3 units and across 1 unit so the slope is 3/1 or 3. It’s not a negative slope since the line goes upwards and not downwards.

If you substitute the slope and y intercept you get:

y = 3x - 1

~~hope this helps~~

5 0

3 years ago

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Solution to the linear inequality below X-4y<-12