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vichka [17]
4 years ago
11

I NEED HELP IM IN CLASS RN PLEASEE HELP! WILL GIVE BRIANLIEST!

Mathematics
1 answer:
fgiga [73]4 years ago
4 0

Answer:

y=x+12

Step-by-step explanation:

Well the slope is -4/-4 =1

We plug it into the formula, y=mx+b, but m=1

So it is y=1x+b

We know the points, so we plug y and x in which is:

-4=-4*4+b

-4=-16+b

b=12

So the point slope form of that is y=x+12

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Set up but do not solve for the appropriate particular solution yp for the differential equation y′′+4y=5xcos(2x) using the Meth
taurus [48]

Answer:

So, solution of  the differential equation is

y(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos  2x+c_1e^{-2it}+c_2e^{2it}\\

Step-by-step explanation:

We have the given differential equation: y′′+4y=5xcos(2x)

We use the Method of Undetermined Coefficients.

We first solve the homogeneous differential equation y′′+4y=0.

y''+4y=0\\\\r^2+4=0\\\\r=\pm2i\\\\

It is a homogeneous solution:

y_h(t)=c_1e^{-2i t}+c_2e^{2i t}

Now, we finding a particular solution.

y_p(t)=A5x\cos 2x\\\\y'_p(t)=A5\cos 2x-A10x\sin 2x\\\\y''_p(t)=-A20\sin 2x-A20x\cos 2x\\\\\\\implies y''+4y=5x\cos 2x\\\\-A20\sin 2x-A20x\cos 2x+4\cdot A5x\cos 2x=5x\cos 2x\\\\-A20\sin 2x=5x\cos 2x\\\\A=-\frac{x}{4} \cot 2x\\

we get

y_p(t)=A5\cos 2x\\\\y_p(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos  2x\\\\\\y(t)=y_p(t)+y_h(t)\\\\y(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos  2x+c_1e^{-2it}+c_2e^{2it}\\

So, solution of  the differential equation is

y(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos  2x+c_1e^{-2it}+c_2e^{2it}\\

7 0
3 years ago
Let t be time in seconds and let r(t) be the rate, in gallons per second, that water enters a reservoir: r(t)=700−40t. a) For 0≤
Flura [38]
What you don't want is the value of r(t) becoming negative. Surely that would represent water escaping the reservoir.

How big can (t) get before water actually starts escaping the reservoir?

Essentially, to figure this out r(t) would have to be equal to 0. 

700 - 40t = 0

40t=700

t=700/40=17.5

So the first answer is 17.5 seconds. After this amount of time has elapsed the reservoir will start to lose water as r(t) would become negative.

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

The reservoir had the least amount of water in it before it was being filled. That was when t=0. The volume of water in the reservoir wasn't negatively impacted as not enough water had escaped it during the 17.5 to 30 second period.
7 0
3 years ago
HELP HELP HELP HELP GFG
liraira [26]

Answer:

y=mx + b

the slope is -3,2

y= -0.67x + 5

this is what. i got i could be wrong, sorry if i am

Step-by-step explanation:

8 0
2 years ago
How many positive integers not exceeding 1000 are not divisible by either 4 or 6?
san4es73 [151]
\left\lfloor\dfrac{1000}4\right\rfloor=250

\left\lfloor\dfrac{1000}6\right\rfloor=166

\left\lfloor\dfrac{1000}{\mathrm{lcm}(4,6)}\right\rfloor=\left\lfloor\dfrac{1000}{12}\right\rfloor=83

250+166-83=333
7 0
3 years ago
Mai, Eric, and Dean served a total of 103 orders on Monday. Mai served 8 more orders than Eric. Dean served 3 times as many orde
mel-nik [20]
Let the number of orders Eric served be x

Eric = x
Mai =  x+ 8         [Mai served 8 more than Eric]
Dean = 3x           [Dean served 3 times as many as Eric]

Given that the total is 103
x + x + 8 + 3x = 103  
5x + 8 = 103
5x = 103 - 8
5x = 95
x = 19


x = 19
x + 8 = 19 + 8 = 27
3x = 19 x 3 = 57

Eric served 19
Mai served 27
Dean served 57





3 0
3 years ago
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