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3 years ago

Please help me solve this problem. I'm stuck!

Mathematics

1 answer:

mezya [45]3 years ago

8 0

Answer:

a. 4 hours

b. if studio b increases' its hourly price, the two studios will never have the same price.

Step-by-step explanation:

The function for studio 1 is

cost = 8(hours) + 10

studio 2

cost = 6(hours) + 16

they cost the same after 4 hours. making a table really helps.

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Jef put a small box that is 12 inches long, 8 inches wide, and 4 inches tall inside a box that is 20 inches long,15 inches wide,

alexira [117]

The answer can be found by subtract the volume of the small box from the volume of big box.

Volume of the small box:
12*8*4= 384 inches cube

Volume of the big box:
20*15*9= 2700 inches cube

The space left:
2700 - 384 = 2316 inches cube

8 0

3 years ago

Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x

djverab [1.8K]

I'll assume the ODE is

$y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}$

Solve the homogeneous ODE,

$y'' - 3y' + 2y = 0$

The characteristic equation

$r^2 - 3r + 2 = (r - 1) (r - 2) = 0$

has roots at $r=1$ and $r=2$ . Then the characteristic solution is

$y = C_1 e^x + C_2 e^{2x}$

For nonhomogeneous ODE (1),

$y'' - 3y' + 2y = e^x$

consider the ansatz particular solution

$y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x$

Substituting this into (1) gives

$a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1$

For the nonhomogeneous ODE (2),

$y'' - 3y' + 2y = e^{2x}$

take the ansatz

$y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}$

Substitute (2) into the ODE to get

$b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1$

Lastly, for the nonhomogeneous ODE (3)

$y'' - 3y' + 2y = e^{-x}$

take the ansatz

$y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}$

and solve for $c$ .

$ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16$

Then the general solution to the ODE is

$\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}$

6 0

1 year ago

The expression a[b+(c−d)]

maria [59]

Answer:

Step-by-step explanation:

When you distribute values, 'a' while be multiplied by everything. since there is a plus sign in front of the 'b' then that will not be distributed. so an 'ab' will add the an 'ac' but an 'ad' is still going to subtract away from the equation.

5 0

2 years ago

Y<=x-5, and y<=-x-4 would be points (1,10)? or<br> (-1,10)<br> (10,1)<br> 1,-10)

weeeeeb [17]

It would be (1,-10) <===

4 0

3 years ago

Can 403/72 be reduced?

tresset_1 [31]

Answer:

yes but it would be an incomplete fraction

Step-by-step explanation: