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1 month ago

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Use the method of undetermined coefficients to solve the given nonhomogeneous system. dx dt = 2x + 3y − 5 dy dt = −x − 2y + 4 x(

t), y(t)

2 answers:

Svet_ta [12.7K]1 month ago

5 0

Answer:

The system of non-homogeneous linear equations is

dx/dt=2x+3y-5

dy/dt=-x-2y+4

Employing differential equations and the method of undetermined coefficients, the solution is

y(t,x)=-x^2+2*xt+x

AnnZ [12.3K]1 month ago

4 0

Try this approach (refer to the attachment, which outlines three steps).

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The refrigerant can accommodate 1.92 cubic feet.

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2 months ago

At a hot air ballon festival, Erica spots a red ballon due east at an angle of elevation of 36 degrees. She turns due west and s

Zina [12379]

Answer:

Step-by-step explanation:

Information provided

The eastern balloon makes an elevation angle of $36^{\circ}$ and is positioned at a height of 461 m.

The western balloon creates an elevation angle of $51^{\circ}$ and is positioned at a height of 296 m.

Considering that Erica is 1.6 m tall, the effective height of the Red balloon becomes 459.4 m,

while the effective height of the Blue balloon ends up at 294.4 m.

Utilizing trigonometric principles,

$\tan 36=\frac{459.4}{d_1}$

$\tan 51=\frac{294.4}{d_2}$

$d_1=632.30 m$

$d_2=238.4 m$

Now calculating the distance separating the two Balloons,

$d=d_1+d_2$

$d=870.70 m$

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2 months ago

If 30,000 cm2 of material is available to make a box with a square base and an open top, what is the largest possible volume (in

Inessa [12570]

Answer:

The highest achievable volume for the box is 2000000 cubic meters.

Step-by-step explanation:

Below is an outline of the volume ( $V$ ), measured in cubic centimeters, and surface area ( $A_{s}$ ), measured in square centimeters, for a box featuring a square base:

$A_{s} = l^{2}+h\cdot l$ (1)

$V = l^{2}\cdot h$ (2)

Where:

$l$ - The length of the base's side, in centimeters.

$h$ - The height of the box, in centimeters.

Using (2), we isolate $h$ in the formula:

$h = \frac{V}{l^{2}}$

Then, we substitute into (1) and simplify the outcome:

$A_{s} = l^{2}+ \frac{V}{l}$

$A_{s}\cdot l = l^{3}+V$

$V = A_{s}\cdot l -l^{3}$ (3)

Next, we calculate the first and second derivatives of this expression:

$V' = A_{s}-3\cdot l^{2}$ (4)

$V'' = -6\cdot l$ (5)

If $V' = 0$ and $A_{s} = 30000\,cm^{2}$ , then we find that the critical value for the base's side length is:

$30000-3\cdot l^{2} = 0$

$3\cdot l^{2} = 30000$

$l = 100\,cm$

Subsequently, we assess this outcome using the second derivative's expression:

$V'' = -600$

According to Second Derivative Test, this critical value signifies an absolute maximum. Consequently, the largest volume obtainable for the box is:

$V = 30000\cdot l - l^{3}$

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The highest achievable volume for the box is 2000000 cubic meters.

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1 month ago

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Zina [12379]

The correct response is 176

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