A. 44
B. 112
C. 32
D. 35

Answer:

[tex]y(x)=\frac{5}{3\pi}-\frac{5\pi}{27+3\pi^2}e^{-3x}-\frac{15}{9\pi+\pi^3}cos(\pi x)-\frac{5}{9+\pi^2}sin(\pi x)[/tex]

Step-by-step explanation:

[tex]y''+3y'+2y=5sin(\pi x),\: y(0)=y'(0)=0\\\\\mathcal{L}\{y''\}+3\mathcal{L}\{y'\}+2\mathcal{L}\{y\}=\mathcal{L}\{5sin(\pi x)\}\\\\s^2Y(s)-sy(0)-y'(0)+3[sY(s)-y(0)]+2Y(s)=\frac{5\pi}{s^2+\pi^2}\\\\s^2Y(s)+3sY(s)=\frac{5\pi}{s^2+\pi^2}\\ \\(s^2+3s)Y(s)=\frac{5\pi}{s^2+\pi^2}\\ \\Y(s)=\frac{5\pi}{(s^2+\pi^2)(s^2+3s)}\\ \\Y(s)=\frac{5\pi}{s(s+3)(s^2+\pi^2)}[/tex]

Perform the partial fraction decomposition

[tex]\frac{5 \pi}{s \left(s + 3\right) \left(s^{2} + \pi^{2}\right)}=\frac{A}{s}+\frac{B}{s + 3}+\frac{C s + D}{s^{2} + \pi^{2}}\\5\pi=s \left(s + 3\right) \left(C s + D\right) + s \left(s^{2} + \pi^{2}\right) B + \left(s + 3\right) \left(s^{2} + \pi^{2}\right) A\\\\5 \pi=s^{3} A + s^{3} B + s^{3} C + 3 s^{2} A + 3 s^{2} C + s^{2} D + \pi^{2} s A + \pi^{2} s B + 3 s D + 3 \pi^{2} A\\\\5\pi=s^3(A+B+C)+s^2(3A+3C+D)+s(\pi^2A+\pi^2B+3D)+3\pi^2A[/tex]

Solve for each constant

[tex]\begin{cases} A + B + C = 0\\3 A + 3 C + D = 0\\\pi^{2} A + \pi^{2} B + 3 D = 0\\3 \pi^{2} A = 5 \pi \end{cases}[/tex]

[tex]3\pi^2A=5\pi\\A=\frac{5}{3\pi}[/tex]

[tex]A+B+C=0\\3A+3B+3C=0\\(3A+3B+3C=0)-(3A+3C+D=0)\\3B-D=0\\3B=D[/tex]

[tex]\pi^2A+\pi^2B+3D=0\\\pi^2(\frac{5}{3\pi})+\pi^2B+3(3B)=0\\\frac{5\pi}{3}+\pi^2B+9B=0\\ B(\pi^2+9)=-\frac{5\pi}{3}\\B=-\frac{5\pi}{3(\pi^2+9)}\\B=-\frac{5\pi}{3\pi^2+27}[/tex]

[tex]3B=D\\3(-\frac{5\pi}{3\pi^2+27})=D\\-\frac{5\pi}{\pi^2+9}=D[/tex]

[tex]A+B+C=0\\\frac{5}{3\pi}-\frac{5\pi}{3\pi^2+27}+C=0\\\frac{15\pi^2+135}{3\pi(3\pi^2+27)}-\frac{15\pi^2}{(3\pi)(3\pi^2+27)}+C=0\\\frac{135}{9\pi^3+81\pi}+C=0\\\frac{15}{\pi^3+9\pi}+C=0\\C=-\frac{15}{\pi^3+9\pi}[/tex]

Take the inverse transform and solve for the IVP

[tex]Y(s)=\frac{\frac{5}{3 \pi}}{s}+\frac{- \frac{5 \pi}{27 + 3 \pi^{2}}}{s + 3}+\frac{- \frac{15 s}{9 \pi + \pi^{3}} - \frac{5 \pi}{9 + \pi^{2}}}{s^{2} + \pi^{2}}\\\\Y(s)=\frac{\frac{5}{3 \pi}}{s}-\frac{\frac{5 \pi}{27 + 3 \pi^{2}}}{s + 3}-\frac{ \frac{15 s}{9 \pi + \pi^{3}}}{s^{2} + \pi^{2}}-\frac{\frac{5\pi}{9+\pi^2} }{s^2+\pi^2}\\ \\y(x)=\frac{5}{3\pi}-\frac{5\pi}{27+3\pi^2}e^{-3x}-\frac{15}{9\pi+\pi^3}cos(\pi x)-\frac{5}{9+\pi^2}sin(\pi x)[/tex]

Answer:

snacks, the reason being that it can be anything

Step-by-step explanation:

Answer:

Donuts

Step-by-step explanation:

The donuts are specifically tastier than the options mentioned

Answer:

-3

Step-by-step explanation:

[tex]\downdownarrows\\ -\left|-3\right|[/tex]

Calculate the absolute value

[tex]-3[/tex]

I hope this helps you

:)

Hey there!

Calculating the exterior angles of regular polygons

To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°. The formula for calculating the sum of interior angles is ( n − 2 ) × 180 ∘ where is the number of sides. All the interior angles in a regular polygon are equal.

9514 1404 393

Answer:

Step-by-step explanation:

The given inequality is in vertex form:

  y = a(x -h)^2 +k . . . . . . has vertex (h, k)

so the vertex can be read from the given expression.

  y > (x +2)^2 -1   ⇒   (h, k) = (-2, -1) . . . the vertex

The leading coefficient (+1) is positive so the parabola opens upward.

__

The y > ( ) tells you the boundary line is dashed (is not part of the solution). It also tells you the shading is above the curve, hence inside the parabola.

The two offered points (0, 0), (2, -3) are NOT part of the solution set.

Answer:

depth of -117 feet

Step-by-step explanation:

24 hours 72 feet, so one hour 72/24 = 3 feet

after 15 hours, another 3*15 = 45 feet, so the depth become 72 + 45 = 117 feet

Answer:

y = (-1/3)x + 4

Step-by-step explanation:

m = rise/run =    y2 - y1         3 - 4        -1

                         -----------   =   -------- = ----

                          x2 - x1          3 - 0       3

y = mx + b

y = (-1/3)x + b

Pick either coordinate. For this, I'll pick (0, 4)

4 = (-1/3)(0) + b

4 = b

y = (-1/3)x + 4

If you are certain about M = (-5/6), then replace (-1/3) with (-5/6)

I hope this helps!

Answer:

option 1

Because not all of them are equal lengths

Answer: -122

Step-by-step explanation:

-234+112=-122 hope that helps!

Answer:

-122

Step-by-step explanation:

Answer:

Club A charges $4 per car and club B charges $4 also

Step-by-step explanation:

Answer:

Yes,

Step-by-step explanation:

Club A charges $4 per car and club B charges $4 also

Answer:

[tex]x=\frac{324}{5}[/tex]

Step-by-step explanation:

Given the following question:

[tex]\sqrt{5x} -7-3=8[/tex]

To find the answer we are going to use inverse of operations to isolate the variable x, doing this we can then find the value of the variable and then have our answer.

[tex]\sqrt{5x} -7-3=8[/tex]
[tex]-7-3=-10[/tex]
[tex]\sqrt{5x} -10=8[/tex]
[tex]-10+10=0[/tex]
[tex]8+10=18[/tex]
[tex]\sqrt{5x} =18[/tex]
[tex]\sqrt{5x} =5[/tex]
[tex]18\times18=324[/tex]
[tex]5x=324[/tex]
[tex]5x\div5=x[/tex]
[tex]324\div5=x=\frac{324}{5}[/tex]
[tex]x=\frac{324}{5}[/tex]

Your answer is "x = 324/5."

Hope this helps.

Answer:

Its perimeter is 23 units

Step-by-step explanation:

The perimeter of any figure is the sum of the lengths of its outline sides

The rule of the distance between two points is:

In the given figure ABCD:

Its perimeter = AB + BC + CD + DE + EA

→ Find the length of each side using the rule above

A = (-4, -2), B = (-1, 2), C = (2, 2), D = (5, -1), E = (2, -4)

→ Substitute them in the rule above to find the lengths of its sides

[tex]AB=\sqrt{(-1--4)^{2}+(2--2)^{2}}=\sqrt{(-1+4)^{2}+(2+2)^{2}}\\\\=\sqrt{(3)^{2}+(4)^{2}}=\sqrt{9+16}=\sqrt{25}[/tex]

∴ AB = 5

[tex]BC=\sqrt{(2--1)^{2}+(2-2)^{2}}=\sqrt{(2+1)^{2}+(0)^{2}}\\\\=\sqrt{(3)^{2}+0}=\sqrt{9+0}=\sqrt{9}[/tex]

∴ BC = 3

[tex]CD=\sqrt{(5-2)^{2}+(-1-2)^{2}}=\sqrt{(3)^{2}+(-3)^{2}}\\\\=\sqrt{9+9}=\sqrt{18}[/tex]

∴ CD = [tex]\sqrt{18}[/tex]

[tex]DE=\sqrt{(2-5)^{2}+(-4--1)^{2}}=\sqrt{(-3)^{2}+(-4+1)^{2}}\\\\=\sqrt{(-3)^{2}+(-3)^{2}}=\sqrt{9+9}=\sqrt{18}[/tex]

∴ DE = [tex]\sqrt{18}[/tex]

[tex]EA=\sqrt{(-4-2)^{2}+(-2--4)^{2}}=\sqrt{(-6)^{2}+(-2+4)^{2}}\\\\=\sqrt{(-6)^{2}+(2)^{2}}=\sqrt{36+4}=\sqrt{40}[/tex]

∴ EA = [tex]\sqrt{40}[/tex]

→ Add them to find the perimeter of the figure ABCDE

∴ Its perimeter = 5 + 3 + [tex]\sqrt{18}[/tex] + [tex]\sqrt{18}[/tex] +[tex]\sqrt{40}[/tex] ≅ 22.8098

→ Round it to the whole number

∴ Its perimeter = 23 units

Answer:

Stem  Leaf

5          4 6

6          2 5 6

7          0 2 2 4

8          5 5 8 8 8

9          0 1 2 7 9

Step-by-step explanation:

That is how the stem and leaf plot will look like

Hope this helps

Answer:

line 2.

Step-by-step explanation:

the correct way is provided in the attachment (under the green line). Note, only positive value (it is the length of the side) can be considered as answer.

Answer:

I am sure it's 2

Step-by-step explanation:

Source: Trust me bro

Answer:

The answer is 2 because 1 plus 1 is like having 2 things

Answer:

Q4 part d

Q5 part c

Step-by-step explanation:

Answer:

this question is wrong

Answer:

37/4

Step-by-step explanation:

1/8 + 1/4 + 5/8 + 7/8 + 1 1/8 + 1 5/8 + 1 7/8 + 2 = 3/8 + 3/2 + 13/4 + 33/8 = 37/4

Answer:

A. X =8

Step-by-step explanation:

5/X=12.5/20

cross multiply

12.5X = 20*5

12.5X=100

X=100/12.5

X=8

Answer:

Step-by-step explanation:

The given relationships allow us to write a system of equations in the speeds of the wind and plane.

Let w and p represent the speeds of the wind and the plane, respectively. We know speed is the ratio of distance to time, so ...

  p -w = 6300 km/(7 h) = 900 km/h

  p +w = 8400 km/(6 h) = 1400 km/h

__

Adding these two equations gives ...

  2p = 2300 km/h

  p = 1150 km/h . . . . . . divide by 2

Subtracting the first equation from the second gives ...

  2w = 500 km/h

  w = 250 km/h

The speed of the plane in still air is 1150 km per hour; the speed of the wind is 250 km per hour.

Answer:

-5 -6 = -11

You start at -5 and move to the left by 6 spaces until you get to -11 :)

Hope this helps!

Have a good day!

Please rate and mark brainliest!!

Answer: It changes the slope from positive to negative.

Step-by-step explanation:

Answer:

1050

Step-by-step explanation:

So, we know 4/5 of a gallon can paint 280ft^2, but we don't know how much each gallon can paint, so to find x, do this

4/5x=280ft^2, next multiply both sides by 5/4 to get x by itself

x=350

Now multiply x by 3 to get your new answer.

350*3=1050

Hope this helps, feel free to leave any questions.

Answer:

The number should be 12.

Step-by-step explanation:

We can form a simple equation and solve for the variable:

2x - 7 = 17

2x = 24

x = 12

Answer:

See Below.

Step-by-step explanation:

  Statements:                                              Reasons:

1) [tex]\angle 4\cong \angle 3; c\parallel d[/tex]                                           Given

2) [tex]\angle 1\cong \angle 3[/tex]                                                 Alternate Interior Angles Theorem

3) [tex]\bf{\angle 4 \cong \angle 1}[/tex]                                                 Transitive Property of Congruence

4) [tex]\angle 1\cong \angle 2[/tex]                                                 Vertical Angles Theorem

5) [tex]\bf{\angle 4\cong \angle 2}[/tex]                                                 Transitive Property of Congruence

And we’re done!

Answer:

Kyle has 25 postcards

Step-by-step explanation:

Joanna has 45 postcards in her collection, which is 180% of the number of postcards of Kyle.

If the number of postcards of Kyle is K, and the number of postcards of Joanna is J, then:

J=180% K

Recall a percentage can be expressed in decimal by dividing by 100:

J=180/100*K

To find the value of K, we solve the above equation:

K=100/180*J

Since J=45:

K=100/180*45=25

Kyle has 25 postcards

Answer:

$121.25

Step-by-step explanation:

97 X 1.25 = 121.25

Answer:

D. 0.05

Step-by-step explanation:

5 x 10 = 50

50 as a decimal

0.5