Can you go to grandmas estate and measures 8 inches across by 2 inches high if the actual stadium measures 500 feet across which equation can be used to find ex the height of the stadium in feet

Answer:

Option (d)

Step-by-step explanation:

Given,

y" +y=sin x ...........(1)

The particular solution

Putting the value of y" and y in equation (1)

Therefore 2A =0              -2B=1

              ⇒A=0                

Therefore

Final answer:

The solutions of the differential equation y'' + y = sin(x) are y = cos(x), y = (1/2)sin(x), and y = -(1/2)xcos(x).

Explanation:

To determine which of the given functions are solutions of the differential equation y'' + y = sin(x), we can substitute each function into the equation and check if it satisfies the equation. Let's go through each option:

1. Substituting y = sin(x) into the equation, we get -sin(x) + sin(x) = sin(x), which is not true. So, y = sin(x) is not a solution.
   
   
2. Substituting y = cos(x) into the equation, we get -cos(x) + cos(x) = sin(x), which is true. So, y = cos(x) is a solution.
   
   
3. Substituting y = (1/2)sin(x) into the equation, we get -(1/2)sin(x) + (1/2)sin(x) = sin(x), which is true. So, y = (1/2)sin(x) is a solution.
   
   
4. Substituting y = -(1/2)xcos(x) into the equation, we get (-1/2)xcos(x) + (1/2)xcos(x) = sin(x), which is true. So, y = -(1/2)xcos(x) is a solution.

Therefore, the solutions of the differential equation y'' + y = sin(x) are y = cos(x), y = (1/2)sin(x), and y = -(1/2)xcos(x).

Learn more about Solutions of a differential equation here:

brainly.com/question/33719537

#SPJ3

Answer:

f-1(x)=x-4

f-1(4)=0

Step-by-step explanation:

to get an inverse function, replace x with y, and y with x.

y=x+4  ---> x=y+4

solve for y: x=y+4 --> y=x-4 --> f-1(x)=x-4

f-1(4)=(4)-4=0

9514 1404 393

Answer:

  16.66 cm²  or  8.49 cm²

Step-by-step explanation:

The law of sines is useful for this.

  sin(N)/LM = sin(M)/LN

  M = arcsin(sin(N)×LN/LM) = arcsin(sin(38°)×7.2/4.8)

  M =67.44°  or  112.56°

Angle L is the remaining angle, so will have one of two measures:

  L1 = 180° -38° -67.44° = 74.56°

The area of that triangle is ...

  A = (1/2)LM×LN×sin(74.56°) ≈ 16.66 . . . . cm²

or ...

  L2 = 180° -38° -112.56° = 29.44°

The area of that triangle is ...

  A = (1/2)LM×LN×sin(29.44°) ≈ 8.49 . . . . cm²

Final answer:

To calculate the area of triangle MNL, first calculate the size of angle LMN using the Cosine Rule. Then use that angle and the known side lengths in the formula for the area of a triangle (Area = 0.5 * a * b * sin(C)) to find the area.

Explanation:

To solve this, you need to first calculate the size of angle LMN. This can be done using the Cosine Rule, which states that cos(C) = (a² + b² - c²) / 2ab, where a and b are the sides enclosing angle C. Here, angle C would be LMN, and sides a and b would be ML and LN.

Applying the values from your question, the cosine of LMN would be cos(LMN) = (4.8² + 7.2² - 38²) / (2 * 4.8 * 7.2). After calculating the cosine of the angle, you can find the angle itself using the inverse cosine function, or arccos.

Once you have the size of angle LMN, you can calculate the area of the triangle using the formula Area = 0.5 * a * b * sin(C), where a and b are sides of the triangle and C is the included angle. So, the area of triangle MNL would be Area = 0.5 * ML * LN * sin(LMN).

Learn more about Triangle Area Calculation here:

brainly.com/question/21036800

#SPJ12

If you would like to write an inequality to represent the situation, you can do this using the following steps:

x ... the amount of Alicia's paycheck

x/2 - $42.15 >= $20
x/2 >= $20 + $42.15
x/2 >= $62.15     /*2
x >= $62.15 * 2
x >= $124.3

The correct result would be x >= $124.3.