What does independent variable and dependent variable mean in math?
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- Satellite is approximately <u>2446.43 km</u> from station A.
- Satellite is approximately <u>2441.61 km</u> above the ground.
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Explanation:
I'm assuming tracking stations A and B are at the same elevation and are on flat ground. In reality, this is likely not the case; however, for the sake of simplicity, we'll assume this is the case.
The diagram is shown below. Points A and B describe the two stations, while point C is the satellite's location. Point D is on the ground directly below the satellite. We have these lengths
- AB = 60 km
- AD = x
- CD = h
Focusing on triangle ACD, we can apply the tangent rule to isolate h.
tan(angle) = opposite/adjacent
tan(A) = CD/AD
tan(86.4) = h/x
x*tan(86.4) = h
h = x*tan(86.4)
We'll use this later in the substitution below.
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Now move onto triangle BCD. For the reference angle B = 85, we can use the tangent rule to say
tan(angle) = opposite/adjacent
tan(B) = CD/DB
tan(B) = CD/(DA+AB)
tan(85) = h/(x+60)
tan(85)*(x+60) = h
tan(85)*(x+60) = x*tan(86.4) ............. apply substitution; isolate x
x*tan(85)+60*tan(85) = x*tan(86.4)
60*tan(85) = x*tan(86.4)-x*tan(85)
60*tan(85) = x*(tan(86.4)-tan(85))
x*(tan(86.4)-tan(85)) = 60*tan(85)
x = 60*tan(85)/(tan(86.4)-tan(85))
x = 153.612786190499
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We'll use this approximate x value to find h
h = x*tan(86.4)
h = 153.612786190499*tan(86.4)
h = 2441.60531869599
h = 2441.61 km is how high the satellite is above the ground.
Return to triangle ACD. We'll use the cosine rule to determine the length of the hypotenuse AC
cos(angle) = adjacent/hypotenuse
cos(A) = AD/AC
cos(86.4) = x/AC
cos(86.4) = 153.612786190499/AC
AC*cos(86.4) = 153.612786190499
AC = 153.612786190499/cos(86.4)
AC = 2446.43279498247
AC = 2446.43 km is the distance from the satellite to station A.
Answer:
See explanation
Step-by-step explanation:
Plot the solution sets to both inequalities.
1. For the inequality First, plot the dotted line
(dotted because sign is without notion "or equal to"), then choose correct part by substitution coordinates of the origin.
so the origin does not belong to the needed part. Shade the part, which does not include origin.
2. For the inequality First, plot the dotted line
(dotted because sign is without notion "or equal to"), then choose correct part by substitution coordinates of the origin.
so the origin does not belong to the needed part. Shade the part, which does not include origin.
3. Find the common region of these two shaded parts - this is the solution to the system of two inequalities.
