9514 1404 393
Answer:
t ∈ {19, 85, 109, 175, 199}
or
t ∈ {40, 64, 130, 154, 220}
Step-by-step explanation:
A graphing calculator relieves the tedium of solving for t. The attachments show the times the satellite is 4000 miles from the equator. Since y may be either north or south, the satellite may be 4000 north of the equator for y = 4000 or for y = -4000.
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If y is miles <em>north</em> of the equator, then ...
4000 = 6000cos(z) . . . . . where z=(π/45)(t-7)
z = arccos(4000/6000) ≈ 0.84107 radians
There is another solution at 2π -0.84107 radians, about 5.44212 radians
The corresponding time values are ...
t = 7 +(45/π)(z) ≈ 19.047 and 84.953 . . . . minutes
The period of the function is 90 minutes, the times will be the above times and at 90-minute intervals after each.
The satellite is 4000 miles north of the equator at ...
t ≈ 19, 85, 109, 175, 199 . . . minutes after launch
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The solution is similar if y represents miles <em>south</em> of the equator. Then we have ...
-4000 = 6000cos(z)
z = arccos(-4000/6000) ≈ 2.30052 radians (and 3.98266 radians)
The corresponding time values are ...
t = 7 +(45/π)(z) ≈ 39.952 and 64.047 . . . . minutes
Again, considering the period, the satellite is 4000 miles north of the equator at ...
t ≈ 40, 64, 130, 154, 220 . . . minutes after launch
_____
<em>Additional comment</em>
We might usually think of y as being positive in the northerly direction. However, in this age of political correctness and bias sensitivity, we have to consider that "y is north or south" means exactly that. So, we have also shown the solutions when y is positive south of the equator.
Usually, we prefer that the variables are defined unambiguously.
Answer:
The value of SecФ is .
Step-by-step explanation:
Given as for trigonometric function :
tan²Ф =
Or, tanФ =
∵ tanФ =
So, =
So, Hypotenuse² = perpendicular² + base²
or, Hypotenuse² = ( )² + (
)²
Or, Hypotenuse² = 3 + 8 = 11
Or, Hypotenuse = ( )
Now SecФ =
or, SecФ = =
<u>Second Method</u>
Sec²Ф - tan²Ф = 1
Or, Sec²Ф = 1 + tan²Ф
or, Sec²Ф = 1 +
Or, Sec²Ф =
Or, SecФ =
Hence The value of SecФ is . Answer
(a) Linear Equation:
(b) x-intercept : (10,0)
(c) y-intercept : (0,200)
(d) Domain : {0,1,2,3,4,5,6,7,8,9,10}
Range : {0,1,2,...,200}
Step-by-step explanation:
Step 1: As we can see in graph, money in Carla is decreasing in multiples of 20 can be referred as 20x.
Every week $20 is getting deducted from the total amount of $200.
Step 2: (a) So we can quote it in equation as,
where x represents number of weeks
Step 3: (b) x-intercept is where value of y becomes 0.
So, referring graph we can determine x intercept as x = 10. Point (10,0). which also means no money left in account.
Step 4: (c) y-intercept is where value of x becomes 0.
So, referring graph we can determine y intercept as y = 200. Point (0,200). which is starting value of money in account.
Step 5: (d) Domain : {0,1,2,3,4,5,6,7,8,9,10}
Range : {0,1,2,...,200}
