A manatee swimming 3 feet below the water surface, ascends 2 feet, descends another 5 feet then ascends another 2 feet. Write an expression to find his position relative to the water surface. Then find His position
please help me with this
-3 + 2 - 5 + 2 = ?
The expression is a step function, which has discontinuities between ascents and descents.
Let the number of movements (ascents or descents) be i, and
h(i) = position relative to the surface after the ith movement.
h(0)=-3 (3 feet below surface)
h(1)=-1 (=-3+2)
h(2)=-6 (=-1-5)
h(3)=-4
h(4)=-9
h(5)=-7
...
So
h(i) = -(i/2)*3 -3 for 2|i (i divisible by 2), and
h(i) = -(i+1)/2*3 +2
= -(3i-1)/2 for 2|(i+1) (i not divisible by 2)
Ms Sue, you're right. An expression can be all numeric!
To find the manatee's position relative to the water surface, we start with the initial position of being 3 feet below the water surface and then consider the subsequent changes. Let's break down the changes step by step:
1. Ascends 2 feet: This means the manatee moves upward by 2 feet, which brings it 2 feet closer to the water surface.
2. Descends another 5 feet: This means the manatee moves downward by 5 feet, increasing its distance from the water surface by 5 feet.
3. Ascends another 2 feet: Finally, the manatee moves upward by 2 feet, which decreases its distance from the water surface by 2 feet.
Now let's express this in an equation to find the manatee's position relative to the water surface:
Position = Initial position + (Upward movement - Downward movement)
Using the information given:
Position = -3 + (2 - 5 + 2)
Simplifying the equation:
Position = -3 + (-1)
Position = -4 feet
So, the manatee's position relative to the water surface is 4 feet below the surface.