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Scrat [10]
3 years ago
14

How do you do this question?

Mathematics
1 answer:
ankoles [38]3 years ago
3 0

Step-by-step explanation:

S = ∫ 2π y ds

ds = √(1 + (dx/dy)²) dy

ds = √(1 + (8y)²) dy

ds = √(1 + 64y²) dy

S = ∫₁² 2π y √(1 + 64y²) dy

S = π/64 ∫₁² 128y √(1 + 64y²) dy

S = π/64 [⅔ (1 + 64y²)^(³/₂)] |₁²

S = π/96 (1 + 64y²)^(³/₂) |₁²

S = π/96 (1 + 256)^(³/₂) − π/96 (1 + 64)^(³/₂)

S = π/96 (257√257) − π/96 (65√65)

S = π/96 (257√257 − 65√65)

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To write an equation for this line, you first need to understand how to derive it.

Let's utilize slope-intercept form, as it's the easiest to understand compared to any other form for line functions:

y = mx + b

m: The slope of the line

b: The y-intercept (The point where the line is at the y-axis)

Now that we've defined our variables, how do we go about making the actual equation? Let's start off with the slope, m.

The slope is a measure of how high or low the line is. The number is a ratio between the rise and run of a slope. In other words, it is essentially \frac{rise}{run}

Let's look back at the graph. In the time interval from 1 to 2 seconds, we see that the line rises by 22 feet. Because the time interval is only 1 second, the run is 1 second.

Therefore:

m = \frac{rise}{run}

m = \frac{22}{1}

m = 22

We now have the first variable of the equation.

y = 22x + b

What about b? As we established earlier, b is the value of coordinate y at the y-intercept. Essentially, to find b we need to know what the value of y is when the coordinate x is 0.

As you can see from the graph you made, the value of y when x is 0 is also 0. This makes sense, too. How can the cheetah travel distance at 0 seconds when it obviously hasn't started moving? We now know b = 0. Now, we have gotten all of the variables we need to make a full equation:

y = 22x + 0

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