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gizmo_the_mogwai [7]
2 years ago
12

A bicyclist is riding on a path modeled by the function f(x) = 0.03(10x − x2), where x and f(x) are measured in miles. Find the

rate of change of elevation at x = 1.
Mathematics
1 answer:
REY [17]2 years ago
3 0

Answer: 0.024\ \text{miles per sec}

Step-by-step explanation:

Given

Path is changing according to the function f(x)=0.03(10x-x^2)

Rate of change of the elevation is given by the derivative of the function

\Rightarrow f'(x)=0.03(10-2x)

At x=1\ f'(x) \ \text{is}

\Rightarrow f'(x=1)=0.03(10-2\times 1)\\\Rightarrow f'(x=1)=0.03(8)\\\Rightarrow f'(x=1)=0.24\ \text{miles per sec}

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Really need help with this pls help!!
worty [1.4K]

Let's carry this math sentence over to its natural, "shapey" element. We're going to look at each term not as an ordinary number, but as <em>the area of some shape</em>.

x² (read as "x <em>squared"</em>) can be seen as the area of a square with side lengths of x. 2x can similarly be seen as the area of a <em>rectangle </em>with a length of x and a width of 2. (Picture 1)

What's our question actually asking, though? Something about <em>perfect squares</em>. More specifically, we're looking for something to add on that'll <em>make this thing a perfect square</em>. We're trying to find a missing piece we can slot in to make a square, in other words. Problem is, our shapes don't look much like a square if we put them together right now. We need to do a little cutting and gluing first.

First, we're gonna cut the 2x rectangle lengthwise, getting two rectangles with an area of x, a length of 1, and a width of x. Next, we're going to attach them to the x² square, creating this shape that looks, strangely, like a square with a little bit missing from it (picture 2). What we're trying to do is <em>complete this square, </em>to find the area of that little missing chunk.

As it turns out, we have all the information we need for this. Notice that, using the lengths of the x rectangles, we can find that the square's dimensions are 1 x 1, which means that its area is 1 x 1  = 1.

If we tack this new area on to our original expression, we've "completed the square!" We now have a perfect square with side lengths of (x + 1) and an area of (x + 1)² (picture 3).

So, our final expression is x² + 2x + 1, and the missing constant - the area of the "missing square" we had to find to complete our larger one - is 1.

5 0
3 years ago
Read 2 more answers
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Dima020 [189]

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Step-by-step explanation:

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3 years ago
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Step-by-step explanation:

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6 0
3 years ago
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Step-by-step explanation:

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