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Mariana [72]
3 years ago
7

Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the vec

tor space axioms that fails.
(a) The set of all quadratic functions whose graphs pass through the point (0, 5) with the standard operations.
Mathematics
1 answer:
Scrat [10]3 years ago
6 0

Answer:

It isn't a vector space

Step-by-step explanation:

If f and g were elements of the set, then the sum f+g should be an element of the set. However the sum of quadratic funcitons may not neccesarily be a quadratic function. Lets look at

f(x) = x²+ x + 5

g(x) = -x²+5

Both f and g are quadratic functions and the graphs of both functions contain the point (0,5), because f(0) = g(0) = 5. However f(x) + g(x) = (x²+x+5)+(-x²+5) = x+10, which is not a quadratic funciton. Furthermore, f+g(0) = 10, so its graph doesnt contain the point (0,5). This shows that f+g is not in the set, therefore, the set cant be a vector space.

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The distance that Scott walks is a function of the time he spends walking. Scott can walk 1 half
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Step-by-step explanation:

It is given that,

The distance that Scott walks is a function of the time he spends walking. Scott can walk 1 half  mile every 8 minutes.

Let y is the distance (in miles) and x is time (in minutes).

\dfrac{0.5}{8}=\dfrac{y}{x}\\\\\dfrac{x}{y}=16\\\\y=\dfrac{x}{16}

The attached graph predicts the shape of the function. Hence, this is the required solution.

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Answer:

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3 years ago
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adell [148]
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6 0
3 years ago
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Find the value of y please!
Tems11 [23]

Answer:

Y=4

Step-by-step explanation:

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Murljashka [212]
<h2>Explanation:</h2><h2></h2>

Hello! Remember you have to write clear questions in order to get good and exact answers. Here I'll assume the data given in a comment above. So:

H:height \\ \\ W:Width \\ \\ \\ H=7 \\ \\ W= 2x^2-32x+2

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