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andre [41]
3 years ago
14

Find the magnitude of v. v = -3i+ 40 + 7k v =

Mathematics
1 answer:
kherson [118]3 years ago
5 0

Answer:

The magnitude of the given vector is 40.72 units.

Step-by-step explanation:

The given vector is v=-3\widehat{i}+40\widehat{j}+7\widehat{k}

We know that for any vector 'r' \overrightarrow{r}=x\widehat{i}+y\widehat{j}+z\widehat{k} the magnitude is given by

|r|=\sqrt{x^{2}+y^{2}+z^{2}}

Comparing with the given vector we have

x = -3

y = 40

z = 7

Thus the magnitude equals  

|v|=\sqrt{(-3)^{2}+40^{2}+7^{2}}

|v|=40.72

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Answer:

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Step-by-step explanation:

Since we know we only have 640 feet of fence available, we know that L + W + L = 640, \implies 2L + W = 640. This allows us to represent the width, W, in terms of L: W = 640 – 2L

Remember, the area of a rectangle is equal to the product of its width and length, therefore,

A_{\rm pigpen}=L(640-2L)\implies 640L-2L^2

Notice that, quadratic has been vertically reflected, since the coefficient on the squared term is negative, so the graph will open downwards, and the vertex will be a maximum value for the area.

recall,

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plug in the value of a and b into the first formula:

L_{max}=-(640)/2(-2)\implies 160

A(L)_{max}=640(160)-2(160)^2\implies 76800

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and we're done!

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