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mr_godi [17]
2 years ago
9

Help SOS Stevie needed twine for the gifts she was wrapping for a family party.

Mathematics
1 answer:
lutik1710 [3]2 years ago
8 0

Answer:

Your answer would be:

57.75 or 57 3/4

(I will show how many of each length of twine that is on the graph)

Point 2 1/4:

2

Point 2 3/4:

4

Point 3:

1

Point 3 1/2:

2

Point 3 3/4:

3

Point 4:

1

Point 4 1/4:

4

We can show how much length in total Stevie used with the following equation:

(2 1/4 x 2) + (2 3/4 x 4) + ( 3 x 1 ) + ( 3 1/2 x 2 ) + (3 3/4 x 3 ) + (4 x 1 ) + (4 1/4 x 4)

Each smaller equation in paraphrases shows how much of each length of twine at each point with x's on the number line. Altogether it would equal 57.75 or 57 3/4.

Step-by-step explanation:

Have a great rest of your day

#TheWizzer

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If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional derivative of f at (2, 4, 0) in the direction
valentina_108 [34]

Answer:

a) \nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}.

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Step-by-step explanation:

Given a function f(x,y,z), this function has the following gradient:

\nabla f(x,y,z) = f_{x}(x,y,z)\mathbf{i} + f_{y}(x,y,z)\mathbf{j} + f_{z}(x,y,z)\mathbf{k}.

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We have that f(x,y,z) = x\sin{yz}. So

f_{x}(x,y,z) = \sin{yz}

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f_{z}(x,y,z) = xy \cos{yz}.

\nabla f(x,y,z) = f_{x}(x,y,z)\mathbf{i} + f_{y}(x,y,z)\mathbf{j} + f_{z}(x,y,z)\mathbf{k}.

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(b) find the directional derivative of f at (2, 4, 0) in the direction of v = i + 3j − k.

The directional derivate is the scalar product between the gradient at (2,4,0) and the unit vector of v.

We have that:

\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}

\nabla f(2,4,0) = \sin{0}\mathbf{i} + 0\cos{0}\mathbf{j} + 8 \cos{0}\mathbf{k}.

\nabla f(2,4,0) = 0i+0j+8k=(0,0,8)

The vector is v = i + 3j - k = (1,3,-1)

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|v| = \sqrt{1^{2} + 3^{2} + (-1)^{2}} = \sqrt{11}

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v_{u} = (\frac{1}{\sqrt{11}}, \frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}})

Now, we can calculate the scalar product that is the directional derivative.

Du_{f}(2,4,0) = (0,0,8).(\frac{1}{\sqrt{11}}, \frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}}) = -\frac{8}{\sqrt{11}}

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{\bold{\red{\huge{\mathbb{QUESTION}}}}}

what is the average cost of 7 articles if 3 of them cost 30k each and the rest cost 12.5k each

\bold{ \red{\star{\blue{GIVEN }}}}

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\bold{\blue{\star{\red{TO \:  \: FIND}}}}

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