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2 years ago

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:

Point 2 3/4:

Point 3:

Point 3 1/2:

Point 3 3/4:

Point 4:

Point 4 1/4:

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

b) $Du_{f}(2,4,0) = -\frac{8}{\sqrt{11}}$

Step-by-step explanation:

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

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

(a) find the gradient of f

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

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

$f_{y}(x,y,z) = xz\cos{yz}$

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

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

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

(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 $v = i + 3j - k = (1,3,-1)$

To use v as an unitary vector, we divide each component of v by the norm of v.

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

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

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

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

6 0

3 years ago

PLEASE HELP! GIVING BRAINLIEST! DUE SOON PLEASE HELP!

Mrrafil [7]

Answer:

4-9 = 4+(-9)

-6-7 = -6+(-7)

-4-(-9) = -4 + 9

6-(-7) = 6+7

Step-by-step explanation:

Double negatives means a positive and one positive and one negative is a negative.

Please give brainliest. I am working hard to get it.

7 0

2 years ago

Read 2 more answers

Find the length of segment AB.

12345 [234]

The answer is D.
explain:
A^2 + b^2 = c^2

8 0

3 years ago

Read 2 more answers

Answer to this question please?

egoroff_w [7]

7 mphs faster...............

7 0

3 years ago

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

LenKa [72]

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

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

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

TOTAL NUMBER OF ARTICLE= 7

ARTICLES FOR 30K = 3

ARTICLES FOR 12.5K = 7-3= 4

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

Average cost of 7 articles

$\bold{ \green{ \star{ \orange{FORMULA \: USED}}}}$

$\red{AVERAGE = \frac{TOTAL \: COST}{ NUMBER \: OF\: ARTICLES }}$

$\huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}$

$Average \: cost \: of \: 7 \: articles - > \\ \frac{(3 \times 30k) + (12 .5k \times 4)}{7} \\ \frac{90k + 50k}{7} \\ \frac{140k}{7} \\ \blue {Average \: cost \: of \: 7 \: articles - >} \\ 20k$

5 0

2 years ago