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sasho [114]
3 years ago
12

24 ten thousands + 11 thousands on a chart

Mathematics
1 answer:
enot [183]3 years ago
8 0
0.0035 is the answer brainliest plz
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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}

So

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
In ΔEFG, e = 8.9 cm, f = 7.7 cm and g=2.2 cm. Find the measure of ∠F to the nearest degree.
Setler79 [48]

Answer:

51 degrees

Step-by-step explanation:

gave up on delta math

7 0
2 years ago
I need help please, I will give brainliest to the first person that answers. Also extra points.
Papessa [141]

Answer:

B)

a + c = 7

9a + 4c = $43

Step-by-step explanation:

There're 7 tickets which were bough in total. Two different types of tickets, one which represented children, the other for adults. The adult ticket is represented by <em>a </em>and is 9 dollars. The children's ticket is represented by <em>c </em>and is 4 dollars.

<em>Have a nice April Fool's XD.</em>

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2 years ago
Find the value of y.<br> m&lt;1 = 3y + 6
Rufina [12.5K]

Step-by-step explanation:

m > 1 = 3y  + 6\\  \frac{m >  -1 - 6}{3}  =  \frac{3y}{3}  \\ y =  \frac{m >  - 5}{3}

7 0
2 years ago
3(5+3)^2 +14<br><br><br> help me pls i cannot deal w my parents again
Scilla [17]

Answer:

206

Step-by-step explanation:

I put it in a calculator

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3 years ago
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