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3 years ago

10

Jasmine uses 1.41 pounds of almonds and 3.27 pounds of raisins to make a trail mix. Then she divides the trail mix equally into

6 bags. How much trail mix is in each bag

2 answers:

Otrada [13]3 years ago

8 0

If I did my math correctly, it should be .78 pounds

jekas [21]3 years ago

7 0

Answer:

I think that he answer should be .78 pounds

Step-by-step explanation:

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Given 3 + 7 + 11 + 15 + ... find S20

nasty-shy [4]

=4n - 1
Since the sequence is add 4 and 3-4 = -1

20 x 4n = 80-1 = 79

6 0

2 years ago

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 a survey of more than 6000 people are 95% of the respondents claimed to prefer Penelope‘s puffy popcorn over any other brand

raketka [301]

Answer:

B. People who were promised free samples of Penelope‘s puffy popcorn for completing the survey

Step-by-step explanation:

This would show likely bias in the result of the survey

5 0

1 year ago

X÷0.4=2 1/9 ÷3 1/6? What does x equal? Explain your answer thoroughly.

Ainat [17]

I would recommend calculatorsoup.com for the fractions part.

3 0

2 years ago

Please help thanks :)

noname [10]

Answer:

The first choice, students tend to have less siblings than teachers

Step-by-step explanation:

If you look at the dot plots you notice that the teachers have more numbers than the students do and that the students have less sibling. It is not answer 2 because the students have less sibling, it is not answer 3 b/c they do not have the same range, and it is not number 4 because they do not look the same or have the same shape.

3 0

2 years ago