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3 years ago

Just part a I’ve done b. Photo provided.

Mathematics

1 answer:

Rasek [7]3 years ago

6 0

Answer:

Step-by-step explanation:

${2}^{x} = \frac{1}{32}$

${2}^{x} = \frac{1}{ {2}^{5} }$

${2}^{x} = {2}^{ - 5}$

$x = - 5$

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Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of

Law Incorporation [45]

Answer:

Step-by-step explanation:

To solve this problem, we will use the following two theorems/definitions:

- Given a vector field F of the form (P(x,y,z),Q(x,y,z),W(x,y,z)) then the divergence of F denoted by $\nabla \cdot F = \frac{\partial P}{\partial x}+\frac{\partial Q}{\partial y}}+\frac{\partial W}{\partial z}$

- (Gauss' theorem)Given a closed surface S, the following applies

$\int_{S} F\cdot \vec{n} dS = \int_{V} \nabla \cdot F dV$

where n is the normal vector pointing outward of the surface and V is the volume bounded by the surface S.

Let us, in our case, calculate the divergence of the given field. We have that

$\nabla \cdot F = \frac{\partial}{\partial x}(x)+\frac{\partial}{\partial y}(2y)+ \frac{\partial}{\partial z}(5z) = 1+2+5 = 8$

Hence, by the Gauss theorem we have that

$\int_{S} F\cdot \vec{n} dS = \int_{V} 8 dV = 8\cdot\text{Volume of V}$

So, we must calculate the volume V bounded by the cube S.

We know that the vertices are located on the given points. We must determine the lenght of the side of the cube. To do so, we will take two vertices that are on the some side and whose coordinates differ in only one coordinate. Then, we will calculate the distance between the vertices and that is the lenght of the side.

Take the vertices (1,1,1) and (1,1-1). The distance between them is given by

$\sqrt[]{(1-1)^2+(1-1)^2+(1-(-1)^2} = \sqrt[]{4} = 2$ .

Hence, the volume of V is $2\cdot 2 \cdot 2 = 8$ . Then, the final answer is

$\int_{S} F\cdot \vec{n} dS =8\cdot 8 = 64$

5 0

3 years ago

Help plz giving out brianlest

svet-max [94.6K]

I don’t think it is a function because you can’t have two 0’s on the Y axis it doesn’t work

4 0

3 years ago

Help me i hate word problems

VMariaS [17]

Is that all? My Algebra is freackin hard compared to this. Anyways, The way I understand this, is that we will have 3 (liters of water) +0.5 (half a liter of lemonade) =3.5 liters of liquid

so the question would be: how many times does fit into 3.5?

if you want to divide by a fraction, you need to multiply by the reverse of it.

so the answer is: 10 servings of lemonade ( and a little bit will be left over for half a serving).
Hope this helps!

4 0

3 years ago

The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of

kondaur [170]

Ouch, kinda crippled w/o answer choices.

But with my calculating, i've made it out to be <span>92.07 %

Please do respond & rate based on my accuracy.
-Feeling confident-
</span>

7 0

3 years ago

Im in no rush just need help

Romashka [77]

Answer:

1. Right: pointing downwards

Left: pointing upwards

2. Right: pointing upwards

Left: pointing upwards

3. Right: pointing downwards

Left: pointing upwards

4a. True

4b. True

Step-by-step explanation:

When the leading coefficient is negative the equation will either open downwards or the y-values will decrease as the x-values increase. The opposite is true for when the leading coefficient is positive. When the degree is odd one end will point downwards while the other points upwards. When the degree is even, both ends point in the same direction.

I hope this helps :)

5 0

2 years ago