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3 years ago

Writing and evaluating & uncuon that moet dreamworlu Situ.

Mathematics

1 answer:

iren [92.7K]3 years ago

6 0

Answer:

$4460

Step-by-step explanation:

P=2500+70N

P=2500+70(28)

P=4460

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An expression is shown below.<br> (x4/3)(x2/3)<br> What is the product of the two factors?

weeeeeb [17]

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3 years ago

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Find the surface area of each shipping package. Which package has the greater surface area? Does the same package have a greater

Kryger [21]

Answer:

greater area: A
no, B has the greater volume

Step-by-step explanation:

The relevant area and volume formulas are ...

A = 2(LW +H(L +W))

V = LWH

When there are multiple instances of the calculations to be done, it is convenient to let a spreadsheet do them. The results are attached.

Figure A has the larger area.

Figure B has the larger volume.

<em>Additional comment</em>

The more "cube-like" the prism is, the less area it will have for the same volume. Here, package B is more "cube-like" than package A. (The ratio of largest-to-smallest dimensions is smaller for package B.)

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1 year ago

Marine biologists have determined that when a shark detectsthe presence of blood in the water, it will swim in the directionin w

siniylev [52]

Solution :

a). The level curves of the function :

$C(x,y) = e^{-(x^2+2y^2)/10^4}$

are actually the curves

$e^{-(x^2+2y^2)/10^4}=k$

where k is a positive constant.

The equation is equivalent to

$x^2+2y^2=K$

$\Rightarrow \frac{x^2}{(\sqrt K)^2}+\frac{y^2}{(\sqrt {K/2})^2}=1, \text{ where}\ K = -10^4 \ln k$

which is a family of ellipses.

We sketch the level curves for K =1,2,3 and 4.

If the shark always swim in the direction of maximum increase of blood concentration, its direction at any point would coincide with the gradient vector.

Then we know the shark's path is perpendicular to the level curves it intersects.

b). We have :

$\triangledown C= \frac{\partial C}{\partial x}i+\frac{\partial C}{\partial y}j$

$\Rightarrow \triangledown C =-\frac{2}{10^4}e^{-(x^2+2y^2)/10^4}(xi+2yj),$ and

$\triangledown C$ points in the direction of most rapid increase in concentration, which means $\triangledown C$ is tangent to the most rapid increase curve.