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3 years ago

PLEASE HELP ASAP ILL GIVE U BRAINLIEST (NO LINKS OR ILL REPORT)

Mathematics

2 answers:

saul85 [17]3 years ago

6 0

Answer:

this answer was (b) ok alright

HACTEHA [7]3 years ago

6 0

The answer is b ur welcome

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Fernando bought 11.2 pounds of potatoes.

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What grade average is 79.2 out of 120

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Step-by-step explanation:

Divide 79.2 by 120 and multiply by 100

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Using the chart "Amount of $1 at Compound Interest" from previous reading section "More Compound Interest", find the total amoun

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Step-by-step explanation:

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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.