Can you help me worth 16 points if your help me all the way

Solution :

a). The level curves of the function :

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

are actually the curves

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

where k is a positive constant.

The equation is equivalent to

[tex]$x^2+2y^2=K$[/tex]

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

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 :

[tex]$\triangledown C= \frac{\partial C}{\partial x}i+\frac{\partial C}{\partial y}j$[/tex]

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

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

[tex]$r(t)=x(t)i+y(t)j$[/tex]  is a parametrization of the most [tex]$\text{rapid increase curve}$[/tex] , then

[tex]$\frac{dx}{dt}=\frac{dx}{dt}i+\frac{dy}{dt}j$[/tex] is a tangent to the curve.

So then we have that [tex]$\frac{dr}{dt}=\lambda \triangledown C$[/tex]

[tex]$\Rightarrow \frac{dx}{dt}=-\frac{2\lambda x}{10^4}e^{-(x^2+2y^2)/10^4}, \frac{dy}{dt}=-\frac{4\lambda y}{10^4}e^{-(x^2+2y^2)/10^4} $[/tex]

∴ [tex]$\frac{dy}{dx}=\frac{dy/dt}{dx/dt}=\frac{2y}{x}$[/tex]

Using separation of variables,

[tex]$\frac{dy}{y}=2\frac{dx}{x}$[/tex]

[tex]$\int\frac{dy}{y}=2\int \frac{dx}{x}$[/tex]

[tex]$\ln y=2 \ln x$[/tex]

⇒ y = kx^2 for some constant k

but we know that [tex]$y(x_0)=y_0$[/tex]

[tex]$\Rightarrow kx_0^2=y_0$[/tex]

[tex]$\Rightarrow k =\frac{y_0}{x_0^2}$[/tex]

∴ The path of the shark will follow is along the parabola

[tex]$y=\frac{y_0}{x_0^2}x^2$[/tex]

[tex]$y=y_0\left(\frac{x}{x_0}\right)^2$[/tex]

Answer:

A- using prior knowledge

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

it's b if I am wrong I am sorry

Answer:

The answer is "[tex]0.02235 \ and \ 0.02501[/tex]".

Step-by-step explanation:

Given:

[tex]x= 1184\\\\n = 50000\\\\c = 95\% = 0.95[/tex]

The sample proportion is computed by subtracting that sample size by both the successes:

[tex]\hat{p}=\frac{x}{n} =\frac{1184}{50000}= 0.02368[/tex]

Determine [tex]z_{\frac{\alpha}{2}} = Z_{0.025}[/tex] using table Z in Table Z for trust level [tex]1 -\alpha = 0.95[/tex]

add using appendix F ((0.025) inside the table, therefore the z-score is the found z-score with negative sign):

So, the boundaries of the confidence interval:

[tex]\to \hat{p}-z_{\frac{\alpha}{2}} \cdot \sqrt{\frac{\hat{p} (1-\hat{p})}{n}} = 0.02368 - 1.96 \cdot \sqrt{\frac{0.02368(1-0.02368)}{50000}}\approx 0.02235 \\\\\to \hat{p}-z_{\frac{\alpha}{2}} \cdot \sqrt{\frac{\hat{p} (1-\hat{p})}{n}} = 0.02368 + 1.96 \cdot \sqrt{\frac{0.02368(1-0.02368)}{50000}}\approx 0.02501\\\\[/tex]

Answer:

163.5 cubes

Step-by-step explanation:

Answer:

A gift box has dimensions of: 8 12 inches, 5 12 inches, and 2 12 inches, respectively. How many cubes with side lengths of 12 inches would be needed to fill the gift box?

116.875 cubes

163.5 cubes

935 cubes

1870 cubes

163.5 cubes

Step-by-step explanation:

A gift box has dimensions of: 8 12 inches, 5 12 inches, and 2 12 inches, respectively. How many cubes with side lengths of 12 inches would be needed to fill the gift box?

116.875 cubes

163.5 cubes

935 cubes

1870 cubes

163.5 cubes

Answer:

x = 3, 8

Step-by-step explanation:

[tex]x^{2} +11x +24\\(x + 8)(x + 3)[/tex]

Answer:

x= -8, -3

Step-by-step explanation:

(x+8)(x+3)

x= -8, -3

Answer: 8/52

Step-by-step explanation:

In a deck of cards, we have a total number of 52 cards. Out of the 52 cards, there are 4 aces and also 4 queens.

Therefore, the probability of picking a queen or an ace will be:

= P(queen) + P(ace)

= 4/52 + 4/52

= 8/52

Answer: Fish tank = 9 other fishtank= 9,000 Jewlery box=9 other jewelry box=320

CANT SEE OTHER SORRY

Step-by-step explanation: Ok first IK UR NOT IN COLLEGE second dont

cheat imma give ya answer to be noice

Answer: $60

Step-by-step explanation:

Here is why:

For 20 -word ad it will be $20 because of twice the amount of the 10 word amount. and another $40 for the photo!

And you get $60!

Any Questions

It will cost $54 for an 20 word ad and a photo.

We have Antique Auto News agency which charges $10 for a 10-word classified ad. Each additional word costs $0.40 and for an extra $40, a seller can include a photo in the ad.

We have to determine much would it cost for a 20-word ad with a photo.

Initial count = x

Count increasing per second = 5

Assume that the bacteria count after t seconds is y. Then -

y = x + 5t

for t = 30 ↔ y = 150 + x

According to the question, we have -

Cost of 10-word classified ad → $10

Additional word cost → $0.40

Additional Photo cost → $40

Therefore -

Assume that for a 20-word ad with a photo costs $x.

Therefore -

x = 10 + 0.40 x 10 + 40

x = 10 + 4 + 40

x = 54

Hence, it will cost $54 for an 20 word ad and a photo.

To solve more questions on Amount estimation , visit the link below-

https://brainly.com/question/8158280

#SPJ2

Hello and good day.

For this question you will use multiplication.

We know that the first same is 2 inches long and the second sample is 14 times long as the first sample.

When some thing says times, it uses multiplication, especially when mentioned in word problems.

So 14 times 2 = 28.

The answer is: The second sample is 28 inches.

28

14x2=28 bro get this right >:P

Answer:

C

Step-by-step explanation:

30 x 60 x 70 = 126,000

90 x 60 x 30 = 288,000

288,000 + 126,000 = 288,000cm^3

Answer: 288,000 [tex]cm^{3}[/tex]

Step-by-step explanation:

first, break down the shape thingy into two different shapes. there's more than one way to do it, but i'll be cutting the shape horizontally at the corner of the L shape (where the 40 cm and 90 cm lines connect)

small prism dimensions: 60 x 30 x 40 = 72,000

large prism dimensions: (30+90) x (70-40) x 60 / 120 x 30 x 60 = 216,000

add them to get 288,000 [tex]cm^{3}[/tex]

Answer:

B. WATER CAN DISSOLVE SO MANY SUBSTANCES

Step-by-step explanation:

Answer:

Hey!!

Step-by-step explanation:

h = d − 5 /10 + x

Hope this helps!

Have a nice day<3

Answer:

Step-by-step explanation:

i) (64+39+18)/(175)=0.691

ii) 64/(64+17)=0.79

iii) 18/(18+15)=0.55

(1) The proportion of branches that are profitable 121/175.

2) Proportion of branches from an urban location that is profitable 64/175.

3) The proportion of branches from a rural location is profitable 33/175.

It is given that:

From the sample of 175 branches,

                Profitable Not Profitable

Urban                64                17

Suburban          39               22

Rural                  18                15

Total number of samples = 175

Proportion is a part, share, or number considered in comparative relation to a whole.

(1) The proportion of branches that are profitable:

= (64+39+18)/175

=121/175

2) Proportion of branches from an urban location that is profitable:

=64/175

3) The proportion of branches from a rural location is profitable:

=(18+15)/175 = 33/175

Therefore, (1) The proportion of branches that are profitable 121/175.

2) Proportion of branches from an urban location that is profitable 64/175.

3) The proportion of branches from a rural location is profitable 33/175.

To get more about proportions visit:

https://brainly.com/question/18437927

Answer: 1/8

Step-by-step explanation:

Concept

Reciprocal is any number that is reverse to the given value. This means the original number times the reciprocal will equal 1. For a more graphical explanation, please refer to the attachment below.

Solve

8×(x)=1

x=1/8

Hope this helps!! :)

Please let me know if you have any questions

Answer:

solve for

x

. To find the y-intercept, substitute in

0

for

x

and solve for

y

.

x-intercept(s):

(

0

,

0

)

,

(

−

3

,

0

)

y-intercept(s):

(

0

,

0

)

Step-by-step explanation:

hope it helps make brainlliest ty the

Answer:

3 x 2 − 2 x -5

Step-by-step explanation:

Answer:

Here are some correct options:

225,891

234,567

232,987

Step-by-step explanation:

Answer:

The equation is 56x - 13 = x - 6

Step-by-step explanation:

Let's say our 'number' is x. If it says it's 56 times our number, it's 56x. Minus 13, which is 56x - 13. If it is equal than 6 less than the number, then it is x - 6.

So the equation is 56x - 13 = x - 6

Answer:

8192

Step-by-step explanation:

The answer is 8192 but in your multiple-choice problem it's [tex]2^{13}[/tex]

Answer: Length: 14; Width: 4

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

The distance between each dot is 25%

From 68 to 70 is 25% and 70 to 74is 25%

Above 68 is 25+25 or 50 %

Answer:

[tex](2 {x}^{3} - 5 {x}^{2} + 8)(x + 3) \\ = (2 {x}^{4} - 5 {x}^{3} + 8x + 6 {x}^{3} - 15 {x}^{2} + 24) \\ = 2 {x}^{4} + {x}^{3} - 15 {x}^{2} + 8x + 24[/tex]

Answer:

[tex]2x^{4} + x^{3} - 15x^{2} + 8x + 24[/tex]

Step-by-step explanation:

Mark as Brainllest

Answer:

Its the third answer choice

Step-by-step explanation:

Hope this helped!!!

Answer: The answer for the second one is solid figure

Step-by-step explanation: In geometry, three-dimensional shapes are solid figures.

Answer:

280.56 in

Step-by-step explanation:

A square has 4 sides

67/4  = 16.75

All 4 sides are 16.75

Now, area of a square

16.75 x 16.75 = 280.5625

Round to Hundreths, 280.56.

280.6

i took the test................................

Answer:

2acd^3b^-1

Step-by-step explanation:

About the domain, I don't understand that but i tried to help you.

9514 1404 393

Answer:

  a≠0 and b≠0 and c≠0 and d≠0

Step-by-step explanation:

No denominator is allowed to be zero. 'c' and 'd' are in the denominator of the numerator and denominator terms. 'a' and 'b' are in the numerator of the denominator term, so will make that term zero if they are zero. In short, none of a, b, c, or d may be zero.

__

The fact that the expression simplifies to ...

  2acd^3/b

does not mean that the only restriction is b≠0.