Calculate the area of the following image:
​

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 %

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:

The magnitude of the complex number is 26.

Step-by-step explanation:

Magnitude of a complex number:

The magnitude of a complex number in the format of a + bi is:

[tex]\sqrt{a^2 + b^2}[/tex]

What is the magnitude of -10 + 24i?

a = -10, b = 24. So

[tex]\sqrt{(-10)^2 +(24)^2} = \sqrt{100+576} = \sqrt{676} = 26[/tex]

The magnitude of the complex number is 26.

Answer:

Hey!!

Step-by-step explanation:

h = d − 5 /10 + x

Hope this helps!

Have a nice day<3

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:

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: The answer for the second one is solid figure

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

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:

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

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:

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:

744 miles

Step-by-step explanation:

each hour is 31 miles

the drive is 24 hours

31*24=744

Answer:

744 miles

Step-by-step explanation:

Answer:

8192

Step-by-step explanation:

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

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:

A- using prior knowledge

Step-by-step explanation:

Answer:

Here are some correct options:

225,891

234,567

232,987

Step-by-step explanation:

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:

B. WATER CAN DISSOLVE SO MANY SUBSTANCES

Step-by-step explanation:

Answer:

20 schools is your answer

Have a good day

Answer:

20 is ur answer!

Step-by-step explanation:

I took the test and got it right, also credit goes to the other guy! Have a good day/night! <3

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:

3 x 2 − 2 x -5

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

it's b if I am wrong I am sorry

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

Answer:

y = -7/3 or -2.333

Step-by-step explanation:

3(y+2 / 5) = -1/5 ------- First you need to do what is outside of the paranthesis which is 3, so divide both sides by 3.

(y + 2 / 5) = -1/15 ------- Next, you multiply both sides by 5 given the denominator is 5 on the left side.

y + 2 = -1/3 -------- Now you just subtract 2 from both sides.

y = - 7 /3 ---------- Answer

Answer:

-1

Step-by-step explanation:

Assuming problem is: x->2 (x^3 -3x^2 +3)

Since the expression is continuous at x=2,

then the limit can be found just by evaluating the expression at x=2.

2^3-3(2)^2+3

8-3(4)+3

8-12+3

-4+3

-1

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.