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3 years ago

3. Which of the following has a value of 13? (5.02.2)

Mathematics

1 answer:

algol [13]3 years ago

4 0

C - Parenthesis first (3-1)=2, then distribute the 4. 4x2=8, next add 5, 8+5=13.

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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.

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

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

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

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

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

Using separation of variables,

$\frac{dy}{y}=2\frac{dx}{x}$

$\int\frac{dy}{y}=2\int \frac{dx}{x}$

$\ln y=2 \ln x$

⇒ y = kx^2 for some constant k

but we know that $y(x_0)=y_0$

$\Rightarrow kx_0^2=y_0$

$\Rightarrow k =\frac{y_0}{x_0^2}$

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

$y=\frac{y_0}{x_0^2}x^2$

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

7 0

3 years ago

If f(x) = 6x - 4, what is f(x) when x = 8?

NNADVOKAT [17]

The answer is 44

To find this answer, we replace x with 8 and use PEMDAS (order of operations) to simplify

f(x) = 6*x - 4
f(8) = 6*8 - 4
f(8) = 48 - 4
f(8) = 44

4 0

4 years ago

Read 2 more answers

A bakery sold 246 vanilla cupcakes in a day, which was 82% of the total number of cupcakes sold that day. How many total cupcake

IRINA_888 [86]

The total number of cupcakes were 300.

5 0

3 years ago

mckenna had $32 when she got to the carnival . after riding 6 rides , she had $20 left . write an eqaution and solve to find the

Aneli [31]

Answer:

$2 per ride

Step-by-step explanation:

$32-$20=$12

McKenna rode 6 rides so $12 divided by 6 rides is $2 for every ride

8 0

3 years ago

An urn contains 5 red, 6 blue, and 8 green balls. If a set of 3 balls is randomly selected, what is the probability that each of

monitta

Answer:

As a fraction, the answer is exactly 86/969

In decimal form, the answer is approximately 0.08875

=====================================================

Work Shown:

The assumption is that no replacements are made for each selection.

5 red, 6 blue, 8 green

5+6+8 = 19 total

A = P(3 red) = (5/19)*(4/18)*(3/17) = 10/969

B = P(3 blue) = (6/19)*(5/18)*(4/17) = 20/969

C = P(3 green) = (8/19)*(7/18)*(6/17) = 56/969

D = P(3 all same color)

D = A+B+C

D = 10/969 + 20/969 + 56/969

D = (10+20+56)/969

D = 86/969

D = 0.08875

6 0

3 years ago