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3 years ago

Pick all the names for this shape. Sides that appear to be parallel are parallel

Mathematics

2 answers:

Lesechka [4]3 years ago

4 0

The correct answer is A

Wewaii [24]3 years ago

3 0

Answer:

I would say a parrallelogram

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.

$r(t)=x(t)i+y(t)j$ 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

Kaci bought a birthday cake like the one shown below. If a=5inches,b=5inches,c=10 inches, and d=3inches what is the volume of th

Gnom [1K]

Answer:

75+150=225 in^2

Step-by-step explanation:

Separate each layer.

Area1+Area2= Total area

A1= a*b*d

A2=a*c*d

A1=5*5*3=75 in^2

A2=5*10*3=150 in^2

75+150=225 in^2

7 0

3 years ago

Wanna be the Brainiest

masha68 [24]

Answer:

156cm^3

Step-by-step explanation:

V= 1/2 a*c*h

a=3

c=8

h=13

3*8*13=312

312/2=156

5 0

3 years ago

Blake is a member of a golf club. When he became a member, he deposited money into his club account. For each round of golf that

Leno4ka [110]

Answer:

D) Blake's account initially had $320, which is decreasing at the rate of $20 per round.

Step-by-step explanation:

Here, according to the question:

x: The total number of golf rounds played

y: Represents the amount, in dollars, left in his account after playing x rounds

Let as assume A is the amount deposited initially.

y = A - n x here n : rate of each round played

Also, here

if x = 2, then y = 280

if x =4, then y = 240

If x = 2 and y = 280, then:

y = A - n x ⇒ 280 = A - 2 n ... (1)

If x = 4 and y = 240, then:

y = A - n x ⇒ 240 = A - 4 n ... (2)

Solving (1) and (2) by (1) - (2), we get:

40 = 2 n or, n = 20

Putting n = 20 in 280 = A - 2 n, we get: A = 280 + 2(20) = 320

⇒ A = $320, n = $20

⇒ The amount initially deposited is $320 and the rate per round is $20

Hence ,Blake's account initially had $320, which is decreasing at the rate of $20 per round.

4 0

3 years ago

2. Solve the below proportion. Please help me.

antoniya [11.8K]

32 3t try add it all up maybe it work but that's the answer

4 0

2 years ago

Read 2 more answers