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3 years ago

Noah says 4/9 is equivalent to 20/45. Check his work by completing the table of equivalent ratios.

Mathematics

2 answers:

g100num [7]3 years ago

7 0

Noah is correct!!!! 20/45 simplified is 4/9. hope this helps!

Sveta_85 [38]3 years ago

5 0

Answer:

noah is correct

Step-by-step explanation:

i just checked on my graphing calculator

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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

Another algebra question I need help with

zzz [600]

7x -7/2 y = -49
7/2 y = 7x + 49
y = 2x + 14
y - intercept = 14
x - intercept : 2x + 14 = 0 so x = -7

answer is C.
x - intercept : -7
y - intercept : 14

4 0

3 years ago

Pls help I’ll brainlest and add extra points

Phoenix [80]

Answer:

26. D) $252

27. A) -6.7 + 6.8

Step-by-step explanation:

26. 400 * 0.3 = 120

400 - 120 = 280

280 * 0.1 = 28 (because the 10% is additional, cannot add it to the original 30%)

280 - 28 = 252

27. -4.5 + 4.4 = -0.1

- 6.7 + 6.8 = 0.1

-0.1 + 0.1 = 0

6 0

3 years ago

What is happening to this graph when the x-values are between 4 and 8?

Nikolay [14]

Answer: it remains constant

Step-by-step explanation: because between 4 and 8 there is no change

3 0

3 years ago

Two consecutive odd integers whose sum is 76.

ollegr [7]

Answer:

37 and 39

Step-by-step explanation:

5 0

3 years ago

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