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2 years ago

12

Find the derivative of cscx/3sinx

1 answer:

Neporo4naja [7]2 years ago

3 0

$\frac{csc x}{3sinx} = \frac{1}{3sin ^{2}x }$

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Draw a model to show a fraction that is equivalent to one third

Irina-Kira [14]

Hope this helps :) (the first circle is a fraction of thirds and the second circle is a fraction of sixths)

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2 years ago

What are the solutions to the equation? x2(x+2)(x+6)=0 Enter your answers in the boxes. x = or x = or x =

Talja [164]

$x^2(x+2)(x+6)=0\\\\x^2=0 \vee x+2=0 \vee x+6=0\\\\x=0 \vee x=-2 \vee x=-6$

5 0

2 years ago

Read 2 more answers

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

2 years ago

How to find the greatest common factor of 24 and 90?

love history [14]

Well, they're both divisible by 2 (24 ÷ 2 = 12) (90 ÷ 2 = 45)

3 0

3 years ago

Milly has a equal number of 20p coins and 50p coins . The value of her 20p coins is £2.80 . Work out the total value of her 20p

Zinaida [17]

Answer:

£9.80

Step-by-step explanation:

The calculation of the total value is given below:

Provided that that

The value of 20p coins is £2.80

So 1p = £2.80 ÷ 20

= £0.14

For 50p it would be

= £0.14 × 50

= £7

Now the total value is

= £2.80 + £7

= £9.80

3 0

2 years ago