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2 years ago

What is 6x^-2 simplified

2 answers:

6 0

Pemdas
parnthasees
exponnets
mult or div
add or sub

6x^-2 means
6 times x^-2

rmemeber
x^-m=1/(x^m)
6 times x^-2=6 times 1/(x^2)=6/(x^2)= $\frac{6}{x^{2}}$

Ghella [55]2 years ago

4 0

Good evening

6x^-2

6 * 1/(x*x)

= 6/(x*x)

= 6/x²

I hope that's help:)

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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

2 years ago

Hi, does anyone know the answer to this question? I’m bad at geometry and I’m struggling to answer it.

arsen [322]

Answer:

QT = 16

Step-by-step explanation:

ΔQRS ~ ΔQRT

In similar triangles, corresponding angles are in same ratio.

$\frac{QS}{QR}=\frac{QR}{QT}\\\\\frac{25}{20}=\frac{20}{QT}$

Cross multiply,

QT * 25 = 20 * 20

$QT =\frac{20*20}{25}\\\\QT = 4*4\\\\QT = 16$

3 0

2 years ago

Can someone please help !!!

Vera_Pavlovna [14]

Answer:

A = 6.3033315211545 in2 or 6.3

Step-by-step explanation:

7 0

3 years ago

WhT is this rounded to the nearest hundredth

Sergio [31]

Answer:

32.02

Step-by-step explanation:

The number that is in the hundredths place is five. You can remember this by knowing that the decimal point counts as one and all the number to the right of the decimal point count as zero. So 0 is in the tenths place, 1 is in the hundredths place, 5 is in the thousandths place, 6 is in the ten thousandths place and so on. So if you round this number to the nearest hundredth, you'll get 32.02 because if you're rounding a number and the number you're rounding with (knowing that the number you're rounding will always be rounded with the number to the right of it) is 5 or greater than 5, that number that you have to round will go up one unit.

I hope this helped!

3 0

2 years ago

A ray is a portion of a line that begins at a point and extends endlessly in one direction.

viva [34]

Answer: T

Step-by-step explanation:

cuz i practice geometry.

4 0

3 years ago