Which line from "I'm Not Thirteen Yet" shows Jamie’s excitement as she plays soccer?

Is (5,3) a solution to this system of equation <br> X+y=8<br> 17x+17y=8

Degger [83]

(5, 3)

x y

Plug in:

x + y = 8

5 + 3 = 8

8 = 8

Plug in:

17(5) + 17(3) = 8

85 + 51 = 8

136 = 8

Answer - No, (5, 3) is not a solution to this system of equations.

5 0

3 years ago

A line's y -intercept is 10,and its slope is 9 . What is its equation in slope-intercept form?

LenaWriter [7]

Answer:

y = 9x + 10

Step-by-step explanation:

y = mx + b

Here, m is slope and b is y-intercept

y = 9x + 10

3 0

3 years ago

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

32 + a > 44; 11, 12, 13

Levart [38]

Download Photo math it will help u a lot with steps

4 0

3 years ago

I need help on ratio of x-coordinates and ratio of y-coordinates

ad-work [718]

Answer:

Ratio of x-coordinates:

$\frac{-1}{-2}=\frac{1}{2}$

$\frac{2}{4}=\frac{1}{2}$

$\frac{-2}{-4}=\frac{1}{2}$

Ration of y-coordinates:

$\frac{2.5}{5}=\frac{1}{2}$

$\frac{1}{2}=\frac{1}{2}$

$\frac{-2}{-4}=\frac{1}{2}$

Step-by-step explanation:

The table is asking for the ratio of x-coordinates for each point (A, B, C and D) for both the image and pre-image. The ratio is the image 'x' or 'y' value ÷ the pre-image 'x' or 'y' value. Each ratio should be expressed in simplest form and should show the same pattern of dilation, or same scale factor. In this case, the second figure is 1/2 the size of the original figure.

5 0

3 years ago