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denpristay [2]
3 years ago
6

A TV that usually sells for $183.26 is on sale for 25% off. If sales tax on the TV is 9%, what is the price of the TV, including

tax?
Mathematics
1 answer:
Hatshy [7]3 years ago
3 0
183.26 times .25 = 45.815
183.26 minus 45.815 = 137.445
137.445 times 0.09 = 12.37005
137.445 plus 12.37005 = 149.81505
Which =149.82 rounded
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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
You spent these amounts on natural gas for the past four months: $112, $108, $99, $89. what should you budget for natural gas th
miskamm [114]

If you wanted to compute for your budget for natural gas this month using the data you have recorded about your consumption of natural gas for the past four months, the best estimate to be budgeted this month would be the average consumption for the past 4 months. To get the average, you have to add the four numbers and divide it by four.

$112 + $108 + $99 + $89 = $408/4 = $102

 

7 0
3 years ago
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abruzzese [7]

Craig practiced 15 hours


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Plz help me I am freaking out
DanielleElmas [232]

Answer:

Wanchen has the weaker flavor, no need to freak out.

Step-by-step explanation:

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mr Goodwill [35]

Answer:

Answers is D

Step-by-step explanation:

2x = 60° because they are vertically opposite angles.

x=60÷2=30°

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