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3 years ago

Find the distance between the pair of points. (17.-6) and (7.-12)

Mathematics

1 answer:

aleksley [76]3 years ago

4 0

Using the distance formula:-

Distance = square root [ (17 -7)^2 + (-6 - -12)^2 ]

= square root ( 136)

= 11.66 answer

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A patient weighs 93 pounds (lb). Meperidine hydrochloride is ordered for pain at a dosage of 6 milligrams (mg) per kilogram of b

Ymorist [56]

Convert the dose into mg / lb

1 lb = .45 Kg

so the does = 6 * .45 = 2.7 mg/lb

so the daily dose of the patient is 93 * 2.7 = 251.1 mg

injections are available in 50mg per mL

to calculate the daily dose in mL 251.1 / 50 = 5 mL

7 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

3 years ago

Solve for x. Show each step of the solution. 4.5(4 − x ) + 36 = 202 − 2.5(3x + 28)

Marrrta [24]

Answer:

sgsrgrsdg

Step-by-step explanation:

6 0

3 years ago

Help ASAP , 15 points and a brainy.

Step2247 [10]

Answer:

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Which of the following is a solution of x² + 14x + 112 = 0? If necessary, round to the nearest hundredth.

Readme [11.4K]

To determine the solution of the quadratic equation, use the quadratic formula which states that,
x = ((-b +/- sqrt (b² - 4ac)) / 2a
From the equation, a = 1, b = 14, and c = 112. Substituting these to the quadratic formula,
x = <span>((-14 +/- sqrt (14² - 4(1)(12)) / 2(1) = indeterminate
Thus, the equation does not a real number solution. </span>

6 0

4 years ago

Read 2 more answers