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3 years ago

5

find two numbers that have square roots between 7 and 8. one number should have a square root closer to 7 and the other should h

ave a square root closer to 8. justify your answer.

1 answer:

Bad White [126]3 years ago

8 0

Step-by-step explanation:

7 = √49

8 = √64

So any positive integer between 50 to 63, both inclusive, have a square root between 7 and 8.

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The original price was $20,000 the sales price was $18,000 what is the percent discount

lord [1]

Answer:

10 percent :)

Step-by-step explanation:

Discount = Original Price x Discount %/100

Discount = 20000 × 10/100

Discount = 20000 x 0.1

You save = $2,000.00

Final Price = Original Price - Discount

Final Price = 20000 - 2000

Final Price = $18,000.00

i hope this helps! pls stay happy and healthy, friend! :))

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3 years ago

What’s the minimum cuts needed to cut a circle into 8 equal parts

OlgaM077 [116]

Answer:

4 cuts

Step-by-step explanation:

you first do a vertical cut

then a horizontal cut

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3 years ago

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A box contains 300 raffle tickets. Only 15 tickets are winning tickets. What is the

Roman55 [17]

Answer:

5%

Step-by-step explanation:

15/300 = 0.05

5%

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2 years ago

What is the sum of number 13

pychu [463]

Pretty simple, really - all you have to do us divide 509 by 14 before you're left with an answer of <span>36.35. Now, the number '36' is closer to 0 than 100, so we'll round down instead of up, therefore the number of floors to the building is 36! </span>

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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

$y=\frac{y_0}{x_0^2}x^2$

$y=y_0\left(\frac{x}{x_0}\right)^2$

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2 years ago