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3 years ago

How many digits are in the product of 91 and 10^17 please explain. Thanks.

1 answer:

7 0

It should be 19 because originally, it would be 910, but then add 16 more 0's, and 16 + 3 = 19 (and the three is from here -------^)!
Check this out ->:https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=91*10%5E17
and https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#safe=strict&q=91000000000...
They equal.

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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

In the formula l=p+prt, what does l equal when p=500,r=20%, t=2

Juliette [100K]

Just plug in 500 for p, 0.2 for r (because 20% is equivalent to 0.20), and 2 for t:

$I=p+prt\\I=(500)+(500)(0.2)(2)\\I=500+200\\I=700$

So, if you start with $500 and charge an interest rate of 20% for 2 years, you will gain $200 to get $700 in total.

7 0

3 years ago

What is the answer??????????

Troyanec [42]

The answer is 91 ............

4 0

2 years ago

Read 2 more answers

What is the answer to <br> -3-7x - 41 - 7>68

Makovka662 [10]

Answer:

x < -17

Step-by-step explanation:

-3-7x - 41 - 7>68

Combine like terms

-7x-51>68

Add 51 to each side

-7x-51+51>68+51

-7x > 119

Divide each side by -7, remembering to flip the inequality

-7x/-7 < 119/-7

x < -17

7 0

3 years ago

Help with question B please <br> No scam brainliest will be given

erma4kov [3.2K]

Are you still looking for a answer? If so I would love to give you mine.

4 0

3 years ago