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3 years ago

What is 34/6 as a mixed number? :)

Mathematics

1 answer:

Bingel [31]3 years ago

6 0

34 4
__. = 5 __
6. 6 2
In simplest form it would be 5 __
3

So, 34/6 = 5 2/3
5 wholes and 2/3

Hope this helps. :3

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Identify a solution of the equation: log2x+log(x−5)=2

Harrizon [31]

Answer:

3.x= 10

Step-by-step explanation:

log 2x + log (x - 5) = 2
log (2x(x - 5)) = 2
2x(x - 5) = 10²
2(x² - 5x) = 100
x² - 5x - 50 = 0
x² + 5x - 10x - 50 = 0
x(x + 5) - 10(x + 5) = 0
(x - 10)(x + 5) = 0
x = 10
x = -5, this root is discounted as log should be positive.

Correct choice is 3.

6 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

Jake cuts out five-pointed stars. They are different sizes, but they

Verdich [7]

Answer:

Step-by-step explanation: 12L + 1/2 = 72.5

72.5 - 24 - 8.5 + 20

72.5 -24 = 48.5 - 8.5 = 40

40 + 20 = 60

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3 years ago

Write these numbers in order from least to greatest. ( 3-3/10), (3.1) , (3-1/4)

Orlov [11]

Our three numbers are...

3 3/10 = 3.3

3.1

3 1/4 = 3.25

So, if we order those from least to greatest, we have...

3.1, 3.25, 3.3

which, in the forms given, is...

3.1, 3-1/4, 3-3/10

7 0

3 years ago

A group of 6 students was asked, "How many hours did you watch television last week?" Here are their responses:

vaieri [72.5K]

Answer:

Mean: 11.2

Median: 11

Mode: There is none

Step-by-step explanation:

mean -you add all the numbers and divide by the number of numbers

median- you arrange the data set by numerical value (increasing) and it is basically the "middle number" for example 1, 2, 3, (2 would be the "middle" number" )

mode- is the number that appears most often. in this scenario, all numbers appear the same amount of times (1) so there is no mode.

3 0

3 years ago

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