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3 years ago

Given the function f(x) = 0.5(3)x, what is the value of f−1(7)? 1) 0.565 2) 1.140 3) 1.771 4) 2.402

Mathematics

2 answers:

murzikaleks [220]3 years ago

6 0

Answer:7=0.5 |x-4| -3

+3 +3

10=0.5 |x-4|

10/0.5=0.5/0.5 |x-4|

20=|x-4|

-20=x-4 20=x-4

+4 +4 +4 +4

-16=x 24=x

The answers are -16=x and 24=x

Hope this helps, an if it pleases you put as the brainliest answer!

Read more on Brainly.com - brainly.com/question/3508210#readmore

Step-by-step explanation:

myrzilka [38]3 years ago

5 0

Y = .5(3)x = 1.5x
The inverse is x = 1.5 y which is f^-1(x)
Then y = x/1.5
f^-1(7) = 7/1.5 = 14/3 which is not an answer.
Is the problem written correctly.

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The length of a rectangular garden is 7 meters longer than its width. if its perimeter is ( 12 x + 14) meters, find its length i

cluponka [151]

L=7+w
P=(12x+14)=2(6x+7)
l+w= P/2 = 2(6x+7)/2= 6x+7
l+w=6x+7
2l = 6x+7
l = (6x+7)/2
l=7+w
-> w= l-7
= [(6x+7)/2] -7
= (6x+7-14)/2
= (6x-7)/2

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3 years ago

Find an equation of the line that passes through the given point and has the indicated slope m.

Darina [25.2K]

Answer:

y = -5.5

Step-by-step explanation:

The only lines that have a slope of 0 are horizontal lines. Horizontal lines are always in the form y = c where c is a constant. Basically, on a horizontal line, no matter what x is, y will always be the constant c. Therefore, the x coordinate of our given point does not matter and we only have to look a the y-coordinate, which is -5.5. Therefore, the equation is y = -5.5.

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2 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

2 years ago

Not sure how to complete #14

pashok25 [27]

14. Add the line times the outside number
X(X+4)= (2√3)^2
X^2+4X= 4√9
X^2+4X= 4times 3
X^2+4X=12
X^2+4X-12=0
(X+6)(X-2)=0
X=-6 X=2
Answe can't be negative so it's X=2

3 0

2 years ago

Find the value of the variable that results in congruent triangles

sdas [7]

Answer:

y = 5

Step-by-step explanation:

The triangles will be congruent when corresponding sides are congruent. __

We already have ...

KL ≅ NP . . . = 15 mm

JL ≅ MP . . . = 22 mm

So, we need ...

JK ≅ MN

4y +12 = 32 . . . . substitute given values

This will be the case when ...

4y = 20 . . . . . subtract 12

y = 5 . . . . . . . divide by 4

The value of y that makes the triangles congruent is 5.

8 0

1 year ago