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2 years ago

7. If f(x) = -8x +11, find f(-4).

Mathematics

2 answers:

Tomtit [17]2 years ago

5 0

Answer:

F(-4)=43

Step-by-step explanation:

1.Replace X to -4

f(-4)= -8(-4)+11

2.Solve

Multiplying two negative give you a positive (-8 x -4=32).

Then you Add.

32+11=43.

Hope this help!

kobusy [5.1K]2 years ago

3 0

Answer:

Step-by-step explanation:

f(x) = -8x +11, for f(-4).

= -8(-4)+11

= 32 + 11

= 43

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kap26 [50]

Y = 7

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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.