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2 years ago

Which literal equations are equivalent to ? Choose all answers that are correct.

1 answer:

7 0

$a.\\g=\frac{w}{m}\ \ \ \ |multiply\ both\ sides\ by\ m\neq0\\\\w=gm\ \boxed{c.}\\\\therefore:\boxed{a.}\ is\ equivalent\ to\ \boxed{c.}\\\\b.\\g=\frac{m}{w}\ \ \ \ |multiply\ both\ sides\ by\ w\neq0\\\\gw=m\ \ \ \ |divide\ both\ sides\ by\ g\neq0\\\\w=\frac{m}{g}\ \boxed{d.}\\\\therefore:\boxed{b.}\is\ equivalent\ to\ \boxed{d.}$

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If a work group consistently achieves 80 % of its quarterly goals and the work group generally has 25 objectives per quarter how

arlik [135]

20 objectives per quarter.

6 0

2 years ago

Find a polynomial of degree 3 with real coefficients and zeros of -3,-1, and 4, for which f(-2)=-24

Zanzabum

We want to find a polynomial

f(x) = a x³ + b x² + c x + d

such that the roots of f are x = -3, x = -1, and x = 4, and f(x) takes on a value of -24 when x = -2.

The factor theorem for polynomials tells us that we can factorize f(x) as

a x³ + b x² + c x + d = a (x + 3) (x + 1) (x - 4)

Expand the right side:

(x + 3) (x + 1) (x - 4) = x³ - 13x - 12

So we have

a x³ + b x² + c x + d = a x³ - 13a x - 12a

In order for both sides to be equal, the coefficients of both polynomials on terms of the same degree must be equal. This means

a = a (of course)

b = 0 (there is no x² term on the right)

c = -13a

d = -12a

We also have that f (-2) = -24, which means

f (-2) = a (-2 + 3) (-2 + 1) (-2 - 4)

-24 = 6a

a = -4

which in turn tells us that c = 52 and d = 48.

So we found

f(x) = -4x³ + 52x + 48

4 0

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.