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3 years ago

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When Maria started her career at the age of 24, she deposited $800 into a savings account that earns 8.75% interest compounded s

emiannually. If she
makes no other deposits or withdrawals, find the total amount in the
account when she retires at the age of 65.
a. $11,378.17
b. $26,791.81
c. $27,817.94
d. $209,234.59

1 answer:

Dominik [7]3 years ago

4 0

Answer: Answer is b

Step-by-step explanation:

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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

Put the numbers in order from least to greatest.

loris [4]

Answer:

B. -.9,-4, 1, .2, .8

Hope this helps!:)

7 0

3 years ago

Read 2 more answers

Can someone pls help??

Vlad1618 [11]

Answer:

a. The y coordinates for A are either 10 or -14

b. The y coordinates for A are either -11 or 7

Step-by-step explanation:

distance = sqrt ((x2-x1)^2+(y2-y1)^2)

We know Point B and the x coordinate of point A as well as the distance

15 = sqrt ((-4-5)^2+(-2-y1)^2)

15 = sqrt ((-9)^2+(-2-y1)^2)

15 = sqrt (81+(-2-y1)^2)

Square each side

15^2 =sqrt (81+(-2-y1)^2)^2

225 = 81+(-2-y1)^2

Subtract 81 from each side

225-81 = 81-81 +(-2-y1)^2

144 = (-2-y1)^2

Take the square root of each side

±sqrt 144 = sqrt(-2-y1)^2

±12 = (-2-y1)

Add 2 to each side

2±12 = 2-2-y1

2±12 = -y1

14 = -y1 or -10 = -y1

Multiply by -1

-14 = y1 or 10 = y1

The y coordinates for A are either 10 or -14

Now move B to -7,-2

15 = sqrt ((-7-5)^2+(-2-y1)^2)

15 = sqrt ((-12)^2+(-2-y1)^2)

15 = sqrt (144+(-2-y1)^2)

Square each side

15^2 =sqrt (144+(-2-y1)^2)^2

225 = 144+(-2-y1)^2

Subtract 144 from each side

225-144 = 144-144 +(-2-y1)^2

81 = (-2-y1)^2

Take the square root of each side

±sqrt 81 = sqrt(-2-y1)^2

±9 = (-2-y1)

Add 2 to each side

2±9 = 2-2-y1

2±9 = -y1

11 = -y1 or -7 = -y1

Multiply by -1

-11 = y1 or 7 = y1

The y coordinates for A are either -11 or 7

3 0

3 years ago

Identify the property used in the first four steps to solve the equation 4(x-7)=2x-6

myrzilka [38]

Answer:

x = 11

distributive law

additive law

multiplication property

Step-by-step explanation:

Given in the question an equation

4(x-7) = 2x-6

Distributive law

a(b+c) = ab +ac

4x - 4(7) = 2x - 6

4x -28 = 2x - 6

Use the addition property of equality to reduce the 2x on the right.

4x - 2x - 28 = 2x - 2x -6

4x -2x -28 = -6

Use the addition property of equality to reduce -28 to zero on the left.

4x - 2x- 28 + 28 = -6 + 28

2x = 22

Use the multiplication property of equality to reduce 2x to just x

2x2 = 22/22

x = 22/2

x = 11

4 0

3 years ago

The x values are the

dem82 [27]

The horizontal value in a pair of coordinates: how far along the point is. The X Coordinate is always written first in an ordered pair of coordinates (x,y), such as (12,5). In this example, the value "12" is the X Coordinate. Also called "Abscissa"

4 0

3 years ago