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3 years ago

12

Corine open a savings account with a starting balance of $200 and plans to deposit $75 each week after opening the account. Her

savings over time is represented by the graph below. How would this graph change of Corine decided to deposit $50 each week instead

1 answer:

icang [17]3 years ago

7 0

Answer:

less steep

Step-by-step explanation:

200=75x

200=50x

hard to explain, without seeing the graph, but i hope this helps

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Name/ Uid:1. In this problem, try to write the equations of the given surface in the specified coordinates.(a) Write an equation

Gemiola [76]

To find:

(a) Equation for the sphere of radius 5 centered at the origin in cylindrical coordinates

(b) Equation for a cylinder of radius 1 centered at the origin and running parallel to the z-axis in spherical coordinates

Solution:

(a) The equation of a sphere with center at (a, b, c) & having a radius 'p' is given in cartesian coordinates as:

$(x-a)^{2}+(y-b)^{2}+(z-c)^{2}=p^{2}$

Here, it is given that the center of the sphere is at origin, i.e., at (0,0,0) & radius of the sphere is 5. That is, here we have,

$a=b=c=0,p=5$

That is, the equation of the sphere in cartesian coordinates is,

$(x-0)^{2}+(y-0)^{2}+(z-0)^{2}=5^{2}$

$\Rightarrow x^{2}+y^{2}+z^{2}=25$

Now, the cylindrical coordinate system is represented by $(r, \theta,z)$

The relation between cartesian and cylindrical coordinates is given by,

$x=rcos\theta,y=rsin\theta,z=z$

$r^{2}=x^{2}+y^{2},tan\theta=\frac{y}{x},z=z$

Thus, the obtained equation of the sphere in cartesian coordinates can be rewritten in cylindrical coordinates as,

$r^{2}+z^{2}=25$

This is the required equation of the given sphere in cylindrical coordinates.

(b) A cylinder is defined by the circle that gives the top and bottom faces or alternatively, the cross section, & it's axis. A cylinder running parallel to the z-axis has an axis that is parallel to the z-axis. The equation of such a cylinder is given by the equation of the circle of cross-section with the assumption that a point in 3 dimension lying on the cylinder has 'x' & 'y' values satisfying the equation of the circle & that 'z' can be any value.

That is, in cartesian coordinates, the equation of a cylinder running parallel to the z-axis having radius 'p' with center at (a, b) is given by,

$(x-a)^{2}+(y-b)^{2}=p^{2}$

Here, it is given that the center is at origin & radius is 1. That is, here, we have, $a=b=0,p=1$ . Then the equation of the cylinder in cartesian coordinates is,

$x^{2}+y^{2}=1$

Now, the spherical coordinate system is represented by $(\rho,\theta,\phi)$

The relation between cartesian and spherical coordinates is given by,

$x=\rho sin\phi cos\theta,y=\rho sin\phi sin\theta, z= \rho cos\phi$

Thus, the equation of the cylinder can be rewritten in spherical coordinates as,

$(\rho sin\phi cos\theta)^{2}+(\rho sin\phi sin\theta)^{2}=1$

$\Rightarrow \rho^{2} sin^{2}\phi cos^{2}\theta+\rho^{2} sin^{2}\phi sin^{2}\theta=1$

$\Rightarrow \rho^{2} sin^{2}\phi (cos^{2}\theta+sin^{2}\theta)=1$

$\Rightarrow \rho^{2} sin^{2}\phi=1$ (As $sin^{2}\theta+cos^{2}\theta=1$ )

Note that $\rho$ represents the distance of a point from the origin, which is always positive. $\phi$ represents the angle made by the line segment joining the point with z-axis. The range of $\phi$ is given as $0\leq \phi\leq \pi$ . We know that in this range the sine function is positive. Thus, we can say that $sin\phi$ is always positive.

Thus, we can square root both sides and only consider the positive root as,

$\Rightarrow \rho sin\phi=1$

This is the required equation of the cylinder in spherical coordinates.

Final answer:

(a) The equation of the given sphere in cylindrical coordinates is $r^{2}+z^{2}=25$

(b) The equation of the given cylinder in spherical coordinates is $\rho sin\phi=1$

7 0

3 years ago

Need help filling in the blanks: selling price using markup.

Xelga [282]

Answer:

Refer to the explanation.

Step-by-step explanation:

Let's take each one at a time.

1.

To solve for the complement, we simply subtract our markup rate by 100%.

100% - 30% = 70%

Now to solve for the selling price, we use the formula

$SellingPrice=\dfrac{Cost}{ComplementOfMarkupRate}$

$SellingPrice=\dfrac{86.74}{0.70}$

Selling Price = $123.91

2.

We do the same process with the first number.

100% - 40% = 60%

$SellingPrice=\dfrac{Cost}{ComplementOfMarkupRate}$

$SellingPrice=\dfrac{220.00}{0.60}$

SellingPrice = $366.67

3.

The same as the first two.

100% - 20% = 80%

$SellingPrice=\dfrac{Cost}{ComplementOfMarkupRate}$

$SellingPrice=\dfrac{89.50}{0.80}$

SellingPrice = $111.88

4.

Now to solve for the markup rate, we use the formula:

$MarkupRate=\dfrac{Markup}{SelingPrice}$

In this case we first need to find the markup. The markup is the difference between the selling price and the cost.

Selling Price = $235.28

Cost = $199.99

Markup = $235.28 - $199.99

Markup = $35.29

Now the we know our markup, we can then solve for the markup rate using the formula.

$MarkupRate=\dfrac{Markup}{SelingPrice}$

$MarkupRate=\dfrac{35.29}{235.28}$

MarkupRate = 0.1499 x 100 = 14.99% or 15%

5.

Now for the last one, we need to find for the cost. Let's use the selling price formula to find for the cost.

$SellingPrice=\dfrac{Cost}{ComplementOfMarkupRate}$

Selling Price = $30.77

Complement = 65% or 0.65

This will then give us.

$30.77=\dfrac{Cost}{0.65}$

We multiple both sides of the equation by 0.65 to leave our cost alone.

30.77 x 0.65 = Cost

Cost = $20

4 0

3 years ago

What equation could generate the curve in the graph below

Marianna [84]

Answer:

A

Step-by-step explanation:

We know the y intercept is positive so that eliminates choice D.

y = 3x^2 -2x+1

This does not intercept the x axis

y = 3x^2 -6x+3

= 3(x^2 -2x+1)

3(x-1)^2

This intercepts the x axis at 1

This is not the equation for the graph

y = 3x^2 -7x+1

Let x = 1

y = 3-7+1

= -3

This will cross the x axis, so this cannot be the graph

5 0

3 years ago

What is the answer to 10-(8p+3)=9(2p-5) ?

aniked [119]

Use distribution.
10 - (8p + 3) = 10 - 8p - 3 = 7 - 8p
9(2p - 5) = 18p - 45

So...
-8p + 7 = 18p - 45
Subtract 7 from both sides
-8p = 18p - 52
Subtract 18p from both sides
-26p = 52
Divide both sides by -26.
p = -2

There's your answer :D

6 0

3 years ago

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Write 863.141 in expanded form

Mashutka [201]

Eight hundred sixty three and 1 hundred 41 thousandths

6 0

2 years ago

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