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3 years ago

14

as a member of a music club you can order CDs for $14.99 each. the music clib also charges $4.99 for each shipment the expressio

n 14.99 + 4.99 represents the cost of n CDs find the total cost for ordering 3 CDs

2 answers:

alina1380 [7]3 years ago

5 0

14.99n + 4.99

If we ordered 3 CDS, we need to replace 3 for n.

14.99(3) + 4.99
44.97 + 4.99
49.96

Answer: $49.96

N76 [4]3 years ago

3 0

The equation is y=14.99n+4.99
Make n=3 because you order 3 CDs
y=14.99(3)+4.99= $49.96
Hope this helps.

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Which statement describes the graph of f(x)=-4x^3-28x^2-32x+64

lord [1]

The only that has the shape of the one below.

y = -4(x^3 + 7x^2+8x - 16)
Let x = 1
y = - 4(1 + 7 + 8 - 16)
y = 0

y = -4(x -1)(x^2 + 8x + 16)
y = -4(x - 1)(x + 4)^2

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3 years ago

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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 $\rho sin\phi=1$

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3 years ago

F(x+h) = (x+h)² + 3(x+h)^3<br><br> How would I distribute this?

Leno4ka [110]

Answer:

f(x + h) = 3x³ + x² + 9h²x + 3h³ + h² + 9hx² + 2hx

General Formulas and Concepts:

Order of Operations: BPEMDAS
Distributive Property
Expand by FOIL (First Outside Inside Last)
Combining like terms

Step-by-step explanation:

<u>Step 1: Define function</u>

f(x) = x² + 3x³

f(x + h) is x = x + h

<u>Step 2: Simplify</u>

Substitute: f(x + h) = (x + h)² + 3(x + h)³
Expand by FOILing: f(x + h) = (x² + 2hx + h²) + 3(x + h)³
Rewrite: f(x + h) = (x² + 2hx + h²) + 3(x + h)²(x + h)
Expand by FOILing: f(x + h) = (x²+2hx+h²) + 3(x² + 2hx + h²)(x+h)
Distribute/Expand: f(x + h) = (x²+2hx+h²) + 3(x³+3hx²+3h²x+h³)
Distribute 3: f(x + h) = (x²+2hx+h²)+(3x³+9hx²+9h²x+3h³)
Combine like terms: f(x + h) = 3x³+x²+9h²x+3h³+h²+9hx²+2hx

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3 years ago

Jeremiah makes $150 a week.he spent 112.what fraction of his weekly pay has he spent

Paraphin [41]

112/150, then reduce. the answer is 56/75

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3 years ago

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The temperature in Ottawa starts at -4°C, rises 14°C, and then falls 8°C. What is the final temperature?

Molodets [167]

Answer:

2C

Step-by-step explanation:

-4C+14C=10C

10C-8C=2C

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3 years ago

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