(1,3) ez la respuesta
Name/ Uid:1. In this problem, try to write the equations of the given surface in the specified coordinates.(a) Write an equation for the sphere of radius 5 centered at the origin incylindricalcoordinates.(b) Write an equation for a cylinder of radius 1 centered at the origin and running parallel to thez-axis inspherical coordinates.
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:
[tex](x-a)^{2}+(y-b)^{2}+(z-c)^{2}=p^{2}[/tex]
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,
[tex]a=b=c=0,p=5[/tex]
That is, the equation of the sphere in cartesian coordinates is,
[tex](x-0)^{2}+(y-0)^{2}+(z-0)^{2}=5^{2}[/tex]
[tex]\Rightarrow x^{2}+y^{2}+z^{2}=25[/tex]
Now, the cylindrical coordinate system is represented by [tex](r, \theta,z)[/tex]
The relation between cartesian and cylindrical coordinates is given by,
[tex]x=rcos\theta,y=rsin\theta,z=z[/tex]
[tex]r^{2}=x^{2}+y^{2},tan\theta=\frac{y}{x},z=z[/tex]
Thus, the obtained equation of the sphere in cartesian coordinates can be rewritten in cylindrical coordinates as,
[tex]r^{2}+z^{2}=25[/tex]
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,
[tex](x-a)^{2}+(y-b)^{2}=p^{2}[/tex]
Here, it is given that the center is at origin & radius is 1. That is, here, we have, [tex]a=b=0,p=1[/tex]. Then the equation of the cylinder in cartesian coordinates is,
[tex]x^{2}+y^{2}=1[/tex]
Now, the spherical coordinate system is represented by [tex](\rho,\theta,\phi)[/tex]
The relation between cartesian and spherical coordinates is given by,
[tex]x=\rho sin\phi cos\theta,y=\rho sin\phi sin\theta, z= \rho cos\phi[/tex]
Thus, the equation of the cylinder can be rewritten in spherical coordinates as,
[tex](\rho sin\phi cos\theta)^{2}+(\rho sin\phi sin\theta)^{2}=1[/tex]
[tex]\Rightarrow \rho^{2} sin^{2}\phi cos^{2}\theta+\rho^{2} sin^{2}\phi sin^{2}\theta=1[/tex]
[tex]\Rightarrow \rho^{2} sin^{2}\phi (cos^{2}\theta+sin^{2}\theta)=1[/tex]
[tex]\Rightarrow \rho^{2} sin^{2}\phi=1[/tex] (As [tex]sin^{2}\theta+cos^{2}\theta=1[/tex])
Note that [tex]\rho[/tex] represents the distance of a point from the origin, which is always positive. [tex]\phi[/tex] represents the angle made by the line segment joining the point with z-axis. The range of [tex]\phi[/tex] is given as [tex]0\leq \phi\leq \pi[/tex]. We know that in this range the sine function is positive. Thus, we can say that [tex]sin\phi[/tex] is always positive.
Thus, we can square root both sides and only consider the positive root as,
[tex]\Rightarrow \rho sin\phi=1[/tex]
This is the required equation of the cylinder in spherical coordinates.
Final answer:
(a) The equation of the given sphere in cylindrical coordinates is [tex]r^{2}+z^{2}=25[/tex]
(b) The equation of the given cylinder in spherical coordinates is [tex]\rho sin\phi=1[/tex]
Instant Dinner comes in packages with weights that are normally distributed, with a standard deviation of 0.5 oz. If 2.3% of the dinners weigh more than 13.2 oz, what is the mean weight?
Answer:
12.2
Step-by-step explanation:
2.3%= 0.023
So that is the probability that it will be over 13.2 oz, or .977 is the prob that it will be below 13.2
z-score = (real score - mean)/standard deviation
I found .977 at a z-score of 2.00
so 2.00 = (13.2-m)/0.5
=> m=12.2
Mr Tay had 265 m of wire.
He cut the wire into 4 equal pieces with 25 m left over.
What was the length of each equal piece of wire?
Answer:6
Step-by-step explanation:
265-25
240/4
6
Answer:
60
Step-by-step explanai o
n:
265 -25= 240
240/4=6 0
I already did the equation for you, but can somebody tell me the answer?
Answer:
if you put that equation into a graphing calculator the answer is 4188.37
3x + 1 over 4y2
What is the value of the expression above when x = 3 and y = 4? You must show all work and calculations to receive full credit.
Answer: Pretty sure its the value of the expression is 11
Step-by-step explanation:
Step 1. Add and evaluate 4x and 1/3y^2
Step 2. After evaluating, add 4(2) and 1/3 (3)^2
Step 3. 8 + 1/3(9)
Step 4. 8 + 3 = 11
Step 5. Value of Expression = 11
Answer:
13
Step-by-step explanation:
What is tan 0 when csc 0= 2/3
Answer:
[tex]\tan{\theta} = \frac{\sqrt{11}}{11}[/tex]
Step-by-step explanation:
Cosecant:
The cosecant is one divided by the sine. Thus:
[tex]\csc{\theta} = \frac{1}{\sin{\theta}}[/tex]
Tangent is sine divided by cosine, so we first find the sine, then the cosine, to find the tangent.
Sine and cosine:
[tex]\sin{\theta} = \frac{1}{\csc{\theta}} = \frac{1}{2\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{6}[/tex]
[tex]\sin^{2}{\theta} + \cos^{2}{\theta} = 1[/tex]
[tex]\cos^{2}{\theta} = 1 - \sin^{2}{\theta}[/tex]
[tex]\cos^{2}{\theta} = 1 - (\frac{\sqrt{3}}{6})^2[/tex]
[tex]\cos^{2}{\theta} = 1 - \frac{3}{36}[/tex]
[tex]\cos^{2}{\theta} = \frac{33}{36}[/tex]
First quadrant, so the cosine is positive. Then
[tex]\cos^{2}{\theta} = \sqrt{\frac{33}{36}} = \frac{\sqrt{33}}{6}[/tex]
Tangent:
Sine divided by cosine. So
[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}} = \frac{\frac{\sqrt{3}}{6}}{\frac{\sqrt{33}}{6}} = \frac{\sqrt{3}}{\sqrt{33}} = \frac{\sqrt{3}}{\sqrt{3}\sqrt{11}} = \frac{1}{\sqrt{11}} \times \frac{\sqrt{11}}{\sqrt{11}} = \frac{\sqrt{11}}{11}[/tex]
The answer is:
[tex]\tan{\theta} = \frac{\sqrt{11}}{11}[/tex]
PLEASE CHECK MY WORK
The function given in the table is quadratic:
true***
false
Answer:
false
Step-by-step explanation:
The function given in the table is a linear function:
f(x) = 3x+2
The graph shows the relationship between the number of hours that Michelle has been driving and the distance that she has left to travel to get to her destination.
A graph on a coordinate plane titled Distance Remaining Over Time. The x-axis is labeled time (in hours), numbered 1 to 8, and the y-axis is labeled miles to destination, numbered 50 to 400. A straight line with a negative slope starts at point (0, 350) and ends at point (7, 0).
Which statement is true?
It took Michelle 6 hours to complete the trip.
For each hour that Michelle drove, she traveled an additional 50 miles.
In the first 6 hours, Michelle had traveled a total of 50 miles.
In the first 3 hours, Michelle had traveled a total of 200 mile\
Answer:
(b) For each hour that Michelle drove, she traveled an additional 50 miles.
Step-by-step explanation:
Given
[tex](x_1,y_1) = (0,350)[/tex] ---- start
[tex](x_2,y_2) = (7,0)[/tex] --- end
Required
Which is true
(a): Journey = 6 hours
This is false, because:
[tex]x = x_2 - x_1[/tex]
[tex]x = 7-0[/tex]
[tex]x = 7[/tex] ---- 7 hours
(b): The average rate is 50 miles per hour
To do this, we calculate the slope (m) using:
[tex]m = \frac{y_2 -y_1}{x_2- x_1}[/tex]
[tex]m = \frac{0 - 350}{7-0}[/tex]
[tex]m = -\frac{350}{7}[/tex]
[tex]m = -50[/tex]
This means that the rate is 50 miles driven in 1 hour.
(b) is correct
Others are incorrect
Answer:
B
Step-by-step explanation:
I did it
Malachy rolls a fair dice 720 times.
How many times would Malachy expect to roll a five?
Answer:
120 times
Step-by-step explanation:
On a dice, there are 6 sides.
Since one of these sides is a 5, the chance of rolling a five is 1/6.
Find how many times Malachy can expect to roll a five by multiplying 720 by 1/6:
720(1/6)
= 120
So, Malachy can expect to roll a five 120 times
What is the equation of the following line? Be sure to scroll down first to see
(-1/2, 3) (0,0)
A. y = 1/2 X
B. y = -1/2 X
C. y = 3 X
D. y= 2X
E. y= 6
F. y= -6

a p e x :(
Answer: (f)
Step-by-step explanation:
Given
Line that passes through [tex](-\frac{1}{2},3)[/tex] and [tex](0,0)[/tex]
Using two point form, equation of a line is given by
[tex]\Rightarrow \dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Insert the values
[tex]\Rightarrow \dfrac{y-0}{x-0}=\dfrac{3-0}{-\frac{1}{2}-0}\\\\\Rightarrow \dfrac{y}{x}=-6\\\\\Rightarrow y=-6x[/tex]
Thus, option (f) is correct
How many different committees can be formed from 6 teachers and 37 students if the committee consists of 4 teachers and 4 students?
The committee of 8 members can be selected in
BLANK different ways.
Answer:
The committee of 8 members can be selected in 990,675 different ways.
Step-by-step explanation:
The order in which the teachers and the students are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
4 teachers from a set of 6.
4 students from a set of 37.
Then
[tex]T = C_{6,4}C_{37,4} = \frac{6!}{4!2!} \times \frac{37!}{4!33!} = 990675[/tex]
The committee of 8 members can be selected in 990,675 different ways.
Which sequence of transformations maps quadrilateral ABCD onto quadrilateral EFGH
Answer:
C. reflection across the x-axis, translation 6 units left
I cannot get the range on this one right, can someone help? I had (-infinity, -5) and it said it was wrong.
Answer and Step-by-step explanation:
Try putting a bracket ( ] ), so it looks like this:
(-infinity, -5]
this is because the -5 is included and that's where it stops.
#teamtrees #PAW (Plant And Water)
Step-by-step explanation:
The range of a parabola that opens up starts at its vertex (1,−5)(1,-5) and extends to infinity.
Interval Notation:
[−5,∞)[-5,∞)
Set-Builder Notation:
{y|y≥−5}{y|y≥-5}
Determine the domain and range.
Domain: (−∞,∞),{x|x∈R}(-∞,∞),{x|x∈ℝ}
Range: [−5,∞),{y|y≥−5}
John estimated the height of his office building to be 13m . The actual height of his office building was 14.7m .
Find the absolute error and the percent error of John's estimate. If necessary, round your answers to the nearest tenth.
Answer:
Percent error = 11.6%
Step-by-step explanation:
Given the following data;
Actual height, A = 14.7 m
Estimated height, E = 13 m
a. To find the absolute error;
Absolute error = A - E
Absolute error = 14.7 - 13
Absolute error = 1.7
b. To find the percent error;
Percent error can be defined as a measure of the extent to which an experimental (estimated) value differs from the actual or theoretical value.
Mathematically, it is given by this expression;
[tex] Percent \; error = \frac {experimental \;value - theoretical \; value}{ theoretical \;value} *100[/tex]
Substituting into the equation, we have;
[tex] Percent \; error = \frac {13 - 14.7}{14.7} *100[/tex]
[tex] Percent \; error = \frac {1.7}{14.7} *100[/tex]
[tex] Percent \; error = 0.1157 *100[/tex]
Percent error = 11.57 ≈ 11.6%
PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELP MEEEEEEEEEEEEEEEEEEEEEEEEE
Task #1 Creating A Table Task
Create a table of x and y values that represents a proportional relationship.
a) Explain how you know the relationship is proportional.
b) What equation models the values in the table?
2) Create a table of x and y values that represents a linear, non-proportional relationship.
a) Explain how you know the relationship is non-proportional.
b) What equation models the values in the table?
Answer:
b
Step-by-step explanation:
The equation y = 50(1.05)x models the growth of a mule deer population introduced into Guadalupe National Park in December 2015. "X" represents the number of years after December 2015 while "y" represents the population at time "x". In what year will the mule deer population first reach 1500?
F.2084
G.2044
H.2043
J.2085
9514 1404 393
Answer:
J. 2085
Step-by-step explanation:
Fill in the desired value for y and solve for x.
1500 = 50(1.05^x)
30 = 1.05^x . . . . . . . divide by 50
log(30) = x·log(1.05) . . . . . take logarithms
x = log(30)/log(1.05) ≈ 69.71
Since x represents years after December 2015, x = 69.7 will be some time in mid 2085.
Convert the rational expression to radical form.
x^{4/3}y^{1/3}z^{2/5}
Plz help
Answer:
[tex]a \frac{x}{n} = \sqrt[n]{a}^x .
\sqrt[3]{x}^4 \sqrt[3]{y} \sqrt[5]{z}^2 [/tex]
Evaluate -2yx - 4y what's the answer
Answer:
-2y (x+2)
Step-by-step explanation:
remove greatest common factors.
both terms have a (y) and a (-2)
Answer:
-2y ( x - 2 )
Step-by-step explanation:
- 2yx - 4y
factor out -2y from the equation
-2y ( x - 2 )
PLEASE NO LINKS I CAN'T SEE THEM
Which equation represents the solution of the equation 7x + 12 = 6?
A. x = 18 / 7
B. x = 6/7
C. x = - 6/7
D. x = - 18/7
Answer:
c
Step-by-step explanation:
because I have a great day and I will be in the representation
Step-by-step explanation:
7x + 12 = 6
7x=-6
x=-6/7
Don't enter into link, it contains viruses
Can I get the awnsers for these two? Any help is appreciated.
Answer:
y = 4x - 5
Step-by-step explanation:
for slope intercept form
y = mx + c
where m is the slop so
M = 4
point = (1, -1)
a point on the line must satisfy the equation so replacing y and x by -1 and 1 respectively to get to c.
-1 = 4 × 1 + c
-1 - 4 = c
-5 = c
placing these values in y = mx + c
y = 4x - 5
Answer:
y = 4x - 5.
Step-by-step explanation:
First write it in point-slope form:
y - y1 = m(x - x1)
y - (-1) = 4(x - 1)
y + 1 = 4x - 4
y = 4x - 4 - 1
y = 4x - 5. <------- Slope-intercept.
How many years (to two decimal places) will it take $15000 to grow to $17500 if it is invested at 8% compounded semi- annually?
Answer:
1.97 years
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 8/100
r = 0.08 per year,
Then, solve the equation for t
t = ln(A/P) / n[ln(1 + r/n)]
t = ln(17,500.00/15,000.00) / ( 2 × [ln(1 + 0.08/2)] )
t = ln(17,500.00/15,000.00) / ( 2 × [ln(1 + 0.04)] )
t = 1.965 years
:D
Seven-eighths of a number is -35. What is the number?
Let the number be x
7/8 of the number is 7/8x and it equals -35:
7/8x = -35
Find x by dividing both sides by 7/8
When you divide by a fraction, flip the fraction over and then multiply:
x = -35 x 8/7 = (-35 x 8) / 7 = -280/7 = -40
The number is -40
Find the area and circumference of each circle
Answer:
Step-by-step explanation:
Area = [tex]Area = \pi r^2 = \pi(3)^2 = 9\pi = 28.27\\Circumference = 2\pi r = 2\pi 3 = 6\pi = 18.85[/tex]
Answer:
[tex]area = 28.27 {m}^{2} \\ c = 18.84m[/tex]
Explanation is attached to the picture
Hope this helps you.
15 friends want to order pizza for dinner. If each friend can eat 1/3 of a pizza, how many pizzas should they order?
Answer:
5
Step-by-step explanation:
[tex]\frac{15}{3} =5\\3 friends=1 pizza\\15 friends=5 pizzas\\[/tex]
76 is what percent of 79
Answer:
79
100
0.79%
76
100
0.76%
Solve for c. 2 abc + d=3
Question 18 of 28 Which of the following equations can be used to find the length of EF in the triangle below? A. (EA)2 = 242-122 B. (ER2 = 242 +122 O C. EF = 24 - 12 D. EF = 24 + 12
Answer: A
Step-by-step explanation:
Tania is buying a guitar. Guitar Central has 20% off coupons available, and has the guitar Tania wants for $349. Music Mart has the guitar Tania wants for $419, but is offering a $200 rebate. Which is the better deal? _________________________________________________________________________________________
Answer:
Music Mart offers a better deal, given that the price of the guitar is $ 219 compared to $ 279.20 for Guitar Central.
Step-by-step explanation:
Since Tania is buying a guitar, and Guitar Central has 20% off coupons available, and has the guitar Tania wants for $ 349, while Music Mart has the guitar Tania wants for $ 419, but is offering a $ 200 rebate, to determine which is the better deal the following calculations must be performed:
Guitar Central
100 - 20 = 80
349 x 0.8 = X
279.20 = X
Music mart
419 - 200 = X
219 = X
Therefore, Music Mart offers a better deal, given that the price of the guitar is $ 219 compared to $ 279.20 for Guitar Central.
see image for question
Answer:
no because it is apporxametely 1/4th of the pizza
Step-by-step explanation:
this is not a trick question, anyone adding more than 2 sentances on their explanation is tricking themselves and is thinking too hard
Answer:
No I actually received 1/4 of the pizza
Step-by-step explanation:
Piece B shows 1/4 of the pizza meaning I'm receiving less than half of the pizza
If I receiveed 2/4 of the pizza, it would've maked senes for me to receive 1/2 of the pizza because 2/4 = 1/2
Consider a maximization linear programming problem with extreme points xi, x2, Xz. and x4. and extreme directions d1,. d2, and dz. and with an objective function gradient e such that cx1 =4, cx2 = 6, cx3= 6, cx4=3, cd1= 0, cd2=0, and cd3=2. Characterize the set of alternative optimal solutions to this problem.
Answer:
Set of alternative optimal solution : 0 ≤ z ≤ 1.5
Hence There will be an infinite set of Alternative optimal solution
Step-by-step explanation:
considering Cx1 = 4
∴ C = 4 / x1
Cx2 = 6
∴ 4x2 - 6x1 = 0
2x2 - 3x1 = 0 ------ ( 1 )
considering Cx3 = 6
C = 6/x3
Cx4 = 3
∴ (6/x3) x4 - 3 = 0
= 2x4 - x3 = 0 ---- ( 2 )
attached below is the remaining part of the solution
set of alternative optimal solution : 0 ≤ z ≤ 1.5
There will be an infinite set of Alternative optimal solution