Consider the scatter plot.


Scatter plot with line of best fit of y equals 0.75x plus five.



The line of best fit is y = 0.75x + 5.



Choose the best representation for the slope.



The slope of the line of best fit shows that each additional minute, the distance increases by 0.75 feet.

The slope of the line of best fit shows that each additional minute, the distance decreases by 5 feet.

The slope of the line of best fit shows that each additional minute, the distance decreases by 0.75 feet.

The slope of the line of best fit shows that each additional minute, the distance increases by 5 feet.

Consider The Scatter Plot. Scatter Plot With Line Of Best Fit Of Y Equals 0.75x Plus Five. The Line Of

Answers

Answer 1

Answer:

The correct answer option is: The y-intercept of the line of best fit shows that when time started, the distance was 5 feet.

Step-by-step explanation:

We are given a scatter plot with a best fit line as shown on the given graph.

The equation of the best fit line is given by:

y = 0.75x + 5

So with the help of the equation and by looking at the given graph, we can conclude about the representation of the y intercept that the the y-intercept of the line of best fit shows that when time started, the distance was 5 feet.

Since the distance shown on the y axis is already 5 when the time started at 0 minutes.


Related Questions

Based on the polynomial remainder theorem, what is the value of the function when x=-5
f(x)=x^4+9x^3+17x^2-8x+50

Answers

Answer: 15

Step-by-step explanation:

Using synthetic division:

-5  |  1    9     17    -8    50

    |  ↓   -5   -20   15   -35            

       1     4   -3      7     15  ← this is the remainder


Check:

f(x) = x⁴ + 9x³ + 17x² - 8x + 50

f(-5) = (-5)⁴ + 9(-5)³ + 17(-5)² - 8(-5) + 50

      = 625 - 1125 + 425 + 40 + 50

      = 15

Math help!
What is the value of a?

Answers

Answer:

a = 8

Step-by-step explanation:

Put the given information into the function equation and solve for a.

f(x) = a/(x-h) +k . . . . for (h, k) = (4, 2) and (x, y) = (12, 3)

3 = a/(12 -4) +2 . . . . . . . givens substituted in

1 = a/8 . . . . . . subtract 2

8 = a . . . . . . . multiply by 8

Which parachute has a slower decent: a red parachute that falls 0 feet in seconds or a blue parachute that falls 2 feet in seconds? Math problem

Answers

Answer:

Blue

Step-by-step explanation:

2>0

Kellyanne bought a pair of shoes that cost $98.00. Sales tax on the shoes was 7.5%. What was the total cost of the shoes including tax?

Answers

Answer:

105.35

Step-by-step explanation:

:)

Write the equation of a line that is perpendicular to the given line and that passes through the given point. y-3=-1/5(x+2); (-2, 7)
A. y=5x+7
B. y=5x+17
C. y=(1/5)x-2
D. y=-2x+3

Plz answer quickly!! Thank you :) <3

Answers

Final answer:

To find the equation of a line perpendicular to a given line, find the negative reciprocal of the slope and use the point-slope form of a line.

Explanation:

To find the equation of a line that is perpendicular to the given line and passes through the given point, we first need to determine the slope of the given line. The given line has a slope of -1/5, which is the negative reciprocal of the slope we want for the perpendicular line. The negative reciprocal of -1/5 is 5/1 or 5. Now we have the slope of the perpendicular line and a point it passes through (-2, 7), we can use the point-slope form of a line to find the equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.

Substituting the values, we get: y - 7 = 5(x - (-2))
y - 7 = 5(x + 2)
y - 7 = 5x + 10
y = 5x + 10 + 7
y = 5x + 17

Therefore, the equation of the line that is perpendicular to the given line and passes through the given point (-2, 7) is y = 5x + 17. Option B is the correct answer.

Learn more about Equation of a line here:

https://brainly.com/question/21511618

#SPJ3

The correct answer is B. y=5x+17.

To write the equation of a line that is perpendicular to the given line y-3=-1/5(x+2) and that passes through the point (-2, 7), first, we need to find the slope of the given line and then determine the slope of the perpendicular line, which will be the negative reciprocal of the given line's slope. The slope of the given line is -1/5, so the slope of the line perpendicular to it will be 5 (since the negative reciprocal of -1/5 is 5).

Next, we use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point through which the line passes. Plugging in our slope of 5 and the point (-2, 7), the equation becomes:

y - 7 = 5(x - (-2))

Expand and simplify to solve for y:

y - 7 = 5x + 10

y = 5x + 17

The correct answer is B. y=5x+17.

If you flip a coin or roll a 6-sided die, what is the probabilty that you will flip a tails and roll a 2?

Answers

Answer:

[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

P(tail) = [tex]\frac{1}{2}[/tex]

P(2) = [tex]\frac{1}{6}[/tex]

P(tail and 2 ) = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{6}[/tex] = [tex]\frac{1}{12}[/tex]


What is the value of A in the matrix equation below?

Answers

A=
[tex] \binom{ - 3 \: \: \: - 14 \: \: \: \: \: \: 7 \: \: \: \: 18}{ - 3 \: \: \: \: \: \: \: \: 2 \: \: \: \: \: \: \:5 \: \: \: \: - 6 } [/tex]
Answer:The third image(Option B)

Answer:

Option (b) is correct.

The matrix A is [tex]\begin{pmatrix}-3&-14&7&18\\ -13&2&-5&-6\end{pmatrix}[/tex]

Step-by-step explanation:

Given : A matrix form,

[tex]A+\begin{pmatrix}3&9&-1&-8\\ \:16&-2&3&13\end{pmatrix}=\begin{pmatrix}0&-5&6&10\\ \:3&0&-2&7\end{pmatrix}[/tex]

we have to find the value of matrix A

Consider the given matrix form,

[tex]A+\begin{pmatrix}3&9&-1&-8\\ \:16&-2&3&13\end{pmatrix}=\begin{pmatrix}0&-5&6&10\\ \:3&0&-2&7\end{pmatrix}[/tex]

when A + B = C

Then A = C - B

That is

[tex]A=\begin{pmatrix}0&-5&6&10\\ \:3&0&-2&7\end{pmatrix}-\begin{pmatrix}3&9&-1&-8\\ \:16&-2&3&13\end{pmatrix}[/tex]

Subtract the elements in the matching position, we get,

[tex]A=\begin{pmatrix}0-3&\left(-5\right)-9&6-\left(-1\right)&10-\left(-8\right)\\ 3-16&0-\left(-2\right)&\left(-2\right)-3&7-13\end{pmatrix}[/tex]

Simplify, we get,

[tex]A=\begin{pmatrix}-3&-14&7&18\\ -13&2&-5&-6\end{pmatrix}[/tex]

Thus, The matrix A is [tex]\begin{pmatrix}-3&-14&7&18\\ -13&2&-5&-6\end{pmatrix}[/tex]

What is the first step in simplifying the following expression: 2 + 3(4 + 5×2) − 8 + 3^2

Question options:


2 + 3



5 x 2



3^2


4 + 5

Answers

Answer:

5 x 2 inside the parenthesis

Step-by-step explanation:

We need an order of operations to ensure we always arrive at the correct answer. It gives us a consistent way to work with numbers. We use the mnemonic device like PEMDAS to remember the correct order.

P-parenthesis

E-exponents

M-multiplication

D-division

A-add

S-subtract.

We apply them left to right doing inner operations before outer operations.

There fore our first step is in the parenthesis and multiplication because it is the inner most operations. 5 x 2 inside the parenthesis.

Please help me with these problems

Answers

Answer:

1.a=2

2.  C  x=2  and x=-3

Step-by-step explanation:

The standard form for the quadratic function is  

ax^2 +bx+c

so  we need to rewrite the function to be in this form

2x^2 -10 = 7x

Subtract 7x from each side

2x^2 -7x-10 = 7x-7x

2x^2 -7x-10 = 0

a =2, b= -7  c=-10


2.  The quadratic formula is

-b ± sqrt(b^2 -4ac)

----------------------------

2a


2x^2 + 2x=12

Lest get the equation in proper form

2x^2 + 2x-12 = 12-12

2x^2 +2x-12 =0

a=2  b=2 c=-12

Lets substitute what we know

-2 ± sqrt(2^2 -4(2)(-12))

----------------------------

2(2)

-2 ± sqrt(4+96)

----------------------------

2(2)

-2 ± sqrt(100)

----------------------------

4

-2 ± 10

----------------------------

4

-2 + 10               -2-10

-----------   and  --------------

4                             4

8/4   and -12/4

2  and -3

A fruit stand has to decide what to charge for their produce. They need \$10$10 for 44 apples and 44 oranges. They also need \$12$12 for 66 apples and 66 oranges. We put this information into a system of linear equations. Can we find a unique price for an apple and an orange?

Answers

Answer: No, we can't find a unique price for an apple and an orange.

Step-by-step explanation:

Since we have given that

Cost of 4 apples and 4 oranges = $10

Cost of 6 apples and 6 oranges = $12

We need to find the unique price for an apple and an orange.

According to question, our equations will be

[tex]4x+4y=\$10\\\\6x+6y=\$12[/tex]

since it is equation of parallel lines, as

[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}\\\\\frac{4}{4}=\frac{6}{6}\neq \frac{10}{12}[/tex]

Hence, No, we can't find a unique price for an apple and an orange.

help!!
1.does y vary directly with x? If it does, write an equation for the direct variation.

x|y
−3|2.25
1 |−0.75
4 |−3

Answers

Answer:

y = -.75 x

Step-by-step explanation:

To determine if y varies directly with x, we look at y/x and see if it is a constant

y/x = 2.25/-3 = -.75

     = -.75/1 = -.75

     =-3/4 = -.75

Since it is a constant, it has direct variation.  The constant of variation is -.75

y = -.75 x

How much money should be deposited today in an account that earns 3 % compounded semiannually so that it will accumulate to $8000 in three? years

Answers

Final answer:

To calculate the amount that should be deposited today in an account that earns 3% compounded semiannually to accumulate to $8000 in three years, we can use the compound interest formula.

Explanation:

To calculate the amount that should be deposited today in an account that earns 3% compounded semiannually to accumulate to $8000 in three years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future value, P is the principal, r is the interest rate, n is the number of compounding periods per year, and t is the number of years. In this case, the future value (A) is $8000, the interest rate (r) is 3% or 0.03, the number of compounding periods per year (n) is 2 (semiannual compounding), and the number of years (t) is 3. Plugging these values into the formula, we get:

A = P(1 + r/n)^(nt)

$8000 = P(1 + 0.03/2)^(2*3)

$8000 = P(1 + 0.015)^(6)

$8000 = P(1.015)^(6)

To find the value of P, we divide both sides of the equation by (1.015)^6: P = $8000 / (1.015)^6. Using a calculator, we find that P ≈ $7383.42. Therefore, approximately $7383.42 should be deposited today in the account.

Learn more about Compound interest calculation here:

https://brainly.com/question/13160996

#SPJ3

As a membership fee a health club charges a one-time amount of $40 in charges $25 for each month the total fee after M months is $240 what is the value of M

Answers

40 + 25M = 240
25M = 200
M = 8
8 months

The equation for this problem is x=25(m)+40

If the value of x=240, then the value of m=8.

Which points lie on more than one plane? M and R A and S X and Y M and S

Answers

X and Y.............

Answer:

Points X and Y lie on more than one plane.

Step-by-step explanation:

From the  figure attached we have to find the points which lie on more than one plane.

M and R :

These are the points which lie on only one plane painted in yellow color.

A and S

These points lie on a plane perpendicular to the plane painted in yellow color.

X and Y :

These points lie on both the planes, painted in yellow color and the plane perpendicular to this.

M and S :

Point M lies on a plane in yellow color and point S lies on a plane perpendicular to the yellow plane.

Therefore, points X and Y lie on more than one plane.

check my answer?

what are the real and imaginary parts of the complex number?
-7+8i
the real part :: -7 ( my answer )
the imaginary part :: 8i ( my answer )

Answers

Answer:

The real part is -7

The imaginary part 8i

Step-by-step explanation:

A complex number is in the from a +bi

The real part is a and the imaginary part is bi

-7+8i

The real part is -7

The imaginary part 8i

Quentin has 6 5/8 feet of lumber but needs another 2 3/4feet to complete the project he's working on. How much total wood will the project have used when finished?

Answers

Answer:

Total wood required for the project will be 9 3/8 feet.

Step-by-step explanation:

As given in the question Quentin has lumber of length = 6 5/8

feet =53/8 feet.

Now Quentin needs more lumber = 2 3/4 feet =11/4 feet or 22/8 feet.

So we can get total wood required by adding these two figures

That is = 53/8 + 22/8

           = (53 +22)/8

           = 75/8

            = 9 3/8 feet

Answer:

[tex]The\ total\ wood\ will\ the\ project\ have\ used\ be\ 9 \frac{3}{8}.[/tex]

Step-by-step explanation:

As given

[tex]Quentin\ has\ 6 \frac{5}{8}\ feet\ of\ lumber\ but\ needs\ another\ 2 \frac{3}{4}\ feet\ to\ complete\ the\ project\ he's\ working\ on.[/tex]

i.e

 [tex]Quentin\ has\ \frac{53}{8}\ feet\ of\ lumber\ but\ needs\ another\ \frac{11}{4}\ feet\ to\ complete\ the\ project\ he's\ working\ on.[/tex]        

 [tex]Total\ wood\ will\ the\ project\ have\ used =\frac{53}{8} + \frac{11}{4}[/tex]

L.C.M of (8,4) = 8

Than

[tex]Total\ wood\ will\ the\ project\ have\ used =\frac{53 + 11\times 2}{8}[/tex]                              

[tex]Total\ wood\ will\ the\ project\ have\ used =\frac{53 + 22}{8}[/tex]       [tex]Total\ wood\ will\ the\ project\ have\ used =\frac{75}{8}[/tex]  

[tex]Total\ wood\ will\ the\ project\ have\ used = 9 \frac{3}{8}[/tex]  

[tex]Therefore\ the\ total\ wood\ will\ the\ project\ have\ used\ be\ 9 \frac{3}{8}.[/tex]


If there are 1.61 kilometers in a mile and also 5280 feet in a mile, the how many feet are there in 3 kilometers

Answers

Answer:

9,839 ft

Step-by-step explanation:

Please help on this one ?

Answers

1 ║ 1               2                  -3               2

                       1                   3               0

--------------------------------------------------------------------

       1              3                   0              [tex]\boxed{2}[/tex]

⇒ The Remainder is 2

Monday Janel and $16 for two hours of babysitting getting paid the same rate she earns $40 for babysitting on Saturday how many hours did you know babysit on Saturday

Answers

She babysat for five hours.

To get this answer, you need to first divide 16 by 2 to get her hourly rate, which is 8. Then, you divide 40 by the hourly rate and you should get your answer as 5. Hope this helped!

use the given information to prove that FG=HF

Answers

1. EG = HJ (Given)

2. EG = EF + FG, HJ = HF + FJ (Seg. Add. Prop.)

3. EF + FG = HF + FJ (Subst. Prop.)

4. EF =  FJ (Given)

5. FG = HF (Subtraction Prop.)

It's challenging to demonstrate that FG equals HF as these may represent different elements or variables in different mathematics or physics contexts. At its simplest, FG seems to represent the gravitational force between two masses, and HF would need to represent the same force to hold true.

The equation given seems to pertain to gravitational forces where FG represents the gravitational force between two masses, electron and proton.

Given that FG = GMM where G is the gravitational constant (6.67×10-¹1 N·m²/kg²), m and M represent the masses of the electron and proton, to prove that FG=HF, it implies that HF represents the same gravitational pull.

However, without more detailed context or information, I can't further demonstrate or prove that FG does equal HF as these terms may refer to different elements or variables in different contexts of mathematics or physics problems.

For more such questions on gravitational force, click on:

https://brainly.com/question/18961003

#SPJ2

Someone plz help!!!!!!!!
The table shows different geologic time periods:


Period Number of Years Ago

Jurassic 2.08 ⋅ 10^8

Silurian 4.38 ⋅ 10^8

Tertiary 6.64 ⋅ 10^7

Triassic 2.45 ⋅ 10^8

Order the time periods from oldest to youngest.

A. Tertiary, Jurassic, Triassic, Silurian

B. Jurassic, Triassic, Silurian, Tertiary

C. Silurian, Triassic, Jurassic, Tertiary

D. Triassic, Silurian, Jurassic, Tertiary

Answers

answer: C. Silurian, Triassic, Jurassic, Tertiary

Points A and B on the coordinate grid below show the positions of two midfield players of a soccer team: Coordinate grid shown from negative 4 to positive 4 on x-axis and negative 4 to positive 4 on y-axis. From the origin, point A is located 1 unit to the left and 3.5 units down. From the origin, point B is located 1 unit to the right and 3.5 units down. Which statement best describes the relationship between the positions of the two midfield players? B is A reflected across the y-axis; only the signs of the x-coordinates of A and B are different. B is A reflected across the y-axis; only the signs of the y-coordinates of A and B are different. B is A reflected across the x-axis; only the signs of the x-coordinates of A and B are different. B is A reflected across the x-axis; only the signs of the y-coordinates of A and B are different.

Answers

Answer:

Point B is Point A reflected across the y-axis.

Step-by-step explanation:


Answer:

B is A reflected across the y-axis; only the signs of the x-coordinates of A and B are different.

Step-by-step explanation:

When a point is reflected across the y-axis, the x-coordinate of the point is negated.  Algebraically,

(x, y)→(-x, y)

Point A is located at (-1, -3.5) and point B is located at (1, -3.5).  The only difference between the two points is that the x-coordinate is negated; this means it is a reflection through the y-axis.

The arrow at the maze entrance indicates that the robot will be heading east when it enters the maze. When programming the robot, let the complex number d represent the direction the robot is facing. As the robot changes direction, the value of d will also change; so, the value of d is dependent on where the robot is in the maze. At the start of the maze, what is the value of d?

Answers

Answer:

d=1

Step-by-step explanation:

If North is i and South is -i

East is 1 and West is -1

The robot is facing East as it enters the maze, it will have a starting value of 1

Answer:

The value of d at the start of the maze will be 1 because 1 represents East .

The triangles are similar. The area of the larger triangle is 200 cm².
What is the area of the smaller triangle?


12.5 cm²

50 cm²

100 cm²

200 cm²

Answers

Answer:

The correct answer option is 12.5 cm[tex]^2[/tex].

Step-by-step explanation:

We are given two triangles that are similar with one of the corresponding sides with known values.

The ratio of the corresponding sides of the smaller triangle to the larger triangle is [tex]\frac{16}{64} =\frac{1}{4}[/tex]. So the ratio between the areas of these triangles will be [tex]\frac{1}{4^2} =\frac{1}{16}[/tex].

If the area of the larger triangle is 200 cm[tex]^{2}[/tex] then the area of the smaller triangle will be = [tex]\frac{1}{16} *200=12.5[/tex].

Therefore, the area of the smaller triangle is 12.25 cm[tex]^2[/tex].

Formula to find Area of a triangle is

A=(height×base)/2

base of bigger triangle is=64cm^2

base of smaller triangle is=16cm^2

Area of bigger triangle is =200cmCm^2

area of smaller triangle=?

we imagine

height = base

then area of bigger trianglewillbe=64*64/2=2048

and area of smallertriangle will be=16*16/2==128

but we are given thatarea of bigger triangle is 200

when we  divide 2048/10

it approximately gives 200

similarly when we divide 128/10

it approximately gives 12.5cm^2

hence area of smaller triangle is 12.5cm^2

13. Find a cubic function with the given zeros. 7, -3, 2

Answers

[tex]\bf \begin{cases} x=7\implies &x-7=0\\ x=-3\implies &x+3=0\\ x=2\implies &x-2=0 \end{cases}~\hspace{7em}(x-7)(x+3)(x-2)=\stackrel{y}{0} \\\\\\ (x^2-4x-21)(x-2)=y \\\\\\ x^3-4x^2-21x-2x^2+8x+42=y\implies x^3-6x^2-13x+42=y[/tex]

Write an addition equation that will have a new thousand, a new hundred, and a new ten. Then solve. Explain how you chose your numbers.

Answers

Answer:

1987 + 1257 = 3247

Step-by-step explanation:

We are going to use a base number to start from. That number is 1,987 where the thousand is 1, the hundred is 9 and the ten is 8.

Then we are going to add 1,257 which will be 3,247. Thus we will have a new thousand which is 3 (formerly 1), a new hundred which is 2 (formerly 9), and finally, a new ten which is 5 (formerly 7).

1987 + 1257 = 3247 gives you a new thousand, a new hundred and a new ten.

Answer:

Step-by-step explanatcagion:

What is the growth factor of the following example? Assume time is measured in the units given.
Water usage is increasing by 3% per year.

Answers

Answer: Growth factor is 1.03 per year.

Correct option is C option.


Step-by-step explanation:

Given that water usage is increasing by 3% per year.

Time is measured in the years as given.

We need to find the growth factor for 3% increase per year.

We know a percent can be written decimal form by dividing by 100.

Therefore, 3% could be written as 3/100 = 0.03.

But the water usage would be increase by the factor of 1+0.03 that is 1.03.

Therefore, growth factor of increase in water usage would be 1.03.

If William has 5 different shirts and 7 different pairs of pants, how many different combinations could he wear?

Answers

Final answer:

The question is asking how many different outfit combinations William can form if he has 5 shirts and 7 pants. It's a simple multiplication of the two numbers (5*7) resulting in 35 different combinations. Therefore, William could wear a different outfit for 35 days without repeating.

Explanation:

The subject of this question is combinatorics, a branch of mathematics concerned with counting, both as a means and an end. In this specific context, we are looking at the number of different combinations that William can wear with the clothes he has. Since each shirt can be worn with any pair of pants, this translates into a simple product calculation.

William has 5 different shirts and 7 different pairs of pants. So, the total number of combinations of outfits he can put together is calculated by multiplying these numbers together. Hence, 5 shirts * 7 pants = 35 combinations.

This means that if William chooses a different combination each day, he could go for 35 days without wearing the same outfit twice.

Learn more about Combinations here:

https://brainly.com/question/37999460

#SPJ3

An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events:
a. chocolate chosen
b. strawberry chosen
c. vanilla chosen
d. ice cream on a cone
e. ice cream in a cup
Find the probability that the ice cream was sold on a cone and was strawberry flavor

Answers

Answer:


Step-by-step explanation:

Sales of the chocolate ice cream is 45%, 30% for strawberry and 25% (100%-45%-30%) of vanilla.

Percentages of cone sales for chocolate, strawberry and vanilla are 75%, 60% and 40%respectively.

A. Probability chocolate chosen: 45%=0.45

B. Probability strawberry chosen: 30%=0.30

C. Probability vanilla chosen:25%=0.25

D. Probability ice cream on a cone: 75%×45%+60%×30%+40%×25%

                                                          =0.75×0.45+0.60×0.30+0.40×0.25

                                                          =0.3375+0.18+0.1

                                                          =0.6175

E. Probability ice cream in a cup: 1- Probability ice cream in a cone

                                                     =1-0.6175

                                                     =0.3825

Probability that the ice cream sold on a cone and was strawberry flavoured is : 30%×60%

=0.30×0.60

=0.18

Answer: 0.18.

 

Step-by-step explanation: Let us define the following events

A= event that chocolate chosen,

B=event that strawberry chosen,

C=event that vanilla chosen,

D=event of choosing ice-cream on a cone

and

E=event of choosing ice-cream on a cup.

Then, according to the given information, we have

P(A)=0.45, P(B)=0.30, P(C)=0.25, P(A\D)=0.75, P(B\D)=0.60 and P(C\D)=0.40.

Therefore, the probability that the ice-cream was sold on a cone and was strawberry flavour is given by

[tex]P(B\cap D)=P(B)\times 0.60\\\Rightarrow P(B\cap D)=0.30\times 0.60\\\Rightarrow P(B\cap D)=0.18.[/tex]

Thus, the required probability is 0.18.

Find a parametric representation for the surface. The part of the sphere x2 + y2 + z2 = 144 that lies between the planes z = â’6 and z = 6. (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of θ and/or Ď•.) (where â’6 < z < 6)

Answers

Final answer:

The parametric equations that represent the sphere surface between the planes z=±6 are x = 12*sin(θ)*cos(φ), y = 12*sin(θ)*sin(φ), and z = 12*cos(θ), with θ and φ being between π/3 and 2π/3, and 0 and 2π respectively.

Explanation:

This question involves a mathematical concept known as parametric representation of a surface, specializing in spheres and planes. In a 3D coordinate system, the equation of a sphere is given by x² + y² + z² = r² where r is the radius of the sphere, but we restrict the z variable to lie in a certain range, which is between -6 and 6 in this situation.

To represent the sphere in parametric form, we often use spherical coordinates. The relationships between Cartesian coordinates and spherical coordinates are as follows: x = r*sin(θ)*cos(φ), y = r*sin(θ)*sin(φ), z = r*cos(θ). Here r = √144 =12, is the radius of the sphere.

Given the restrictions z = ±6, we have cos(θ) = ±6/12 = ±1/2, or θ = π/3 and 2π/3. So, the spherical coordinates range within 0 <= φ <= 2π and π/3 <= θ <= 2π/3.

This gives the parameters of the restricted surface in terms of θ and φ those are as follows: x = 12*sin(θ)*cos(φ), y = 12*sin(θ)*sin(φ), and z = 12*cos(θ).

Learn more about Parametric Representation here:

https://brainly.com/question/34159526

#SPJ3

Final answer:

The parametric equations which represent the part of the sphere x² + y² + z² = 144 that lies between the planes z = -6 and z = 6 are: x = 12*sin(θ)*cos(Ď•), y = 12*sin(θ)*sin(Ď•), z = 12*cos(θ), with 60° ≤ θ ≤120° and 0° ≤ Ď• ≤ 360°.

Explanation:

The question asks for a parametric representation of part of a sphere lying between two planes. The given sphere equation is x² + y² + z² = 144, and the two planes are defined by z = -6 and z = 6. This is a common problem in multivariable calculus, and we solve it using spherical coordinates. In spherical coordinates, x= r*sin(θ)*cos(Ď•), y= r*sin(θ)*sin(Ď•) and z= r*cos(θ) where r is the radius, θ is the inclination angle, and Ď• is the azimuthal angle. For the given sphere, r = √144 = 12.

The bounds for z adds constraints to our inclination angle θ. Given -6 ≤ z ≤ 6, we determine corresponding bounds on θ. For z = r*cos(θ), we have -6 ≤ 12cos(θ) ≤ 6, or -1/2 ≤ cos(θ) ≤ 1/2. This yields θ values between 60° and 120°. The parametric equations describing the part of the sphere between the planes z = -6 and z = 6 are:

x = 12*sin(θ)*cos(Ď•)

y = 12*sin(θ)*sin(Ď•)

z = 12*cos(θ)

where 60° ≤ θ ≤120° and 0° ≤ Ď• ≤ 360°.

Learn more about Parametric Representation of Sphere here:

https://brainly.com/question/34776915

#SPJ11

Other Questions
what is the relative humidity when the air temperature is 28 degrees celcius and the wet bulb temperature is 20 degrees celcius? What was the result of the Korean War?A.Korea reunited as a single nation.B.Both sides occupied nearly the same territory as at the start of the war.C.Chinese troops under Mao Zedong succeeded in taking over South Korea.D.UN troops under Douglas MacArthur drove the communists out of North Korea. In One hour a bakery sold five muffins and nine bagels for a total of $25.50 the next hour the bakery sold three muffins and 12 bagels for a total of $28.50 let M represent the price of one muffin and B represent the cost of one bagel Draco wrote the following system of linear equations to solve for the cost of each item. 5m+9b=28.50 3m+12b=25.50 What is Dracos error? A.) Draco should have set the first equation equal to 25.50 and the second equation equal to 28.50. B.) Draco should have written the first equation as 3m+9b= 25.50. C.) Draco should have written 9b in the second equation and 12b in the first equation. D.) Draco should have written the second equation as 5m+12b=28.50. The equation shows cellular respiration during cellular respiration glue close combined with oxygen to form carbon dioxide water in ATP what happens to the energy and bonds and glue closeC6H1206 + 602 + 6H20 +ATP Scientists who study the anatomy of the systems in the human body focus their studies on How did saul rule the people of ancient israel What is the approximate solution to the equation 2t=38 ? 0.1906 3.6380 5.2479 19.0000 In what way was Latin America impacted by the Great Depression? A. Exports from Latin American countries increased. B. Latin America was insulated from the Great Depression because of little trade with the rest of the world. C. US investment money was cut off, causing large economic downturns. D. US investment money increased due to new opportunities in Latin America. Please help me solve this. A mutant strain of E. coli produces -galactosidase in the presence and in the absence of lactose. Where in the operon might the mutation in this strain occur and why?A-in the operator region, where the mutation leads to the failure of the operator to normally bind the repressorB-in the CAP binding site, where the mutation leads to the inefficiency of RNA polymerase activityC-in the promoter region of the operon, where the mutation leads to the failure of the RNA polymerase to bind to the promoterD-near the lacI gene, where the mutation leads to increased levels of lac repressor being madeE-in the lacI gene, which leads to an inactive lac repressorF-in the operator region, which leads to increased binding of the lac repressor to the operator Which layer in the atmosphere contains the most water vapor and gases? A. thermosphere B. stratosphere C. mesosphere D. troposphere Which statement best explains why cellular respiration in plants and other organisms is dependent on photosynthesis Who has became Britains prime minister in 1757 affected the outcome of the war in America between the British and French 1. Benjamin Franklin 2. James Wolfe 3.Louis de Montcalm 4. William Pitt What did the book How the Other Half Lives dramatize?HELP ASAPPLEASE HELP ME According to the Partnership for 21st Century Learning, what are three critical skill sets that modern employers look for in employees Find the number of units that produce a maximum revenue, R =95x-0.1x^2, where R is the total revenue in dollars and x is the number of units sold I need the correct answer, please don't guess !! WORTH 50 POINTS!!In many ecosystems a shortage of _________ limits the growth of many producersa. oxygenb. waterc. bacteria Can someone show me step by step? which description is most accurate of fine, thin hair? The perimeter of the base of a pentagonal prism is 45 cm. what is the width of the rectangular side of that prism? Steam Workshop Downloader