On a coordinate plane, a curved line begins at point (1, 2) and ends at (5, 4).
What is the range of the function on the graph?
all real numbers
all real numbers greater than or equal to 0
all real numbers greater than or equal to 1
all real numbers greater than or equal to 2
Answers
Step-by-step explanation:
there must be something missing here (I guess, the graph).
because just by looking at the 2 points, all 4 answer options could be wrong, or all 4 could be right.
just basing on the point coordinates I see the functional values (y) go from 2 to 4.
but we have no clue about what that curved function does in between these 2 points.
please provide the full information.
Related Questions
what is the length of RU?
Answers
Answer:
Length of RU is 20 units.
Step-by-step explanation:
In ΔRSt and ΔRUT,
ST ≅ TU [Given]
RT ≅ RT [Reflexive property]
∠RTS ≅ ∠RTU [Both the angles are the right angles]
ΔRTS ≅ ΔRTU [By SAS property of congruence]
Therefore, RS ≅ RU [By CPCTC (corresponding parts of the congruent triangles are congruent]
8x = 6x + 5
8x - 6x = 5
2x = 5
x = 2.5
Length of RU = (6x + 5)
= 6(2.5) + 5
= 15 + 5
= 20
Length of RU is 20 units.
Community Gym charges a $70 membership fee and a $55 monthly fee. Workout Gym charges a $170 membership fee and a $45 monthly fee. After how many months will the total amount of money paid to both gyms be the same? What will the amount be?
Answers
Answer:
10 months and the amount is $620
Answer:
Months: 10
Amount: $620
Step-by-step explanation:
CG=Community Gym
CW=Workout Gym
A membership fee would be a one-time cost so you start by adding the membership cost.
CG: +70
CW: +170
A monthly fee would be a continuing cost so you multiply the fee by the number of months. If you don't know the number of months then you put a variable next to the cost of the continuing charge. Think of it as the number multiplied by the variable like this example (5*x+3). A variable can be any letter, it is m here to remind you that we're trying to figure out months.
CG: 55m+70
CW: 45m+170
Once you have your continuing fee and the one-time fee you substitute the variable for a number until you get the right number. The number that you substitute for the variable is the number of months.
CG:
(55*1)+70=125
(55*2)+70=180
(55*3)+70=235
(55*4)+70=290
(55*5)+70=345
(55*10)+70=620
CW:
(45*1)+170=215
(45*2)+170=260
(45*3)+170=305
(45*4)+170=380
(45*5)+170=395
(45*10)+170=620
Hope this was helpful, Sorry if I missed anything
HELP ME PLEASE I NEED A EXPLIANTION
Answers
Answer:
i DONT KNOW THIS BECAUSE I HAVEN'T GONE OVER THIS IN SCHOOL
Step-by-step explanation:
tonya and jill each opened savings accounts. tonya started with $60 and deposited $20 each month. jill started with $20 and deposited $40 each month. if they continue to make deposits at the same rate, when will they have the same amount of money
Answers
The month they would have the same amount of money is 2 months.
When would they have the same amount of money?The linear equation that can be used to represent the total amount of money saved by each person is
Total amount saved = amount started with + (amount deposited per month x number of months)
Amount saved by Tonya = $60 + $20m
Amount saved by Jull = $20 + $40m
When they save the same amount of money, the two two above equations would be equal:
60 + 20m = 20 + 40m
In order to determine the value of m, take the following steps:
60 - 20 = 40m - 20m
40 = 20m
m = 40 / 20
m = 2
Substitute for m in the equation that represents the total amount of money saved by Tonya:
$60 + $20(2)
$60 + $40 = $100
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The area, Acm², of a patch of mould is measured daily. The area, n days after the measurements started, is given by the formula A = Asub0b^n". When n = 2, A = 1.8 and when n = 3, A = 2.4. Find the value of b.
Answers
Answer:
b = (4/3), with rounding
Step-by-step explanation:
Area = A, in cm^2
n = days
A(n) = \(A_{0}\)\(b^{n}\)
------------------
Data:
n = 2, A = 1.8
A(n) = \(A_{0}\)\(b^{n}\)
1.8 = \(A_{0}\)\(b^{2}\)
n = 3, A = 2.4
2.4 = \(A_{0}\)\(b^{3}\)
Although we are not given the initial area, we can still make the calculation since we have two data points and each has the same initial area, \(A_{0}\). Lets take the first equation and multiply it by b, in order to bring the \(b^{2}\) to \(b^{3}\)
1.8 = \(A_{0}\)\(b^{2}\)
b(1.8 = \(A_{0}\)\(b^{2}\))
1.8b = \(A_{0}\)\(b^{3}\)
We can know from the second equation that 2.4 = \(A_{0}\)\(b^{3}\) . We can eliminate this term in the above relationship by substituting 2.4:
1.8b = \(A_{0}\)\(b^{3}\)
1.8b = 2.4
b = 1.3333
or (4/3)
Check:
Does the value of (4/3) for b work for both data points? To check this, we do need to assume an initial starting area. Lets assume the starting area, \(A_{0}\) = 1.
n = 2, A = 1.8, b = (4/3)
A(n) = \(A_{0}\)\(b^{n}\)
1.8 = 1*\((4/3)^{n}\)
1.8 = 1.78 Close enough?
n = 3, A = 2.4, b = (4/3)
2.4 = \(A_{0}\)\((4/3)^{n}\)
2.4 = 1*\((4/3)^{3}\)
2.4 = 2.37 Close enough?
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Fwam sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
168 visitors purchased no costume.
252 visitors purchased exactly one costume.
47 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase no costume as a percent to the nearest whole number.
Answers
The probability that the next person will purchase no costume is 36% to the nearest whole number.
We have,
To express the probability that the next person will purchase no costume as a percent to the nearest whole number, we need to use the total number of visitors to the website as the denominator and the number of visitors who purchased no costume as the numerator.
The total number of visitors to the website is:
168 + 252 + 47 = 467
The number of visitors who purchased no costume is 168.
So the probability that the next person will purchase no costume is:
168/467 = 0.3609
To express this as a percent, we multiply by 100:
0.3609 × 100
= 36.09
Rounding this to the nearest whole number, we get:
36%
Therefore,
The probability that the next person will purchase no costume is 36% to the nearest whole number.
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Harish's soccer team is trying to raise $5,092 to travel to a tournament in Florida, so they decided to host a pancake breakfast. Each person must pay $38 for the breakfast. How many people need to attend their breakfast in order to raise $5,092?
Answers
Answer: 134 people
Step-by-step explanation:
Data: The soccer team needs to raise $5,092
They are hosting a pancake breakfast to do so and are charging $38 to do so
The number of people they need to attend their breakfast for the money to be raised: $x
Step one, make the equation
$38x=$5,092
Reason: Since we know that the number of people(x) times $38 will equal $5,092 so to put it into an equation will make it easier to solve.
Step two, Isolate x by dividing by 38 on both sides
$38x/38=$5,092/38=x=134
Reason: Since you are trying to find the number of people(x) you have to isolate it. the way to do that is by getting rid of the 38 next to it and by dividing, you cancel out the multplication and get rid of the 38. However, since what you do to one side you do to the other, you divide 5,092 by 38 to get the answer of 134.
Answer: 134 people
I hope this helps!
solve for p: 3p-2=2p/5+p-2/3
Answers
Answer:
P = 0.83 or p= 5/6
Help Pleaseeee........
Answers
Answer:
5/90
Step-by-step explanation:
5/90 is the answer
How to plot 69, 88,94,73,78,90, and 68 in a box and whisker plot (ASAP) also find the 5 part summary
Answers
The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.
To create a box and whisker plot for the given dataset {69, 88, 94, 73, 78, 90, 68}, follow these steps:
Step 1: Arrange the data in ascending order:
68, 69, 73, 78, 88, 90, 94
Step 2: Find the five-number summary:
Minimum: The smallest value in the dataset, which is 68.
First quartile (Q1): The median of the lower half of the dataset. In this case, it's the median of {68, 69, 73}, which is 69.
Median (Q2): The middle value of the dataset. In this case, it's 78.
Third quartile (Q3): The median of the upper half of the dataset. In this case, it's the median of {88, 90, 94}, which is 90.
Maximum: The largest value in the dataset, which is 94.
Step 3: Create the box and whisker plot:
Draw a number line with a range from the minimum (68) to the maximum (94).
Mark the first quartile (Q1) at 69.
Mark the median (Q2) at 78.
Mark the third quartile (Q3) at 90.
Draw a box from Q1 to Q3.
Draw a vertical line (whisker) from the box to the minimum (68) and another vertical line from the box to the maximum (94).
The resulting box and whisker plot for the given dataset would look like this:
|
94| ▄
| ╱ ╲
90| ╱ ╲
| ╱ ╲
88| ▇ ▂
| ▇ ▂
78| ▇ ▂
| ▇ ▂
73| ╱ ╲
| ╱ ╲
69| ▃ ▃
| ╱ ╲
68| ╱ ╲
|_________________________________
68 73 78 88 94
This plot represents the distribution of the given dataset, showing the minimum, maximum, first quartile (Q1), median (Q2), and third quartile (Q3).
The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.
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Suppose annual salaries for sales associates from a particular store have a bell-shaped distribution with a mean of $32,500 and a standard deviation of $2,500. Refer to Exhibit 3-3. The z-score for a sales associate from this store who earns $37,500 is
Suppose annual salaries for sales associates from a particular store have a bell-shaped distribution with a mean of $32,500 and a standard deviation of $2,500. Refer to Exhibit 3-3. The z-score for a sales associate from this store who earns $37,500 is
Answers
To find the z-score for a sales associate who earns $37,500, we can use the formula:
z = (x - μ) / σ
Where:
x is the value we want to convert to a z-score (in this case, $37,500),
μ is the mean of the distribution (in this case, $32,500), and
σ is the standard deviation of the distribution (in this case, $2,500).
Substituting the given values into the formula, we have:
z = (37,500 - 32,500) / 2,500
z = 5,000 / 2,500
z = 2
Therefore, the z-score for a sales associate who earns $37,500 is 2.
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The z-score for a sales associate earning $37,500 in a system where the mean salary is $32,500 and the standard deviation is $2,500 has a z-score of 2. This score indicates that the associate's salary is two standard deviations above the mean.
Explanation:The z-score represents how many standard deviations a value is from the mean. In this case, the value is the salary of a sales associate, the mean is the average salary, and the standard deviation is the average variation in salaries.
We calculate the z-score by subtracting the mean from the value and dividing by the standard deviation, like so:
Z = (Value - Mean) / Standard Deviation
So, the z-score for an associate earning $37,500 would be:
Z = ($37,500 - $32,500) / $2,500
This gives us a z-score of +2, indicating that a salary of $37,500 is two standard deviations above mean.
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Wayne is recording the number of hours he sleeps over different periods of time. The table provided shows the number of hours Wayne sleeps during the respective amount of days.
Number of Days Hours of Sleep
3 15
6 30
9 45
12 60
15 75
What is the rate of change of Wayne's hours of sleep with respect to each day?
A.
6 hours per day
B.
5 hours per day
C.
8 hours per day
D.
3 hours per day
Answers
The rate of change of Wayne's hours of sleep with respect to each day is 5 hours per day.
What is the rate of change of Wayne's hours of sleep?The rate of change of Wayne's hours of sleep with respect to each day is calculated as follows;
Mathematically, the formula is given as;
rate of change of sleep = change in sleep / change in time of sleep
The change in the sleep pattern = 30 - 15 = 15 hours
The change in the time of sleep = 6 - 3 = 3 days
The rate of change of Wayne's hours of sleep with respect to each day is calculated as
rate of change of sleep = ( 15 hours ) / ( 3 days )
rate of change of sleep = 5 hours per day
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What would be the 50th term than?
Answers
The 50th term is 290.
What is an arithmetic sequence?It is a sequence where there is a common difference between each consecutive term.
Example:
12, 14, 16, 18, 20 is an arithmetic sequence.
We have,
-4, 2, 8, 14,
This is an arithmetic sequence.
First term = a = - 4
Common difference.
d = 2 - (-4) = 6
d = 8 - 2 = 6
Now,
The nth term = a + (n -1)d
So,
n = 50
a = -4
d = 6
50th term.
= -4 + (50 - 1) 6
= - 4 + 49 x 6
= - 4 + 294
= 290
Thus,
The 50th term is 290.
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The complete question:
What is the 50th term of the sequence that begins −4, 2, 8, 14, ...?
Reena bought a jacket for £45 . six months later ,she sold it for £34.65.What was her percentage loss?
Answers
When Reena bought a jacket for $45 and after six months later she sold it for $34.65, then the percentage loss is 25%
Given,
Reena bought a jacket for = $45
Selling price of jacket = $34.65
Here, selling price is lower than cost price, so we can consider it as loss
We know,
Loss percentage = (Loss / Initial cost)×100
Loss = Initial cost - Selling price
Loss = 45 -34.65= $10.35
Loss percentage =\((\frac{10.35}{45}) 100\)
=0.25×100
=25%
Hence, when Reena bought a jacket for $45 and after six months later she sold it for $34.65, then the percentage loss is 25%
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( −15/20÷25/30 ) – ( −3/10 x 12 )
Answers
Answer:
2.7
Step-by-step explanation:
the graph of y=-3x+4 is:
Answers
Answer:
(2,-2) & (0,4)
Step-by-step explanation:
Borrar la selección
Pregunta 2: En una restaurante para 94 personas hay 19 mesas en las se pueden
sentar 4,5 o 6 personas. Si sabemos que en el total de mesas con 4 ó 5 sillas se
pueden acomodar 64 personas, ¿Cuántas mesas tienen 4 sillas?
Answers
There are 9 tables with 4 chairs in the restaurant.
Let's establish the variables:
Let x be the number of tables with 4 chairs
Let y be the number of tables with 5 chairs
Let z be the number of tables with 6 chairs
We know that there are a total of 19 tables, therefore:
x + y + z = 19 (equation 1)
We also know that the total number of people that can be accommodated in tables with 4 or 5 chairs is 64, therefore:
4x + 5y = 64 (equation 2)
We want to find the value of x, so we need to eliminate y from the equations above. We can do this by multiplying equation 2 by 4, and then subtracting it from equation 1:
x + y + z - 16x - 20y = 19 - 256
Simplifying:
-15x - 19y = -237
Dividing both sides by -19:
x = 9
Therefore, there are 9 tables with 4 chairs.
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Translated Question: Clear the selection Question 2: In a restaurant for 94 people there are 19 tables that can seat 4.5 or 6 people. If we know that the total number of tables with 4 or 5 chairs can accommodate 64 people, how many tables have 4 chairs?
45 is 3/4 of what number?
Answers
Answer:
See below, please.
Step-by-step explanation:
\(45 \div ( \frac{3}{4} ) = 60\)
Hence, the number is 60.
Answer:
60
Step-by-step explanation:
¾ of X is 45
what is X!???
4/3×45 = 60The sum of 5 consecutive integers is 265.
What is the fifth number in this sequence?
Answers
Answer:
i think the fifth number is 55
Give the slope of y+2=3(x-7) Which one is it? A) The slope is 3 and (7,-2) is on the line ? B) The slope is 7 and (3,2) is on the line ? C) The slope is 3 and (-7,2) is on the line? D) The slope is 2 and (7,3 is on the line?
Answers
Answer:
The answer is "Option A".
Step-by-step explanation:
Given line equation:
\(\to y+2=3(x-7)\)
The standard equation of the line:
\(\bold{y-y_1=m(x-x_1)}\\\\\)
Comparing the values:
\(x_1= 7\\\\y_1=-2\\\\m=3\\\)
So, the points are: (7,-2) and the slope is: 3
That's why Choice "A" is correct.
help me pleaseeee ( measurement )
Answers
Answer: a. 90 b. 65 c. 49 d. 4
a. A scalene and right triangle.
b. An isosceles and acute.
c. An obtuse.
d. An isosceles and acute.
2
Select the correct answer from each drop-down menu.
The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides.
The heights of the pyramids are the same.
The volume of pyramid A is
volume of pyramid B is
the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new
the volume of pyramid A.
Answers
The volume of pyramid A is twice the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is equal to the volume of pyramid A.
How to calculate the volume of a pyramid?In Mathematics and Geometry, the volume of a pyramid can be calculated by using the following formula:
Volume = 1/3 × b × h
Where:
h represent the height of a pyramid.b represent the base area of a pyramid.Volume of pyramid A = (10 × 20 × h)/3 = 200h/3
Volume of pyramid B = (10 × 10 × h)/3 = 100h/3
Since the heights of the two (2) pyramids are equal, we would substitute them as follows;
Volume of pyramid A = (200 × 3 × Volume of pyramid B)/(100 × 3)
Volume of pyramid A = 2 × Volume B
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Complete Question;
The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides. The heights of the pyramids are the same.
The volume of pyramid A is ____ the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is ______the volume of pyramid A.
......................................
Answers
Answer:
C
Step-by-step explanation:
Yeyeyeeyeyeyeeyeeypok2kd
Find the sum of the series if it converges otherwise enter dne infinity e n=1 8/(-3)^n
Answers
The sum of the series does not exist (DNE) as it goes to infinity.
To determine whether the series converges or diverges, we can examine the common ratio of the geometric series. The given series is:
8 / (-3)^n
The common ratio (r) can be calculated by dividing any term by its preceding term:
r = (-3)^(n+1) / (-3)^n
Simplifying the expression for r, we get:
r = (-3) / 1
r = -3
Since the absolute value of the common ratio (|-3| = 3) is greater than 1, the series will diverge.
Therefore, the sum of the series does not exist (DNE) as it goes to infinity.
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Several children and adults visited a zoo last week. The
number of children was 4 more than 2 times the number of
adults. Let c represent the number of children and a represent
the number of adults. Which equation shows this situation?
C=4a-2
B
C = 4a + 2
C = 2a + 4
D
C = 2a-4
Answers
You want to limit the amount of television you watch to an average of at most 1.5 hours per week during an 8-week period. How many hours x of television must you watch in the eighth week to meet your goal?
Television Viewing
Week....... Hours Watched
1 .......................1
2 .....................1.5
3 .....................0.5
4 .......................3
5 ......................1.5
6 ........................2
7 .......................0.5
Answers
There are 2 hours of television must you watch in the eighth week to meet your goal.
What is television?
The transmission of audio and video data electronically between a source and a recipient.
The primary use of television is to transmit shows for entertainment, information, and education. Television is a system for transmitting visual images and sound that are reproduced on screens.
Given: You want to limit the amount of television you watch to an average of at most 1.5 hours per week during an 8-week period.
Suppose x is the hours of watching television in the 8th week.
Let the average of watching television per week is 1.5.
⇒
\(\frac{1 + 1.5 + 0.5 + 3 + 1.5 + 2 + 0.5 + x}{8} = 1.5\\ \frac{10+x}{8}=1.5 \\10+x = 12\\x = 12-10\\x = 2\)
Hence, there are 2 hours of television must you watch in the eighth week to meet your goal.
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In the figure, ABCF is a rhombus and BCDE is a trapezium. ED//BC, BCF=38 degrees and BED= 79 degrees
Answers
Angle BCF = 38 degrees
Angle BED = 79 degrees
Angle BDE = 63 degrees
Angle B = 79 degrees
Angle C = 79 degrees
Angle ACF = 38 degrees
Angle F = 104 degrees.
We have,
As ED//BC,
We can say that angle EDB = angle BCF = 38 degrees.
Also, in rhombus ABCF, angles BCF and CAF are equal,
So CAF = 38 degrees.
In triangle BED,
We have angle BED = 79 degrees and angle EDB = 38 degrees.
Angle BDE = 180 - (79 + 38) = 63 degrees.
In triangle BDE,
We also has angle B = angle EBD = 180 - (63 + 38) = 79 degrees.
In trapezium BCDE,
Angles B and C are equal, so angle C = 79 degrees.
Finally, in rhombus ABCF, angles CAF and ACF are equal,
So ACF = 38 degrees.
Therefore,
Angles A and C of triangle ACF equal 38 degrees each, and angle F is:
= 180 - (38 + 38)
= 104 degrees.
Thus,
angle BCF = 38 degrees
angle BED = 79 degrees
angle BDE = 63 degrees
angle B = 79 degrees
angle C = 79 degrees
angle ACF = 38 degrees
angle F = 104 degrees.
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The complete question.
In the figure, ABCF is a rhombus and BCDE is a trapezium. ED//BC, BCF=38 degrees, and BED= 79 degrees.
Find the following:
Angle BCF
Angle BED
Angle BDE
Angle B
Angle C
Angle ACF
Angle F
Write an equation in slope intercept form of the line that passes through (4,-4) and (8,4)
Answers
Answer:
y = 2x - 12
Step-by-step explanation:
To write the equation of the line in slope intercept form, we need to determine the slope of the line and the y-intercept of the line. Once we determine the slope and the y-intercept of the line, we can substitute them into the slope intercept equation to determine the equation of the line.
Question: How to determine the slope and the y-intercept?
The slope of the line can be determined by applying the slope formula and the y-intercept can be determined by substituting the "determined slope" and any point whereas the line passes through that point, into the slope intercept form equation.
[Step-1] Finding the slope of the line:
The formula that can be used to find the slope of a line are as follows:
\(\underline{\text{Slope of a line}:} \ \boxed{\frac{y_{2} - y_1 }{x_2 - x_1} }\)
Let us substitute (4, -4) and (8, 4) into the slope formula by substituting into their respective places. As a result, the slope will be as follows:
\(\implies \dfrac{4 - (-4)}{8 - 4} = \dfrac{4 + 4}{4} = \dfrac{8}{4} = 2\)
Therefore, the slope is 2.
[Step-2] Finding the y-intercept of the line:
According to the instruction stated above, we have to substitute the slope of the line and the x/y coordinates of any point, whereas the line passes through that point, into the slope intercept form equation.
\(\implies \text{y = mx + b (Slope intercept form equation)}\)
Slope is usually known as "m" in the slope intercept form equation and y-intercept is usually known as "b" in the slope intercept form equation.
Therefore, we have: \(m = 2\)
\(\implies \text{y = (2)x + b}\)
Further, let us substitute the coordinate of any point, whereas the line intersects that point. I will choose the point [8, 4].
Now, let us expand the coordinate (8, 4) to determine the x and y coordinates. Since we have 8 as the x-coordinate and 4 as the y-coordinate, we can say that: x = 8; y = 4
\(\implies \text{(4) = (2)(8) + b}\)
Then, let us solve for b. The value of "b" will be the y-intercept.
\(\implies \text{4 = 16 + b}\)
\(\implies \text{4 - 16 = \boxed{-12 = b}}\)
Therefore, the y-intercept is -12.
[Step-3] Determining the equation of the line
According to the instruction stated above, we have to substitute the slope and the y-intercept of the line in the slope intercept form equation to determine the equation of the line in slope intercept form.
\(\implies y = mx + b \longrightarrow \text{Slope intercept form}\)
\(\implies y = (2)x + (-12)\)
Finally, simplify the equation:
\(\implies y = 2x -12\)
Therefore, the equation of the line in slope intercept form is y = 2x - 12.
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Which answer choice includes all solutions to the inequality and identifies which interval(s) contain viable completion times of machine 1?
Answers
The answer choice that includes all solutions to the inequality and identifies the interval(s) containing viable completion times of machine 1 is - **x ≤ 8** (inclusive) represents all solutions to the inequality, and the interval **[0, 8]** contains viable completion times of machine 1.
To determine the solution to an inequality, we need to consider the given conditions. Let's assume the inequality is **x + 2 < 10**, where x represents completion times of machine 1.
To solve the inequality, we subtract 2 from both sides:
x + 2 - 2 < 10 - 2
x < 8
This inequality indicates that the completion times of machine 1 (represented by x) must be less than 8 in order to satisfy the condition.
Since the inequality is strict (**x < 8**), the solution does not include the value 8 itself. However, if the inequality were non-strict (**x ≤ 8**), it would include the value 8 as well.
Hence, the answer choice **x ≤ 8** includes all solutions to the inequality. Now, to identify the interval(s) containing viable completion times of machine 1, we consider the range of values for x.
In this case, the interval [0, 8] represents viable completion times for machine 1 because it includes all values from 0 to 8, inclusive. Any completion time within this interval, including the endpoints, would satisfy the inequality.
Therefore, the answer choice that includes all solutions to the inequality is **x ≤ 8**, and the interval **[0, 8]** contains viable completion times of machine 1.
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potential in a region between x=0 and x=6.00 m is V=a+bx, where a=10.4 V and b=−6.50 V/m. (a) Determine the potential at x=0. v Determine the potential at x=3.00 m. v Determine the potential at x=6.00 m. V (b) Determine the magnitude and direction of the electric field at x=0. magnitude V/m direction Determine the magnitude and direction of the electric field at x=3.00 m. magnitude V/m direction Determine the magnitude and direction of the electric field at x=6.00 m. magnitude V/m direction
Answers
(a) The potential at x = 0 is = 10.4 V
The potential at x = 3 is = - 9.1 V
The potential at x = 6 is = - 28.6 V
(b) At every value of x =0, 3, 6 the electric field is 6.50 V/m and direction is + X axis.
Given that,
V = a + bx
a = 10.4 V and b = - 6.50 V/m.
(a) The potential at x = 0 is,
V = 10.4 - 6.50 * 0 = 10.4 V
The potential at x = 3.0 m is,
V = 10.4 - 6.50 * 3 = - 9.1 V
The potential at x = 6.0 m is,
V = 10.4 - 6.50 * 6 = - 28.6 V
(b) Electric field E can be written as,
E = - dV/dx
E = -d/dx [10.4 - 6.50 x]
E = 6.50 V/m
The direction of electric field is in the direction in which the electric potential decreases. From previous part if we move along positive X the potential decreases, so the direction of electric field at x = 0 is along + X axis.
The electric field is independent of x. So at every value of x the direction along + X axis and the value is 6.50 V/m.
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