Find the slope of the line passing through the points(-5,5) and(5,8)
The slope of the line passing through the points (-5,5) and (5,8) is 0.3.
The slope of a line is the rate at which it rises or falls as it moves from left to right. It is defined as the change in the vertical distance divided by the change in the horizontal distance between any two points on the line.
The slope of a line passing through two points (x₁,y₁) and (x₂,y₂) can be calculated using the slope formula:
slope = (y₂-y₁)/(x₂-x₁)
Using the coordinates (-5,5) and (5,8), we can plug in the values to get:
slope = [tex]\frac{(8-5)}{(5-(-5))}[/tex]
slope = [tex]\frac{3}{10}[/tex]
slope = 0.3
To learn more about slope follow the link: https://brainly.com/question/14511992
#SPJ4
If these two shapes are similar, what is the measure of the missing length s?
Luke is organizing textbooks on his bookshelf. He has an English textbook, a biology textbook, and a history textbook. How many different ways can he line the textbooks up on his bookshelf?
In his bookshelf, Luke can arrange his textbooks in a total of six different ways.
Luke can line up his textbooks in 3! = 321 = 6 different ways. This is because for the first book, he has three choices, for the second book, he has two choices left, and for the third book, he has only one choice left.
Therefore, the number of different ways Luke can line up his textbooks on his bookshelf is 6.
The six possible ways are:
English, biology, history
English, history, biology
Biology, English, history
Biology, history, English
History, English, biology
History, biology, English
To learn more about possible ways visit;
https://brainly.com/question/19738345
#SPJ1
Which two statements about these figures are true?
Figures 1 and 3 are not congruent because figure 1 cannot be mapped onto figure 3 using a
sequence of rigid transformations.
All four figures are congruent because each figure can be mapped onto any other figure using a
sequence of rigid transformations.
Figures 1 and 4 are not congruent because figure 1 cannot be mapped onto figure 4 using a
sequence of rigid transformations.
Figures 2 and 4 are congruent because figure 2 can be mapped onto figure 4 using a sequence of
rigid transformations.
Figures 1 and 2 are not congruent because figure 1 cannot be mapped onto figure 2 using a
sequence of rigid transformations.
The true statements are:
Figures 1 and 3 are not congruent because figure 1 cannot be mapped onto figure 3 using a sequence of rigid transformations.Figures 1 and 4 are not congruent because figure 1 cannot be mapped onto figure 4 using a sequence of rigid transformations.What is meant by translation?A sort of transformation comprehended a translation involves moving each point in a figure the same distance in the same direction.
Reworking text from one language into another while preserving the original message and communication is called translation. But, there are various approaches to translation, and they range in both form and purpose, just like anything else.
An operation is a transformation if it moves, flips, or otherwise alters a figure to produce a new figure. Rigid transformations sometimes referred to as isometry or congruence transformations, do not alter the size or shape of a figure.
therefore, the true statements are:
Figures 1 and 3 are not congruent because figure 1 cannot be mapped onto figure 3 using a sequence of rigid transformations.Figures 1 and 4 are not congruent because figure 1 cannot be mapped onto figure 4 using a sequence of rigid transformations.Learn more about translation Here:
https://brainly.com/question/1046778
#SPJ1
PLEASE HELP WILL GIVE BRAINLIEST!!
Proof attached
Prove AD || EF
Answer:It is given that
In △ABC,
DE∥AC
What is similarity of triangles?
Two triangles are similar if corresponding angles are equal and corresponding sides are in proportion.
Let us consider △BDE and △ABC,
∠B=∠B.....common angles
∠BDE =∠BAC....corresponding angles
so, △BDE∼△ABC
Since △BDE and △ABC are similar so, corresponding sides will be in proportion,
Subtract 1 from both sides,
Thus, we proved using the similarity of triangles.
Step-by-step explanation:
NO UNWANTED ANSWERS !
Allen was not well last week . he consulted a doctor. he doctor told him that his platelet count was 65×10⁹ per L , while the minimum normal value of a healthy human being is 105×10⁹ per L.
accordingly he was prescribed medications and was asked to take care of his health .
a) write the minimum normal value of the platelet count of a healthy person in usual form .
b) write the value of platelet count of Allen in the usual form .
c) how much more count does should Allen gain to reach the normal value ?
Answer:
a) The minimum normal value of the platelet count of a healthy person in usual form is 105,000,000,000 per liter (or 105 x 10^9 per L).
b) The platelet count of Allen in the usual form is 65,000,000,000 per liter (or 65 x 10^9 per L).
c) Allen needs to gain 40,000,000,000 more platelets per liter (or 40 x 10^9 per L) to reach the normal value of a healthy person.
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here's your Answer ~
A.) minimum number of platelet count for a healty person :
[tex]\qquad \sf\dashrightarrow \:105000000000 \: \: per \: litre[/tex]
[ That's the usual form, you just need to add 9 zeros to the value ]
B.) The value of platelet count of Allen :
[tex]\qquad \sf\dashrightarrow \:65000000000 \: \: per \: litre[/tex]
C.) platelet count she should gain to be equal to the normal value :
[tex]\qquad \sf \dashrightarrow \: 105 \times 10 {}^{9} - 65 \times 10 {}^{9} [/tex]
[ taking 10⁹ common ]
[tex]\qquad \sf \dashrightarrow \: 10 {}^{9} (105 - 65)[/tex]
[tex]\qquad \sf \dashrightarrow \: 40 \times 10 {}^{9} \: \: per \: \: litre[/tex]
In normal value, it will be :
[tex]\qquad \sf\dashrightarrow \:40000000000 \: \: per \: litre[/tex]
pls help me with this math assignment ! give you a like
pic down below ⬇️
The three points that are not collinear are J, K and L
The three points that are not collinearIn geometry, points that are not collinear are points that do not lie on the same straight line. i.e. points that are not collinear are points that are not on the same line
Using the above as a guide, the non-collinear points are points J, K and L
How to determine the opposite raysOpposite rays are two rays that have the same endpoint and extend indefinitely in opposite directions.
Using the above definition, we have
Opposite rays = HG and HI
Another name for line JHThe line JH can be named based on its endpoints
So, another name for JH is HJ
Planes that contain HLThree points are required to form a plane
This means that the planes that contain HL can be named as GHL and JHL
There are other planes that contained HL too
Sketch of planes that intersect in line pSee attachment for the sketch
Read more about plane and points at
https://brainly.com/question/12227980
#SPJ1
Your younger cousin Mary is a rising senior in high school this year and has been
researching the cost of attendance at several colleges. She emails you because she knows
that you have just learned about paying for college and she has some serious concerns.
Here are some excerpts from her email:
• Despite her strong academic performance in high school and her interest in pursuing
a career in chemical engineering, Mary reveals, "I'm starting to think that college just
isn't worth it. I don't see how a college degree is going to help me in the future if it
costs so much. Aren't I better off just going straight into a job with my high school
degree and saving my money?"
"I've been looking at the published costs of attendance on college websites, and
they're insanely high! There's no way my family and I can afford such prices."
"I know financial aid is available for students, but I don't know what types there are, let
alone how to apply for financial aid. Even if I knew how to apply, should I apply? I don't
I think I'll qualify and I don't want to put in all that work for nothing.
"I know that I have to start paying my loans right after I graduate college. But what if I
don't have a job by that time? And what if I can't afford my monthly payments? I don't
I want to take that risk."
You recognize that Mary has a few misconceptions and gaps in
knowledge about how to pay for college and want to make sure that she
makes a decision based on the right information. In 4-5 paragraphs,
respond to Mary about each of her concerns.
Answer:
Dear Mary,
I understand your concerns about the cost of attending college and how it might not be worth it in the end. However, earning a college degree can significantly increase your earning potential and lead to greater job opportunities. In fact, individuals with a bachelor's degree earn an average of $1 million more over their lifetime compared to those with only a high school diploma. Moreover, pursuing a degree in chemical engineering can open doors to highly rewarding and well-paying career paths.
I agree that the published costs of attendance on college websites can be overwhelming, but keep in mind that these figures are often the maximum amount and many students receive financial aid to reduce their expenses. Financial aid comes in many forms, including scholarships, grants, work-study programs, and loans. Scholarships and grants do not have to be repaid, so it's worth exploring those options first. Loans can be daunting, but they can also be manageable if you borrow responsibly and budget accordingly.
It's understandable that you may feel uncertain about whether you qualify for financial aid or not, but it's always worth applying. Many families are surprised to find out that they qualify for aid that they didn't expect. The Free Application for Federal Student Aid (FAFSA) is the form used to determine your eligibility for federal and state financial aid, and it's free to complete. Private institutions may also require additional forms, so make sure to check each college's financial aid website for more information.
As for student loans, there are many repayment plans available, and you can choose one that works best for your budget. If you're having trouble finding a job after graduation, you can apply for deferment or forbearance to temporarily suspend your payments. It's important to have a plan in place for repayment, but it's also important not to let the fear of repayment stop you from pursuing your dreams.
I hope this information helps you make a more informed decision about your college plans. Remember, investing in your education can have long-lasting benefits and lead to a brighter future.
Best regards,
[Your Name]
Step-by-step explanation:
Mohal is a waiter at a restaurant. Each day he works, Mohal will make a guaranteed wage of $25, however the additional amount that Mohal earns from tips depends on the number of tables he waits on that day. From past experience, Mohal noticed that he will get about $15 in tips for each table he waits on. How much would Mohal expect to earn in a day on which he waits on 16 tables? How much would Mohal expect to make in a day when waiting on tt tables?
I need to know:
Total earnings with 16 tables:
Total Earnings with tt tables:
Mohal would expect to earn $265 in a day when he waits on 16 tables, and he would expect to earn $15tt + $25 in a day when he waits on tt tables
Describes earnings or wages?Earnings or wages refer to the amount of money an individual receives in exchange for their work or services. This can include a regular salary or hourly wage, as well as bonuses, commissions, and other forms of compensation.
Earnings or wages are typically determined by a variety of factors, including the type of work being performed, the level of skill and experience required, the local job market, and the employer's policies and practices. In some cases, earnings may be negotiated between the employer and the employee, while in other cases they may be set by industry standards or government regulations.
To calculate Mohal's expected earnings in a day when he waits on 16 tables, we can use the formula:
Total earnings = Guaranteed wage + Tips
Guaranteed wage = $25
Tips = $15 x Number of tables
Number of tables = 16
So, Total earnings with 16 tables = $25 + ($15 x 16) = $265
To calculate Mohal's expected earnings in a day when he waits on tt tables, we can use the same formula:
Total earnings = Guaranteed wage + Tips
Guaranteed wage = $25
Tips = $15 x Number of tables
Number of tables = tt
So, Total earnings with tt tables = $25 + ($15 x tt) = $15tt + $25
Therefore, Mohal would expect to earn $265 in a day when he waits on 16 tables, and he would expect to earn $15tt + $25 in a day when he waits on tt tables.
To know more about wage visit:
https://brainly.com/question/17104847
#SPJ1
Answer:
Total earnings with 16 tables: 265
Total Earnings with t tables: 15t+25
Step-by-step explanation:
20 Points................................
Match the description with the step accordingly:
How many times larger is 2 × 10⁻² then 3 × 10⁻⁶: Divide the larger Scientific Notation by the smaller Scientific Notation - divide coefficients and subtract exponents.
Difference between 2 × 10⁻² and 3× 10⁻⁶: Subtract by getting the same exponent to be like terms.
400 times 2 × 10³: Multiply by changing the number to Scientific Notation - multiply coefficients and add exponents.
How to match the description with the step?Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form.
To find How many times larger is 2 × 10⁻² then 3 × 10⁻⁶. Divide the larger Scientific Notation by the smaller Scientific Notation - divide coefficients and subtract exponents. That is:
(3 × 10⁻⁶)/(2 × 10⁻²) = 3/2 × 10⁻⁶⁻⁽⁻²⁾ = 1.5×10⁻⁴
To find the difference between 2 × 10⁻² and 3× 10⁻⁶. Subtract by getting the same exponent to be like terms. That is:
2×10⁻² - 3×10⁻⁶ = (2 × 10⁻²) - (0.0003× 10⁻²)
= (2 - 0.0003) × 10⁻²
= (2 - 0.0003) × 10⁻²
= 1.9997× 10⁻²
For 400 times 2 × 10³. Multiply by changing the number to Scientific Notation - multiply coefficients and add exponents. That is:
400 × 2 × 10³ = 4 × 10² × 2 × 10³
= 4 × 2 × 10³ × 10²
= 4 × 2 × 10³⁺²
= 8 × 10⁵
Learn more about Scientific notation on:
brainly.com/question/27862246
#SPJ1
Which is greater, 3 miles or 1,000 yards? How much greater? Explain. (15pts)
Answer:
1 mile is equal to 1,760 yards. Therefore, 3 miles is equal to 3 x 1,760 = 5,280 yards.
Comparing 5,280 yards to 1,000 yards, we can see that 5,280 yards is greater than 1,000 yards.
To determine how much greater, we can subtract 1,000 from 5,280:
5,280 - 1,000 = 4,280
Therefore, 3 miles is 4,280 yards greater than 1,000 yards.
Please answer this question
[tex] \frac{ {38}^{2} - {22}^{2} }{16} \\ [/tex]
The identity which can be used in this case is :
[tex] \boxed{ {a}^{2} - {b}^{2} = (a - b)(a + b)}[/tex]
Applying the above identity to the given equation , we get
[tex] \frac{ {38}^{2} - {22}^{2} }{16} \\ \\ \implies \: \frac{(38 - 22)(38 + 22)}{16} \\ \\ \implies \: \frac{(\cancel{16})(60)}{\cancel{16} } \\ \\ \implies \: \underline{\underline{60}}[/tex]
hope helpful! :)
For f(x)=2x, find f(9)
Answer:
Step-by-step explanation:
[tex]f(9)[/tex] means we need to find the value of [tex]f(x)[/tex] when [tex]x=9[/tex], so
[tex]f(9)=2[/tex]×[tex]9=18[/tex]
Margo can purchase tile at a store for $0.99 per tile and rent a tile saw for $56. At another store she can borrow the tile saw for free if she buys tiles there for $1.69 per tile. How many tiles must she buy for the cost to be the same at both stores?
A contractor bought 7. 6 ft. ² of sheet metal he has used 3. 5 ft. ² so far it has $65. 60 worth of sheet metal remaining the equation 7. 6 X -3. 5 X equals 65. 6 represents how much sheet-metal is remaining in the cost of the remaining amount how much does the sheet-metal cost per square foot
The cost per square foot of the remaining sheet metal is $4.10.
To find the cost per square foot of the remaining sheet metal, we can first calculate how much sheet metal is remaining by solving the equation:
7.6X - 3.5X = 65.6
where X is the amount of sheet metal remaining in square feet.
Simplifying the left side of the equation gives:
4.1X = 65.6
Dividing both sides by 4.1 gives:
X = 16
Therefore, the amount of sheet metal remaining is 16 square feet.
To find the cost per square foot, we can divide the cost of the remaining sheet metal by the amount of sheet metal remaining:
$65.60 / 16 sq. ft. = $4.10 per square foot.
To know more about cost here
https://brainly.com/question/14332852
#SPJ4
Which of the following is a like radical to 3 x StartRoot 5 EndRoot
Answer: The square root of 45 is a like radical to 3 x √5.
To see why, we can simplify each radical using the product rule of radicals:
3 x √5 = √(3^2 x 5) = √45
Similarly, we can simplify the square root of 45 using the prime factorization of 45:
√45 = √(3 x 3 x 5) = 3√5
Therefore, 3 x √5 is a like radical to √45, and vice versa.
Step-by-step explanation:
Answer:
its D
Step-by-step explanation:
TRUST ME BRO
If possible, factor the following expression. If the expression doesn't have a common factor other than 1 or -1, choose "Not Factorable" or enter the expression. 8x+56
The factored form of the expression is 8(x+7).
The expression 8x+56 can be factored by finding the common factor of both terms. The common factor in this case is 8, since 8 can be evenly divided into both 8x and 56.
To factor the expression, we can use the distributive property to pull out the common factor of 8 from both terms:
8x+56 = 8(x+7)
Therefore, the factored form of the expression is 8(x+7).
Answer: 8(x+7)
To know more about factorization , refer here:
https://brainly.com/question/14549998#
#SPJ11
(a) If three letters are placed at random in three envelopes, what is the probability that exactly one letter will be placed in the correct envelope?
(b) If n letters are placed at random in n envelopes, what is the probability that exactly n−1 letters will be placed in the correct envelopes?
(a) The probability that exactly one letter will be placed in the correct envelope is 1/2.
(b) The probability that exactly n−1 letters will be placed in the correct envelopes is 0.
(a) There are three possible ways that one letter can be placed in the correct envelope (A in A, B in B, or C in C) and six total possible arrangements of the letters (ABC, ACB, BAC, BCA, CAB, CBA).
Solving for the probability:
P = 3/6 = 1/2
(b) If n−1 letters are placed in the correct envelopes, then the remaining letter must also be placed in the correct envelope, resulting in all n letters being placed in the correct envelopes. Therefore, it is impossible for exactly n−1 letters to be placed in the correct envelopes.
Learn more about probability here: https://brainly.com/question/24756209.
#SPJ11
35 percent of 150 is about 50 is this reasonable or unreasonable
The statement that 35 percent of 150 is about 50 is completely false and hence unreasonable as 35 percent of 150 is exactly equal to 52.50.
In the given problem which is related to percentage of some specific number, the value is obtained by direct multiplication of percentage with the given number to get the answer. Percentage is defined as the ratio which is given with respect to number 100 or 100 units as a whole. Its symbol is %. It is a dimensionless quantity and hence has no units as ratios does not have units.
The given equation can be represented as follows to obtain the answer:
(35/100) × 150 = 52.50
Since 52.50 cannot be considered close to 50, hence the statement is u reasonable. Though 52.5 can be considered as about 52 or 53.
Learn more about percentage at:
brainly.com/question/24877689
#SPJ4
HELP ASAP Leadership positions for a college social club are up for electionThree people are needed to fill the positions of president vice president, and secretaryOnly 10 members are willing to serve in these positions. Each candidate is eligible for cach position, and a candidate can only hold one leadership position. How many different ways can the three positions be filled using the 10 possible candidates?
Answer: There are 10 candidates for each position, and since a candidate can only hold one leadership position, the number of ways to fill the president position is 10. After the president position is filled, there are 9 candidates remaining for the vice president position. Finally, there are 8 candidates remaining for the secretary position.
The total number of ways to fill the three positions is the product of the number of ways to fill each position. Therefore, the number of ways to fill the three positions is:
10 x 9 x 8 = 720
So there are 720 different ways to fill the three leadership positions using the 10 possible candidates.
Step-by-step explanation:
PLEASE HELP! - I CAN'T SOLVE THE QUESTION
Answer: 16π
Step-by-step explanation:
The area of a full circle is πr^2. We only need a quarter so we'll use, A = 1/4(πr^2)
Area = 1/4(π(8)^2)
Area = 1/4(64π)
Area = 16π
Hope this helps
Answer:
I thing it 16 pi if u get it wrong I'm sry but since I just learned this pi stuff this is what I came up with
Rotate point A 180 counterclockwise about the origin to get point A'. Which of the following coordinate is A'?
Rotate point A 180 counterclockwise about the origin to get point A'. -2,-3 coordinate is A'
What is counterclockwise rotation?
Rotations that are counterclockwise (CCW) travel in the opposite direction from how a clock's hands move. Positive numerals are used to indicate these rotations.
Rotation in either a clockwise or anticlockwise direction refers to a change in the electrical activity flowing through the heart in a horizontal plane. Consider the observer as being at the bedside of the sufferer. It is known as anticlockwise rotation if the patient's heart's electrical activity has shifted more to their right side. It is known as clockwise rotation if the patient's heart's electrical activity has shifted more to the left.
Our point A(x,y) rotates 180 degrees anticlockwise around the origin to become A' (-x,-y). Making both x and y negative is all we do as a result.
Here we can see in the graph ‘A’ is present on (2,3)
So the -2,-3 coordinate is A’.
Hence the correct answer is c, -2,-3
To learn more about counterclockwise rotation from the given link
https://brainly.com/question/26249005
#SPJ1
simplify each expression 5x^2 / 10x^3 - 15x
Step-by-step \frac{1}{2} x^{5} - 15x
9 ft
Find the area of each polygon below.
T6 ft-
T
10 cm
1
15 cm-3 cm-
T
8 m
1-5 m-H4 m-
Form the unlock code by entering the area of
each polygon in order from left to right.
Separate each number with a hyphen.
For example: 50-60-10
the unlock code is: 54-575-26-12-7.5-36.
How to determine?
To find the area of each polygon, we need to use the formula for the area of each respective shape.
Assuming the polygons are rectangles, triangles, and trapezoids, we can find their areas as follows:
The area of the rectangle with length 9 ft and width 6 ft is A = length × width = 9 ft × 6 ft = 54 ft².
The area of the triangle with base 10 cm and height 115 cm is A = (1/2) × base × height = (1/2) × 10 cm × 115 cm = 575 cm².
The area of the trapezoid with bases 5 m and 8 m, and height 4 m is A = (1/2) × (base1 + base2) × height = (1/2) × (5 m + 8 m) × 4 m = 26 m².
The area of the triangle with base 3 cm and height 8 cm is A = (1/2) × base × height = (1/2) × 3 cm × 8 cm = 12 cm².
The area of the rectangle with length 1.5 m and width 5 m is A = length × width = 1.5 m × 5 m = 7.5 m².
The area of the trapezoid with bases 6 ft and 3 ft, and height 4 m is A = (1/2) × (base1 + base2) × height = (1/2) × (6 ft + 3 ft) × 4 m = 9 ft × 4 m = 36 ft².
Therefore, the unlock code is: 54-575-26-12-7.5-36.
Note that the areas are listed from left to right based on the order of the shapes in the original question. Also, the areas are separated by hyphens as requested.
To know more about polygon visit:
https://brainly.com/question/24464711
#SPJ1
The question is in the screenshot:
Answer:
csc(0)= 25/7
sec(0)= 25/24
cot(0)= 24/7
Step-by-step explanation:
Answer:
csc Θ = 25/7
sec Θ = 25/24
cot Θ = 24/7
Step-by-step explanation:
csc Θ = 1/sin Θ
sin Θ = opp/hyp
csc Θ = hyp/opp
csc Θ = 25/7
sec Θ = 1/cos Θ
cos Θ = adj/hyp
sec Θ = hyp/adj
sec Θ = 25/24
cot Θ = 1/tan Θ
tan Θ = opp/adj
cot Θ = adj/opp
cot Θ = 24/7
plications Involving Factoring Polynomials Set up an algebraic equation and then solve. The width of a rectangle is 17 units less than the length. If the area is 60 square units, then find the dimensions of the rectangle. Length: units Width: units
The dimensions of the rectangle are: length: 20 units and width: 3 units.
To solve the problem, we can set up an algebraic equation using the formula for the area of a rectangle, which is A = length × width.
Let x be the length of the rectangle, and x - 17 be the width.
Then we can set up the equation:
60 = x(x - 17)
Simplifying the equation gives us:
x² - 17x - 60 = 0
Now we can factor the equation:
(x - 20)(x + 3) = 0
This gives us two possible solutions for x:
x = 20 or x = -3
However, since the length of a rectangle cannot be negative, we can disregard the second solution.
Therefore, the length of the rectangle is 20 units, and the width is 20 - 17 = 3 units.
Learn more about algebraic equation here: https://brainly.com/question/2164351.
#SPJ11
If the value of a is negative and the value of b is negative, which best describes the translation?
Best describes the translation of the figure moves Left and down.
Describe the term translation?A translation is a transformation that moves every point of a figure or object by the same distance and in the same direction without changing its shape, size, or orientation. It is a type of rigid transformation that preserves the distance between points and angles between lines.
A translation can be described using the horizontal and vertical shift or displacement of the object. If a point (x, y) is translated by a distance of 'a' units to the right and 'b' units upwards, the new location of the point would be (x + a, y + b).
Question says that a figure is translated using the mapping (x, y) → (x + a, y + b).
If the value of 'a' is negative and the value of 'b' is negative in the mapping (x, y) → (x + a, y + b), it means that the figure is being translated to the left and downwards.
The x-coordinates are being decreased by the absolute value of 'a', which means that the figure is moving left. Similarly, the y-coordinates are being decreased by the absolute value of 'b', which means that the figure is moving downwards.
Therefore, the best description of the translation is "the figure moves left and down"
To know more about Coordinates, visit:
https://brainly.com/question/24394007
#SPJ1
The sum of a number and it’s reciprocal is 2 1/6 find the number
Let's assume the number to be x.
According to the problem statement, the sum of a number and its reciprocal is 2 1/6 or 13/6.
So we can set up the equation:
x + 1/x = 13/6
Multiplying both sides by 6x, we get:
6x^2 + 6 = 13x
Bringing all the terms to one side, we get:
6x^2 - 13x + 6 = 0
We can solve for x using the quadratic formula:
x = [13 ± sqrt(13^2 - 4(6)(6))] / (2*6)
x = [13 ± sqrt(169)] / 12
x = [13 ± 13] / 12
So, x can be either 2/3 or 3/2. Therefore, the number is either 2/3 or 3/2.
The surface charge density on a long straight metallic pipe is σ. What is the electric field outside and inside the pipe? Assume the pipe has a diameter of 2a.
(Enter the magnitudes. Use any variable or symbol stated above along with the following as necessary: r for the radial distance from the axis of the pipe and
€0= the Gauss’s Law Symbol)
Outside the pipe E(r) =
Inside the pipe E(r) =
The electric field outside the pipe is E(r) = σa² / ε_0r².
The electric field inside the pipe is E(r) = σa²/ ε_0r.
What is the surface charge density?Assuming the metallic pipe is infinitely long, we can use Gauss's Law to determine the electric field both inside and outside the pipe.
Let's consider a cylindrical Gaussian surface of radius r and length L, with its axis coinciding with that of the pipe.
By Gauss's Law, the electric flux through the surface is given by:
Φ_E = ∫ E . dA = E x 2πrL
where;
E is the magnitude of the electric field at a distance r from the axis of the pipe, and dA is an element of area on the surface.The charge enclosed by the Gaussian surface is given by:
Q_enc = σ x π(2a)² x L
= 4πa²σL
where;
σ is the surface charge density.By Gauss's Law, the electric flux through the Gaussian surface is also given by:
Φ_E = Q_enc / ε_0
where;
ε_0 is the electric constant (permittivity of free space).Equating the two expressions for Φ_E, we get:
E x 2πrL = 4πa²σL / ε_0
Simplifying, we get:
E = σa² / ε_0r for r < a
E = σa² / ε_0r^2 for r > a
Therefore, the electric field inside the pipe (r < a) is inversely proportional to the distance from the axis, while outside the pipe (r > a) it is inversely proportional to the square of the distance from the axis.
To summarize:
Outside the pipe: E(r) = σa² / ε_0r²
Inside the pipe: E(r) = σa² / ε_0r
Learn more about surface charge density here: https://brainly.com/question/14306160
#SPJ1
Pls Help!!! Dilate ABCD by a scale factor of k = 2 centered at (-3, 4). Be sure to label your image.
The vertices of the image of the triangle BCD are B'(x, y) = (- 3, 13), C'(x, y) = (0, 19) and D'(x, y) = (18, 10). The representation of the resulting figure is in the image attached below.
How to find the image of a triangle seen in Cartesian plane
Herein we find the representation of a triangle on Cartesian plane, whose image, that is, the result of a dilation, must be found. The formula to be used is introduced below:
P'(x, y) = P(x, y) + k · [P(x, y) - O(x, y)]
Where:
O(x, y) - Center of dilationP(x, y) - Original pointP'(x, y) - Resulting pointk - Scale factorIf we know that B(x, y) = (- 3, 7), C(x, y) = (- 2, 9), D(x, y) = (4, 6), O(x, y) = (- 3, 4) and k = 2, then the coordinates of the vertices of the image are listed below:
B'(x, y) = (- 3, 7) + 2 · [(- 3, 7) - (- 3, 4)]
B'(x, y) = (- 3, 7) + 2 · (0, 3)
B'(x, y) = (- 3, 7) + (0, 6)
B'(x, y) = (- 3, 13)
C'(x, y) = (- 2, 9) + 2 · [(- 2, 9) - (- 3, 4)]
C'(x, y) = (- 2, 9) + 2 · (1, 5)
C'(x, y) = (- 2, 9) + (2, 10)
C'(x, y) = (0, 19)
D'(x, y) = (4, 6) + 2 · [(4, 6) - (- 3, 4)]
D'(x, y) = (4, 6) + 2 · (7, 2)
D'(x, y) = (4, 6) + (14, 4)
D'(x, y) = (18, 10)
Now we proceed to plot the image by means of a graphing tool.
To learn more on dilations: https://brainly.com/question/13176891
#SPJ1