Which statement is true about the transformation of segment AB?
0 a
O b
0 c
0 d
AB is reflected over the y-axis and is congruent to the image.
AB is translated 2 units left and is congruent to the image
AB was reflected over the x-axis and is not congruent to the image.
AB is rotated around the origin clockwise and is not congruent to the image
Answers
The statement that is true about the transformation of segment AB is;
AB is reflected over the y-axis and is congruent to the image.
What is the reflection transformation used?A reflection is a type of transformation that behaves like a mirror. Thus, It swaps all pairs of points that are on exactly opposite sides of the line of reflection. The line of reflection can be defined by an equation or by two points it passes through.
Now, the transformation rule for reflection about the y-axis is;
(x, y) = (-x, y)
In this graph, it is exactly a reflection about the y-axis and as such we can say that option A is the correct answer.
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Related Questions
Juan rolls a 6-sided number cube 4 times. Each time, the result is
2. Which best describes the events?
•
Dependent: Each outcome was the same.
Simple: One single number cube was rolled.
•
Independent: Each outcome is unaffected by previous outcomes.
Simple: One single number cube was rolled.
O
Dependent. Each outcome was the same.
Compound: Multiple events occurred.
O
Independent: Each outcome was unaffected by previous outcomes.
Compound: Multiple events occurred.
Answers
The events described are known as a compound probability experiment.
Compound probability experimentThe situation described involves a single 6-sided number cube being rolled four times.The outcome of each roll was the same, resulting in a 2 each time.This can be described as a compound event, as multiple events occurred.The events are also dependent on each other, as each outcome was the same.However, the outcomes were independent of each other, as each one was unaffected by previous outcomes.This is due to the fact that each roll of the cube has an equal chance of landing on any number.Therefore, the chances of rolling a 2 each time are low, but still possible.In this experiment, a single 6-sided number cube was rolled four times and each time, the result was 2. This experiment is composed of multiple events, and each outcome was unaffected by the previous outcomes, making it an independent probability experiment.In other words, the probability of rolling a 2 on the number cube each time is the same, no matter what the result of the previous rolls were. This experiment is a good example of how probability can be used to analyze the likelihood of certain outcomes in a given situation.To learn more about compound probability experiment refer to:
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Choose 3 values that would make this inequality true. 8n + 4 ≤ 2
3
6
13
2
5
14
1
Answers
The three values are not in the given list of options
How to determine the three valuesFrom the question, we have the following parameters that can be used in our computation:
8n + 4 ≤ 2
Subtract 4 from both sides of the expression
So, we have
8n ≤ -2
Divide both sides by 8
This gives
n ≤ -0.25
This means that the values do not exceed -0.25
None of the valies in the option meet this condition
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Find the limit if the limit exists:
Answers
The value of each limit functions are:
72-√512-51/41/513 and 1/2√xLet's try to solve each problem we have:
1. [tex]\lim_{x \to \--3} 2x^2+4x+1[/tex]
= 2(-3)² + 4(-3) +1
= 2(9) + 4(-3) + 1
= 18 - 12 + 1
= 7
2. [tex]\lim_{x \to \-3} \sqrt{x+1}[/tex]
= √(3+1)
=√4 = 2
3. [tex]\lim_{x \to \-3} \frac{\sqrt{x+2} }{x-4}[/tex]
= √(3+2) / (3-4)
= √5 / (-1) = - √5
4. [tex]\lim_{x \to \-2} \frac{x^3-8}{x-2}[/tex] -->hint: use L'hospital rule
= [tex]\frac{(x^3-8)'}{(x-2)'}[/tex]
= 3x² / 1
= 3(2)²
= 12
5. [tex]\lim_{x \to \--1} \frac{2x^2-x-3}{x+1}[/tex]
= [tex]\lim_{x \to \--1} \frac{(2x-3)(x+1)}{(x+1)}[/tex]
= 2(-1) - 3
= -5
6. [tex]\lim_{x\to \-3} \frac{\sqrt{x+1}-2 }{x-3}[/tex]
= [tex]\frac{(\sqrt{x+1}-2)' }{(x-3)'}[/tex]
= 1/2√(x+1)
= 1/2√(3+1)
= 1/4
7.[tex]\lim_{x \to \-0} \frac{sin x}{5x}[/tex]
= [tex]\lim_{x \to \-0} \frac{sin x}{x} .\frac{1}{5}[/tex]
= 1/5 ([tex]\lim_{x \to \-0} \frac{sin x}{x}[/tex])
= 1/5 (1)
= 1/5
8. [tex]\lim_{x \to \pi/2}\frac{cosx}{cotx}[/tex]
= [tex]\lim_{x \to \pi/2}\frac{cosx}{\frac{cosx}{sinx} }[/tex]
= [tex]\lim_{x \to \pi/2}{cosx}.\frac{sinx}{cosx}[/tex]
= [tex]\lim_{x \to \pi/2}\ sinx[/tex]
= sin (π/2)
= 1
9. [tex]\lim_{h \to \-0} \frac{f(x+h)-f(x)}{h}[/tex] = f'(x)
a. f(x) = 3x - 2
f'(x) = 3
b. f(x) = √x
f'(x) = 1/2√x
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Please help me with this question.
Answers
Answer:
See below for truth tables and proofs
Step-by-step explanation:
Let's understand what a tautology is and what a contradiction is
statement which is always true is called a tautology. A statement which
is always false is called a contradiction.
A proposition p ⇒ q has a hypothesis p and a conclusion q
p ⇒ q is False
a) p ⇒ q is False if p is True and q is False. It is True for all other values of p and q
The truth table for p ⇒ q therefore is::
p q (p ⇒ q)
F F T
F T T
T F F
T T T
We have to prove that p AND q ⇒ p is a tautology for all p, q i.e. it is True no matter what the values of p and q are
p AND q ⇒ p can be re-written as (p AND q) ⇒ p since the AND operator has precedence over the implies operator
Here is the truth table for (p ∧ q) ⇒ p.
(∧ is the symbol for logical AND)
Here the hypothesis is (p ∧ q) and the conclusion is p.
It is False if and only if the hypothesis (p ∧ q) is T and p is False. That combination never occurs in the truth table
p q p ∧ q (p ∧ q) ⇒ p
------------------------------------------------------
T T T T
T F F T
F T F T
F F F T
Since the expression (p ∧ q) ⇒ p is True for all values of p and q it is a tautology
b)
Truth Table for (p ∨ ¬p) where ¬p represents not p or p'
p ¬p (p ∧ ¬p)
---------------------------
F T F
T F F
Since the expression is False for any p value, it is a contradiction
What is the simplest form of √2437?
O A.
95√3
OB.
9x³√3x
O c. 27x5√2
OD. 27x³√x
Answers
Answer:
B
Step-by-step explanation:
sqrt(243x⁷) = sqrt(9×9×3x³x³x) = 9x³×sqrt(3x)
find the indicated measure
Answers
According to the problem the indicated measures are given below:
∠QRS = [tex]90^{0}[/tex], ∠QTR = [tex]42^{0}[/tex], TR=16, QU=8
What is measures ?Measures are actions taken to achieve a desired result. They are the means used to improve, control, or solve a problem. Measures can be taken in any area, such as economics, finance, health, safety, environment, productivity, quality, customer service, etc.
In the given figure:
m∠TRS = [tex]42^{0}[/tex] and QS = 16
Seeing the figure we know that:
∠QRT +∠TRS = [tex]90^{0}[/tex]
∴∠QRT= [tex]90^{0} - 42^{0} = 48^{0}[/tex]
∠QRT+∠QTR+∠TQR = [tex]180^{0}[/tex] as it is a right angled triangle.
∴∠QTR = [tex]180^{0} - 90^{0} -48^{0} = 42^{0}[/tex]
∠QRS = [tex]90^{0}[/tex] as it is a right angled triangle.
TR = QS as diagonals bisect each other.
∴TR=16
QU=1/2QS=16/2=8
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13 x - 21 y = 7 what is the y intercept
Answers
Answer:
To find the y-intercept, set x = 0 and solve for y:
13 * 0 - 21 * y = 7
-21 * y = 7
y = -7/21
y = -1/3
So the y-intercept is at (0, -1/3).
Answer: -1/3
Step-by-step explanation:
13x-21y=7
y=13x/21-1/3
y=-1/3
A hypothetical population of 10,000 humans has 6840 individuals with the blood type AA, 2860 individuals with blood type AB and 300 individuals with the blood type BB.
What is the frequency of each genotype in this population?
Answers
The frequency of the A allele is 82.7%.
The frequency of the B allele is 17.3%.
We know that :
10,000 individuals
6,840 individuals have blood type AA
2,860 individuals have blood type AB
300 individuals have blood type BB
AA genotype frequency: 68.4%
AB genotype frequency: 28.6%
BB genotype frequency: 3%
The A allele occurs 6,840 * 2 + 2,860 * 1 = 16,540 times, which is a frequency of 82.7%, meaning the B allele occurs 3,460 times, which is a frequency of 17.3%. In the next generation, 3%, or 750, individuals would have blood type BB.
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The complete question is:
A hypothetical population of 10,000 humans has 6840 individuals with the blood type AA, 2860 individuals with blood type AB, and 300 individuals with the blood type BB.
What is the frequency of each genotype in this population?
What does the frequency of the A allele?
What is the frequency of the B allele?
Problem:
The number is a solution to the equation
5x²+4= 3x + 9.
What is the value of (10x − 3)²?
Answers
Step-by-step explanation:
collect like terms
5x-3x=9-42x= 5Experience shows that few students hand in their statistics exams early; most prefer to hand them in near the end of the test period. This means the time taken by students to write exams is: O a. negatively skewed. O b. positively skewed. O c. symmetric around the mean. O d. bell-shaped
Answers
Experience shows that few students hand in their statistics exams early and most prefer to hand them in near the end of the test period. This means that the time taken by students to write exams is positively skewed.
In statistics, a positively skewed (or right-skewed) distribution is a type of distribution in which most values are clustered around the left tail of the distribution while the right tail of the distribution is longer. The positively skewed distribution is the exact opposite of the negatively skewed distribution.
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In the school garden Winston,Sam and Chris grew carrots.They pulled up 60 carrots and shared them out in the ratio of their familiest. Winston lives in a family of four,Sam in a family of three and Chris in a family of five.
How many carrots did :
Winston recieve:
Sam recieve:
Chris recieve:
Answers
Answer:
winston receives 20carrots
Sam receives 15carrots
Chris receives 25carrots
Step-by-step explanation:
number of carrots are 60
Winston has a family of 4
Sam lives in a family of 3
Chris lives in a family of 5
total =5+3+4=12
thus
Winston - 4/12×60=20 carrots
Sam= 3/12×60=15 carrots
Chris=5/12×60=25 carrots
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I solved the first one, what about the rest
Answers
4.5
45
450
4,500
Let A be a nonempty set of real numbers which is bounded below. Let - A be the set of all numbers - x, where x E A. Prove thatinf A = -sup(-A).
Answers
For a nonempty set of real numbers, A it is proved that inf A = -sup(-A)
Let A be a nonempty set of real numbers that is bounded below
suppose inf A = K
claim:- -sup (-A) = K where -A is the set of all numbers -x show that [tex]$ x \in A$[/tex]
To show that sec (-A) = -K
First, we show that -k is the upper bound of - A
Let [tex]$-x \in-A$[/tex] be any element [tex]$\Rightarrow x \in A \ldots$[/tex] (by definition of -A ).
But inf A = K
K is the lower bound of A
[tex]& \Rightarrow \quad k \leq x \quad \forall x \in A \\[/tex]
Multiply by -1
[tex]& \Rightarrow-k \geqslant-x \quad \forall x \in A \\[/tex]
[tex]& \Rightarrow-k \geqslant-x \quad \forall-x \in-A[/tex]
Therefore -K is the upper bound of -A
suppose l is another upper bound of -A.
[tex]-x \leqslant l & \forall-x \in-A \\[/tex]
Multiply by -1
[tex]x \geqslant-l && \quad $\forall \quad x \in A \\[/tex]
[tex]\Rightarrow-k \geqslant-x \quad & \forall-x \in-A[/tex]
Therefore -k is the upper bound of -A.
Suppose l is another upper bound of -A.
[tex]\Rightarrow-x \leq l \quad \forall-x \in-A[/tex]
Multiply by -1
[tex]$\Rightarrow \quad x \geqslant-1 \quad \forall x \in A$[/tex]
-l is the lower bound of A
But k is the greatest lower bound of A
[tex]-l \leq k$[/tex]
Multiply by -1
[tex]$-l \geqslant-k$[/tex].
-K is the least upper bound of A.
sup (-A) = -k
-sup (-A) = k
inf (A) = -sup (-A)
Hence proved.
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f(x)=x^6+7x^4-17x^2+9 i need all zeros and the behavior and function positive and negattive
Answers
The polynomial y = x⁶ + 7 · x⁴ - 17 · x² + 9 has two real zeros: x = 1, x = - 1. The polynomial diverges to + ∞ when x → ± ∞.
How to find the zeros and end behavior of a sextic equation
Sextic equations are polynomials of grade six, whose form is described below:
y = a · x⁶ + b · x⁵ + c · x⁴ + d · x³ + e · x² + f · x + g
Where a, b, c, d, e, f, g are real coefficients.
According to Bolzano's theorem, given a function f(x) defined for interval [a, b], there is at least a value of x such that f(x) = 0. For polynomials with integer coefficients, zeros may be divisors of grade zero coefficient. Then, the possible candidates for zeros of the sextic equation:
Possible roots = - 9, + 9, - 3, + 3, - 1, + 1
Now we proceed to check possible roots:
x = - 9
y = (- 9)⁶ + 7 · (- 9)⁴ - 17 · (- 9)² + 9
y = 576000
x = 9
y = 9⁶ + 7 · 9⁴ - 17 · 9² + 9
y = 576000
x = - 3
y = (- 3)⁶ + 7 · (- 3)⁴ - 17 · (- 3)² + 9
y = 1152
x = 3
y = 3⁶ + 7 · 3⁴ - 17 · 3² + 9
y = 1152
x = - 1
y = (- 1)⁶ + 7 · (- 1)⁴ - 17 · (- 1)² + 9
y = 0
x = 1
y = 1⁶ + 7 · 1⁴ - 17 · 1² + 1
y = 0
The end behavior of polynomial is defined by sign of lead coefficient, that is, the real coefficient of the highest exponent of the polynomial. In addition, polynomials does not converge at any value for x → ± ∞.
According to given information, the lead coefficient of polynomial y = x⁶ + 7 · x⁴ - 17 · x² + 9 diverges to + ∞ when x → ± ∞, since grade of polynomial is an even number.
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 A student solved the following equation using the following stepsi
4(2 - 3x) = x - 2(2x + 1)
8 - 3x = x - 4x - 2
8 - 3x = -3x - 2
y = 0
Based on the student's work, the equation was solved
The equation solved correctly would show that it has
solution(s).
Word Bank:
correctly
three
infinite
incorrectly
00
TWO
one
Blank 1:
Blank 2:
Answers
Based on the student's work, the equation was solved incorrectly. B. The equation solved correctly would show that it has one solution(s).
What is an equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For instance, 2x - 5 = 13. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign.
In correct solution of the equation is given as:
4(2 - 3x) = x - 2(2x + 1)
8 - 12x = x - 4x - 2
8 - 12x = -3x - 2
8 + 2 = 12x - 3x
10 = 9x
x = 10/9
Hence, based on the student's work, the equation was solved incorrectly.
The equation solved correctly would show that it has one solution(s).
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A recipe for chocolate chip muffins states that it yields 12 muffins, with 250 calories per muffin. You instead decide to make mini-muffins, and the recipe yields 18 muffins. If you eat 3, how many calories will you consume?
Answers
The number of calories that you would consume if you eat 3 mini-muffins is 41.66.
How many calories will each muffin have?To know the number of calories per muffin, let's divide the total of calories (250) by the number of muffins.
Regular muffins: 250 / 12 = 20.83 calories
Mini-muffins: 250 / 18 = 13.88 calories.
This shows that one mini-muffin contains 13.88 calories, while the original recipe contains 20.83 calories per muffin.
How many calories are 3 mini-muffins?13.88 calories x 3 = 41.66 calories
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PLS HELP!!! Find a function of the form
Answers
Step-by-step explanation:
that's your answer im hoping so
 Which statement is true?
O a
0 b
C
0
d
Pythagorean Theorem states that the area of the blue square + the area of the red square = the area of the purple square.
Pythagorean Theorem states that all three squares have 4 right angles.
Pythagorean Theorem states that the area of the purple square + the area of the blue square = the area of the red square
Pythagorean Theorem states that the area of the 3 squares add to be the right triangle's area
Pythagorean Theorem states three squares can always be put together to form a right triangle in the middle,
Answers
Pythagorean Theorem states that the area of the blue square + the area of the red square = the area of the purple square.
State and proof Pythagoras theorem?Consider the triangle
Where “a” is the perpendicular,
“b” is the base,
“c” is the hypotenuse.
According to the definition, the Pythagoras Theorem formula is given as:
Hypotenuse² = Perpendicular² + Base²
c² = a² + b²
The side opposite to the right angle (90°) is the longest side (known as Hypotenuse) because the side opposite to the greatest angle is the longest.
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
Hence, Pythagorean Theorem states that the area of the blue square + the area of the red square = the area of the purple square.
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100 points + solve please ! thank you v muchh
Answers
Answer:
1) Given
2) Given
3) Segment Addition Postulate
4) Segment Addition Postulate
5) Substitution Property of Equality
6) Transitive Property of Equality
7) Definition of congruent segments
Step-by-step explanation:
Segment Addition PostulateIf a line segment has two endpoints, A and C, and a third point B lies somewhere on the line segment AC, the distance from A to B plus the distance from B to C is equal to the distance from A to C:
AB + BC = ACSubstitution Property of EqualityIf two expressions are equal to each other, then we can replace one of them with the other in any equation or expression, and the equality will still hold true
Transitive Property of EqualityIf a = b and b = c, then a = c.
Statements Reasons
1) AB ≅ DE 1) Given
2) BC ≅ EF 2) Given
3) AB + BC = AC 3) Segment Addition Postulate
4) DE + EF = DF 4) Segment Addition Postulate
5) AB + BC = DF 5) Substitution Property of Equality
6) AC = DF 6) Transitive Property of Equality
7) AC ≅ DF 7) Definition of congruent segments
Evaluate the expression for v = -1.
-63+37|v| =
Answers
The expression is -63 + 37|-1|. The absolute value of -1 is 1, so the expression becomes -63 + 37(1) = -26.
What is the value ?The value of depends on the context in which they are used. In general, words can have a variety of different values, such as conveying information, expressing an opinion, or providing entertainment. Each individual word can have different meanings and associations depending on the situation. writing is important in any context in which words are used, as it ensures that the ideas expressed are original and properly attributed.
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Find the largest possible area for a rectangle with a base on the x-axis and both upper vertices on the curve y=5−x2
Answers
The largest possible area for a rectangle with a base on the x-axis and both upper vertices on the curve y=5−x² , is equals to the 20√15/ 9 .
In optimizing the objective function f(x), solve for the critical points by putting the first derivative f′(x), equals to zero. Then the objective function is evaluated at the critical points to determine the it's minimum or maximum. We have, a rectangle with base as x-aixs and both upper vertices on the curve y = 5 − x², which is a parabola equation. Thus width of the rectangle is based from the equation of the parabola y= 5 - x² --(1)
Area of rectangle is expressed as A = xy , where x -->length of it and y-->width or vertices of curve. The length of the rectangle with base x- axis is equal to 2x. Therefore, the area is A = w× l
= 2x( 5 - x² )
A = 10x - 2x³ --(2)
If area is maximum, then dA/dx = 0
Differentiating the equation (2) with respect to x
dA/dx = 10 - 6x²
so, 10 - 6x² = 0
=> 6x² = 10
=> x² = 10/6
=> x² = 5/3
=> x = ±√5/3
but x represents the length so, it's value always be positive. Thus, x = √5/3. The area is equal to A = 10x - 2x³
= 10(√5/3) - 2(√5/3)³
=> A = 10√5/3 - 10/3(√5/3)
=> A = √5/3( 10 - 10/3) = 20√5/3√3
=> A = 20√15/ 9 ( using rationalzation )
Hence, the required area is 20√15/ 9 .
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Andy is hanging wallpaper in his kitchen. He is to cover 2 2/5 of the walls in the room using 6 rolls of paper. What is the number of rolls of paper used per wall?
Answers
The number of rolls of paper used per wall will be 1.5 rolls per wall.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Andy is hanging wallpaper in his kitchen. He is to cover 2 2/5 of the walls in the room using 6 rolls of paper. We know that the room has 4 walls.
Then the number of rolls of paper used per wall is given as,
⇒ 6 / 4
⇒ 1.5 rolls per wall
The number of rolls of paper used per wall will be 1.5 rolls per wall.
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ABC and XYZ are similar. Find the missing side length. A B ?,35,40,C X Y 5, 7, 8,
Answers
Answer: DF is 24
Step-by-step explanation: DEF is 6x larger than triangle ABC so since AC is 4 DF is 24.
I need help with the answer please :)
Answers
Answer:
1.339 Canisters
Step-by-step explanation:
Because you are making 5 meatloafs for a party, and according to the recipe you need 1 1/4 cup of breadcrumbs per each meatloaf. In each canister there is 14/3 cups of breadcrumbs which you can see by multiplying the serving size by the servings per container.
Since you need five meatloafs, you can figure out how many cups of breadcrumbs you need by multiplying 1 1/4 cups by 5. This gives you 6 1/4 or 6.25 cups.
In each canister of breadcrumbs, there are 14/3 cups or 4.667 cups of breadcrumbs.
To figure out how many canisters you need, you divide the amount of breadcrumbs you need (6.25 cups) by the amount of breadcrumbs you have (4.667) which gives you 1.339 canisters.
Fill in the blanks below with the correct units.
(a) Lashonda's finger is about 6 ?
(b) The bucket holds about 6 ?
✓ long.
✓ of water.
(c) Leila used a fork that had a mass of about 32 ?
Answers
Answer:
A) 6centimeters (cm) LONG
B) 6 gallons/Liters of water
C) 32 milligrams
Step-by-step explanation: contact me through discord Acathia#0103, its easier to help, I can help with multiple questions aswell or send me ur SC
Roger ran a total of 6 miles over the course of 3 track practices. How many track practices would it take for Roger to run 20 miles? Solve using unit rates.
Answers
Number of track practices it would take roger to run 20 miles are 10 track practices.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
Given;
Roger ran a total of 6 miles over the course of 3 track practices
3track practices= 6miles
1mile= 1/2 track practices
20miles= 1/2*20
=10 track practices
Therefore, the answer by unitary method will be 10.
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The table gives the probability distribution of the annual rate of return on the stock of MNP Company, Inc. What is the expected value of the rate of return?
Answers
The expected value of the rate of return is 23.5%
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given is a table which gives the probability distribution of the annual rate of return on the stock of MNP Company, Inc. We have to find out the expected value of the rate of return
Let X be the return and p probability
Then
X 15% 20% 30% 35% Total
p 0.2 0.4 0.3 0.1 1
x(p) 3 8 9 3.5 23.5
Hence Expected rate of return
E(x)= 23.5%
Hence, the expected value of the rate of return is 23.5%
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Two cyclists 30 miles apart start riding toward each other at the same time. One of the cyclists bikes 2 times faster than the other. If they meet 2 hours later what is the speed (in miles per hour) what is the speed of the faster cyclist?
Write an equation using the information as it is given above to solve the equation.
Use the variable r to represent the slower bicyclist.
What is the speed of the faster bicyclist?
Answers
The speed of the faster cyclist is 3 miles per hour.
We can use the information given to set up the following equation:
r + (2r) = (r + 2r) / 2t
Where r is the speed of the slower cyclist, (2*r) is the speed of the faster cyclist, t is the time in hours, and the distance between the two cyclists is (r + 2r) miles.
We can use the given information that the two cyclists meet 2 hours later to solve for r:
r + (2r) = 30 / 22
Simplifying the equation we get:
r + (2*r) = 15
3r = 15
r = 5
We know that the faster cyclist is going 2 times faster than the slower cyclist, so we can use the value of r to find the speed of the faster cyclist:
2r = 25 = 10
So, the speed of the faster cyclist is 10 miles per hour.
help what's we Have : (x, y,z) = (1, 2, 3) ; (3,2,1); (1,3,2) ; (2,1,3) ; (2,3,1), and (3,1,2)
For k= 43 we have (x,y,z) = (2,2,3) or (2,3,2) or (3,2,2)
For k = 44 we have ( 8,-7,-5) or (8,-5,-7) or (-5,-7,8) or ( -5,8,-7) or (-7,-5,8) or (-7,8,-5)
For k =54 => (x,y,z) = (13,-11,-7) ,
for k = 55 => (x,y,z) = (1,3,3) or (3,1,3) or (3,1,1)
and (x,y,z) = (10,-9,-6) or (10,-6,-9) or ( -6,10,-9) or (-6,-9,10) or (-9,10,-6) or (-9,-6,10)
For k = 62 => (x,y,z) = (3,3,2) or (2,3,3) or (3,2,3)
For k =64 => (x,y,z) = (0,0,4) or (0,4,0)
Answers
Answer:
For k = 43, the possible values of (x,y,z) are (2,2,3), (2,3,2), and (3,2,2). For k = 44, the possible values of (x,y,z) are (8,-7,-5), (8,-5,-7), (-5,-7,8), (-5,8,-7), (-7,-5,8), and (-7,8,-5). For k = 54, the possible values of (x,y,z) are (13,-11,-7). For k = 55, the possible values of (x,y,z) are (1,3,3), (3,1,3), (3,3,1), and (1,3,1). For k = 62, the possible values of (x,y,z) are (3,3,2), (2,3,3), and (3,2,3). For k = 64, the possible values of (x,y,z) are (0,0,4) and (0,4,0).
You measure three segments of the distance between a diffraction slit an the screen on which the pattern forms: x1 = (15.8 +0.2) cm, x2 = (6.7 +0.1) cm, and x3 = (11.3 0.1). What is the uncertainty of the total distance x1 + x2 + x3? 0.2 cm O 0.1 cm 0.3 cm 0.4 cm 0.5 cm
Answers
The uncertainty of the total distance is 0.2 cm.
As per the given data, the distance between the diffraction slit and the screen on which the pattern forms,
[tex]x_{1}[/tex] = (15.8 ± 0.2) cm
[tex]x_{2}[/tex] = (6.7 ± 0.1) cm
[tex]x_{3}[/tex] = (11.3 ± 0.1) cm
Let, the uncertainty in the measurements,
[tex]x_{1}[/tex], [tex]x_{2}[/tex] and [tex]x_{3}[/tex] is [tex]e_{1}[/tex], [tex]e_{2}[/tex] and [tex]e_{3}[/tex] respectively.
So,
[tex]e_{1}[/tex] = 0.2 cm
[tex]e_{2}[/tex] = 0.1 cm
[tex]e_{3}[/tex] = 0.1 cm
Again, let the uncertainty in the total distance
[tex]\mathrm{x} =\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3[/tex] is e(error propagation).
The impact of a variable's uncertainty on the uncertainty of a function depending on it is known as propagation of uncertainty. When the variables are experimental measurement values, measurement limits cause uncertainties that are propagated via the function's combination of variables.
Then the error propagation is given as,
e = [tex]\sqrt{\mathrm{e}_1^2+\mathrm{e}_2^2+\mathrm{e}_3^2} \\[/tex]
So, e = [tex]\sqrt{(0.2)^2+(0.1)^2+(0.1)^2} \\[/tex]
Therefore e = [tex]\sqrt{0.06} \\[/tex]
e = 0.245 cm
e ≅ 0.2 cm
Therefore uncertainty of the total distance 0.2 cm
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