Answers
Answer: [tex]\displaystyle\\\frac{2\pi }{3},\ \frac{5\pi }{3} .[/tex]
Step-by-step explanation:
[tex]\displaystyle\\tan\theta=-\sqrt{3}\ \ \ \ 0\leq \theta\leq 2\pi \\\theta =\frac{2\pi }{3}+\pi N\ \ \ (N=0,\ 1,\ 2,\ 3\ ...)\\ N=0\\\theta=\frac{2\pi }{3} +\pi *0\\\theta=\frac{2\pi }{3}\ \ \ \ ( 0\leq \theta\leq 2\pi)\\ N=1\\\theta=\frac{2\pi }{3}+\pi *1 \\\theta=\frac{2\pi }{3} +\pi \\\theta=\frac{2\pi +3\pi }{3} \\\theta=\frac{5\pi }{3} \ \ \ ( 0\leq \theta\leq 2\pi)\\[/tex]
[tex]N=2\\\theta=\frac{2\pi }{3}+2\pi \\ \theta=\frac{2\pi +3*2\pi }{3}\\ \theta=\frac{2\pi +6\pi }{3} \\\theta=\frac{8\pi }{3} \\\theta=2\frac{2}{3} \pi \ \ \ \ (\notin0\leq \theta\leq 2\pi).\\[/tex]
Related Questions
A skateboard halfpipe is being designed for a competition. the halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 30 ft above the ground. using the ground as the x-axis, where should the base of the halfpipe be positioned? which equation best describes the equation of the halfpipe?
Answers
The equation of parabola is given by
(X-h)^2 = 4p(Y-k)^2
2p = 30 - 0
p = 15
4p = 4 × 15
= 60
In this case h = 0
So, we have (h,p) = (0,15)
So we get
We have equation: x^2 = 60(y-15)
y = x^2 / 60 + 15
What is a parabola?A parabola is nothing but a U-shaped plane curve. Any point on the parabola is equidistant from a fixed point called the focus and a fixed straight line known as the directrix. The general equation of a parabola is: y = a(x-h)2 + k or x = a(y-k)2 +h, where (h,k) denotes the vertex. The standard equation of a regular parabola is y2 = 4ax. Some of the important terms below are helpful to understand the features and parts of a parabola. Focus: The point (a, 0) is the focus of the parabola.
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The graph compares shoe sizes for a group of 100 two-year-old boys and a
group of 60 three-year-old boys.
Two box and whisker plots showing shoes sizes on a number line from 2.5 to 13. The upper plot represents the group of 2 year-old boys. For this upper plot, the minimum number is 3, the maximum number is 9.5, the right side of the box is 7.5, the left side of the box is 3.5, and the bar in the box is at 6. The lower plot represents the group of 3 year-old boys. For this lower plot, the minimum number is 5, the maximum number is 11.5, the right side of the box is 9.5, the left side of the box is 6.5, and the bar in the box is at 8.
About how many more two-year-old boys have a shoe size of 6 or less, compared to the three-year-old boys?
Answers
The number of two year old boys that wear a size 6 is greater than the number of three year old boys that wear a size 6 by 35.
How many more two year olds wear a size 6?A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines called the whiskers and a box. The whiskers represent the minimum and maximum scores.
On the box, the first line to the left represents the lower (first) quartile. 25% of the score represents the lower quartile. The next line on the box represents the median. 50% of the score represents the median. The third line on the box represents the upper (third) quartile. 75% of the scores represents the upper quartile
50% of the two year olds wear a size 6 = 50% x 100 = 50
25% of the three year olds wear a size 6 = 25% x 60 = 15
Difference in the number : 50 - 15 = 35
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PLEASE ANSWER QUICKLY
Answers
Answer:
3
Step-by-step explanation:
f(x) = 3x² - 2x + 1
f(x) = ax² + bx + c
a = 3
Which is the graph of the equation y- 1 = (x − 3)?
Answers
Answer:
the graph is a linear function
root (2,0) vertical intercept (0,2)
Step-by-step explanation:
(06.01 mc) what is the value of the expression 9 (fraction 1 over 2)4 ⋅ 48? 12 15 17 18
Answers
The value of the given expression is 105.
What are expressions?An expression or mathematical expression is a finite combination of symbols that is well-formed according to context-dependent norms. To help identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.To find the value of the given expression:
Given function - 9 + (fraction 1 over 2)4 ⋅ 48Let, 9 + 1/2 ⋅ 4 ⋅ 48.Follow the PEMDAS order of operations:
Multiply and divide (left to right).
1/2 ⋅ 4 ⋅ 48 = 96 9 + 1/2 ⋅ 4 ⋅ 48 = 9 + 96Add and subtract (left to right)
9 + 96 = 105Therefore, the value of the given expression is 105.
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Valerie ran three and one-fourth laps yesterday, and her coach wants her to run two and one-half times that many laps today. how many laps will she need to run today? choose the expression needed to solve the problem.
Answers
Valerie needs to run [tex]8\frac{1}{8}[/tex] laps.
What are mixed fractions?
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
You can divide any fraction into two pieces. These are the denominator and numerator. A improper fraction is one in which the numerator is greater than the denominator. The numerator must then be multiplied by the denominator by the students. They will then receive a specific form of a fraction. That is referred to as a mixed fraction.
Given,
Number of laps valerie ran = [tex]3\frac{1}{4}[/tex] laps
Number of times her coach wants her to run = [tex]2\frac{1}{2}[/tex] times
Therefore,
total number of laps she needs to run = [tex]3\frac{1}{4} \times 2\frac{1}{2}[/tex]
[tex]= \frac{13}{4} \times \frac{5}{2}[/tex]
[tex]= \frac{65}{8}[/tex] laps
[tex]=8\frac{1}{8}[/tex] laps.
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A cube. the top face has points a, g, e, f and the bottom face has points b, h, d, c. the diagonal from a to e is startroot 288 endroot inches and the diagonal from a to d is startroot 432 endroot inches. what is the length of ed in the given cube? round to the nearest tenth of an inch if necessary. in.
Answers
The length of the line ed according to the description of the cube is; 8.5.
What is the length of ed in the given Cube?First, since the shape is a cube, it follows that the diagonal of the top face can be used to determine the length of the sides of the top face.
Therefore , we have; length of each side of the top face;
ag = ge = ef = fa = √288/2 = 6√2.
Also, the diagonal of a to d is; √432 = 12√3.
Hence, the length of ed in the group as evident from the length of sides of the cube's top face in which case,
Consequently, the length of line ed is;√432 × 8.5.
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if a sum of money of rs 25000 increaes by 1/10 of itsself every year what time eill it amount to rs 30000?
pls answer correctly and quickly!
Answers
Answer:
the answer is 1.5/10 cause the 5000 is added to 30000
Ramiro was on a two day road trip.on the first day he drove at an average speed of 40 mph.on the second day he drove at an average of 60 mph.if he drove 2 hours longer and went 20 miles farther on his first day find the total distance ramiro traveled on his road trip.
Answers
Considering the relationship between velocity, distance and time, it is found that the total distance traveled was of 380 miles.
What is the relationship between velocity, distance and time?Velocity is distance divided by time, that is:
v = d/t.
For the first day, we have that:
v = 40, t = t + 2, d = d + 20, hence:
40 = (d + 20)/(t + 2)
For the second day, we have that:
v = 60
60 = d/t
d = 60t
Then, replacing in the first equation:
40 = (60t + 20)(t + 2)
60t + 20 = 40t + 80
20t = 60
t = 3.
Then the distances are given by:
First day: d = 60t + 20 = 60 x 3 + 20 = 200 miles.Second day: d = 60t = 60 x 3 = 180 miles.Total: 200 miles + 180 miles = 380 miles.More can be learned about the relationship between velocity, distance and time at https://brainly.com/question/28143163
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The point -2,5 is reflected across the y-axis. Which of these is the ordered pair of the image?
A) (-2,5)
B) (2,5)
C) (-2,-5)
D) (2, -5)
Answers
Answer:
B) (2,5)
Step-by-step explanation:
A box contains 6 red, 3 white, 2 green, and 1 black (total 12) identical balls. What is the least number of balls nevessary to take out randomly ( without looking) to be sure getting, atleast one red ball?
Answers
Answer:
7 balls
Step-by-step explanation:
Look for the worst case scenario:
Get 3 white, 2 green, and 1 black.
That adds up to: 3 + 2 + 1 = 6.
+1 red ball: 6 + 1 =7
7 balls
Please help with this geometry question
Answers
It has been proven that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
How to prove a Line Segment?We know that in a triangle if one angle is 90 degrees, then the other angles have to be acute.
Let us take a line l and from point P as shown in the attached file, that is, not on line l, draw two line segments PN and PM. Let PN be perpendicular to line l and PM is drawn at some other angle.
In ΔPNM, ∠N = 90°
∠P + ∠N + ∠M = 180° (Angle sum property of a triangle)
∠P + ∠M = 90°
Clearly, ∠M is an acute angle.
Thus; ∠M < ∠N
PN < PM (The side opposite to the smaller angle is smaller)
Similarly, by drawing different line segments from P to l, it can be proved that PN is smaller in comparison to all of them. Therefore, it can be observed that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
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Circle A is shown. Secant W Y intersects tangent Z Y at point Y outside of the circle. Secant W Y intersects circle A at point X. Arc X Z is 105 degrees and arc W Z is 175 degrees.
In the diagram of circle A, what is the measure of ∠XYZ?
35°
70°
75°
140°
Circle A is shown. Secant W Y intersects tangent Z Y at point Y outside of the circle. Secant W Y intersects circle A at point X. Arc X Z is 105 degrees and arc W Z is 175 degrees.
In the diagram of circle A, what is the measure of ∠XYZ?
35°
70°
75°
140°
Answers
By applying the theorem of intersecting secants, the measure of angle XYZ is equal to: A. 35°.
How to determine angle <XYZ?By critically observing the geometric shapes shown in the image attached below, we can deduce that they obey the theorem of intersecting secants.
What is the theorem of intersecting secants?The theorem of intersecting secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.
By applying the theorem of intersecting secants, angle XYZ will be given by this formula:
<XYZ = ½ × (m<WZ - m<XZ)
Substituting the given parameters into the formula, we have;
<XYZ = ½ × (175 - 105)
<XYZ = ½ × 70
<XYZ = 35°.
By applying the theorem of intersecting secants, we can infer and logically deduce that the measure of angle XYZ is equal to 35°.
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Answer: 35
Step-by-step explanation:
Students in 7th grade took a standardized math test that they also took in 5th grade. The results are shown on the dot plot, with the most recent data shown first.
Find and compare the medians.
7th-grade median:
5th-grade median:
What is the relationship between the medians?
Answers
Using the median concept, it is found that:
The 5th-grade median is of 13.The 7th-grade median is of 17.The relationship is that 7th grade students have a higher median than 5th grade students.What is the median of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.
Researching the problem on the internet, we have that there are 21 5th grade students. It is an odd number, hence the median is the 11th element, as (21 + 1)/2 = 11. Looking at the dot plot, the median is of 13.
There are 23 5th grade students. It is an odd number, hence the median is the 12th element, as (23 + 1)/2 = 12. Looking at the dot plot, the median is of 17.
The relationship is that 7th grade students have a higher median than 5th grade students.
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Select the correct answer. sean used cross multiplication to correctly solve a rational equation. he found one valid solution and one extraneous solution. if 1 is the extraneous solution, which equation could he have solved?
Answers
The equation that Sean woul have solved using the cross multiplication would be option a.
How to solve the question through the use of cross multiplication[tex]\frac{10}{x^2-1} =\frac{15}{3x-3}[/tex]
We have to open the equation by using cross multiplication
10(3x - 3) = 15(x² - 1)
= 30x - 30 = 15x² - 15
we would have to factorize
30(x-1) = 15(x-1)(x+1)
We have to divide by 15(x-1)
2 = x + 1
take the like terms
2 -1 = x
x = 1
Hence the equation that has the extraneous solution is option a because the solution is 1.
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I dive to 56 feet for 47 minutes. After a 30 minute surface interval I do a second dive to 56 feet. Losing track of time, I notice my bottom time is now 25 minutes. According to the General Rules, what should I do
Answers
According to general rules, what you can do now is; Ascend right away to 15 feet and stay there for 8 minutes before going to the surface and not dive for 6 hours
How to solve algebra word problems?We are given;
Initial distance dived = 56 feet
Time for initial dive = 47 minutes
Time from finishing of initial dive to start of second dive = 30 minutes
Second dive distance = 56 ft
Her current bottom time is now 25 minutes
Now, bottom time is defined as the total time, in minutes, from the beginning of a descent to the beginning of an ascent.
Thus, according to general rules, what you can do now is to Ascend right away to 15 feet and stay there for 8 minutes before going to the surface and not dive for 6 hours
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What is the probability that 2 precedes 1 when we randomly select a permutation of {1, 2,. ,n} where n ≥ 4?
Answers
The probability is 1/3.
Probability is sincerely how likely something is to show up. whenever we're unsure about the final results of an event, we will communicate about the probabilities of positive consequences—how probably they're. The evaluation of events governed by way of possibility is called information.
Probability is the branch of mathematics concerning numerical descriptions of ways likely an occasion is to arise, or how in all likelihood it's far that a proposition is actual. The opportunity of an event is more than a few among 0 and 1, wherein, kind of talking, zero suggests impossibility of the occasion and 1 shows the truth.
Chance = the wide variety of approaches to achieving achievement. the whole range of viable consequences. as an example, the opportunity of flipping a coin and its being heads are ½ because there may be 1 manner of getting a head and the overall wide variety of feasible results is two (a head or tail). We write P(heads) = ½.
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Help me pls this is very hard for me and plus i gotta turn this in tomorrow
Answers
Answer: [tex]\Large\boxed{x=40^\circ}[/tex]
Step-by-step explanation:
Given information
∡ 1 = 90°
∡ 2 = 50°
∡ 3 = x°
Total Angle = 180° (Triangle angle sum theorem)
Given formula
∡ 1 + ∡ 2 + ∡ 3 = Total Angle
Substitute values into the formula
(90) + (50) + (x) = (180)
Combine like terms
140 + x = 180
Subtract 140 on both sides
140 + x - 140 = 180 - 140
[tex]\Large\boxed{x=40^\circ}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
A map has a scale of 1:5000000000 .
a. A road on the map is 10cm long . What is the real length of the road in km ?
b. The area of a farm of the map is 6 cm square . What is the real area of the farm in hectares ?
( 1 hectare = 10000 m square = 0.01 km square )
Answers
Considering the definition of scale, you obtain:
the real length of the road is 500,000 km.the real area of the farm is 300 hectares.Definition of mapA map is the conventional graphical representation of a portion of the earth or another celestial body that shows the size and position of elements of the landscape according to the selected scale and projection. That is, a map is a representation of a place, at a size smaller than the actual size.
Definition of scaleThe scale of a cartographic representation, or map scale (m), is the relationship of similarity between the real dimensions of the geographical space represented and those of its image on the map. In general, it is also defined as the ratio of the lengths of a linear element in the plane and its representation on the terrestrial reference surface.
That is, the scale of the map is defined as the proportionality relationship that exists between a distance measured on the ground and its corresponding measurement on the map.
Real length of the roadA map has a scale of 1:5000000000. This indicates that 1 unit on the map is equivalent to 5,000,000,000 in reality.
You know that the road on the map is 10 cm or 0.0001 km long (knowing that 1 km= 100,000 cm).
Then you can apply the following rule of three: if by definition of scale 1 km on the map is equivalent to 5,000,000,000 km in reality, 0.0001 km on the map is equivalent to how much distance in reality?
[tex]real length of the road=\frac{0.0001 kmx 5,000,000,000 km }{1 km}[/tex]
real length of the road= 500,000 km
Finally, the real length of the road is 500,000 km.
Real area of the farmYou know that the area of a farm of the map is 6 cm square, 0.0006 m sr 0.00000006 hectares (knowing that 1 cm square= 0.0001 m square and 10,000 m square= 1 hectare).
Then you can apply the following rule of three: if by definition of scale 1 hectare on the map is equivalent to 5,000,000,000 hectares in reality, 0.00000006 hectares on the map is equivalent to how much area in reality?
[tex]real area of the farm=\frac{0.00000006 hectaresx 5,000,000,000 hectares }{1 hectare}[/tex]
real area of the farm= 300 hectares
Finally, the real area of the farm is 300 hectares.
SummaryIn summary, you get:
the real length of the road is 500,000 km.the real area of the farm is 300 hectares.Learn more about scale:
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The student’s t distribution will approach the standard normal distribution as the number of the degrees of freedom goes up.
a. True
b. False
Answers
Answer:
True student distribution will approach the standard
Find the area of the blue shape below. Use 3.14 for π
If anyone knows the answer please help!
Answers
Answer:
1413.86 ft^2.
Step-by-step explanation:
The diameter of the circle = 50 - 2(18)
= 50-36
= 14 ft.
So its radius is 7 ft.
The total area of the blue shape
= 2(35 * 18) + 3.14*7^2
= 1413.86 ft^2.
When we use the Distributive
Property, we multiply the number in
front of the parenthesis with each
term inside the parenthesis.
Enter the number that belongs in the green box.
3(4x + 2) = [?]x + [ ]
Answers
Answer:
12x+6
Step-by-step explanation:
Can i have brainliest
Answer: 12x + 6
Step-by-step explanation:
In Distributive property, you multiply each of the numbers in the parentheses by the outside number.
The area of the trapezoid is 40 square units.
A trapezoid is shown. The lengths of the bases are 6 and 10, and the height of the altitude is h.
What is the height of the trapezoid?
3 units
5 units
10 units
12 units
Answers
The altitude of the trapezoid, based on the given parameters is 5 units
How to determine the height of the trapezoid?From the question, we have the following parameters about the trapezoid
Base length 1 of the trapezoid = 6
Base length 2 of the trapezoid = 10
Area of the trapezoid = 40
Altitude of the trapezoid = h
The area of the trapezoid is calculated using
Area = 0.5 * (Sum of the two base lengths) * Altitude of the trapezoid
Substitute the given parameters in the above formula
40 = 0.5 * (6 + 10) * h
Evaluate the sum of 6 ad 10 (do not approximate)
40 = 0.5 * (16) * h
Evaluate the product of 0.5 and 16 (do not approximate)
40 = 8 * h
Divide both sides by 8 (do not approximate)
h = 5
Hence, the altitude of the trapezoid, based on the given parameters is 5 units
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Answer:
5 units
Step-by-step explanation:
At a concert for the band Algal Rhythms, 75% of the tickets were sold at the full price of $30. The remaining 25% of tickets were sold at a discounted price of $10. What was the average selling price of a ticket at the Algal Rhythms concert? Express your answer in dollars, rounded to the nearest cent.
Answers
The average selling price of a ticket at the Algal Rhythms concert is $25
How to determine the average selling price of a ticket at the Algal Rhythms concert?The given parameters are:
75% of the tickets were sold for $30.
The remaining 25% were sold for $10.
The average selling price of a ticket at the Algal Rhythms concert is calculated using
Average = Sum of (Price * Percentage)
So, we have
Average = 30 * 75% + 10 * 25%
Evaluate the expression
Average = 25
Hence, the average selling price of a ticket at the Algal Rhythms concert is $25
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The equation h = 7 sine (startfraction pi over 21 endfraction t) 28 can be used to model the height, h, in feet of the end of one blade of a windmill turning on an axis above the ground as a function of time, t, in seconds. how long is the blade? assume that the blade is pointing to the right, parallel to the ground, at t = 0, and that the windmill turns counterclockwise at a constant rate.
Answers
The windmill's blade measures 7 feet in length.
What is an equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =.To find the measure of the windmill's blade:
We have the equation: [tex]h=sin(\frac{\pi }{21t} )+28[/tex]At the time 't' = 0, the end of the blade is parallel to the ground and pointing to the right, indicating that it is the same height as the other end. (Ф = 0°)We may calculate the length of the blade by calculating the greatest height of this end at = 90°.We now know that the general model equation of a circular simple harmonic motion is written as follows: y = A sinωt + kWhere A is the maximum displacement from mean to maximum positionThe angular frequency is ω.When eq1 and eq2 are compared:A = 7As a result, the difference in blade end height at = 0° and = 90° is 7 feet.Therefore, the windmill's blade measures 7 feet in length.
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The correct question is given below:
The equation h=7sin(pi/21t)+28 can be used to model the height, h, in feet of the end of one blade of a windmill turning on an axis above the ground as a function of time, t, in seconds. How long is the blade? Assume that the blade is pointing to the right, parallel to the ground, at t = 0, and that the windmill turns counterclockwise at a constant rate. 7 feet 14 feet 21 feet 28 feet
Consider these situations. in each situation, is the demand for the good elastic or inelastic? as the price of flat-screen televisions decreases, the quantity demanded increases significantly. as the price of bread decreases, the quantity demanded changes only slightly. as the price of a drug used to treat heart disease increases, the quantity demanded remains unchanged.
Answers
Answer:
Step-by-step explanation:
elastic, inelastic, inelastic
Answer: elastic, inelastic, inelastic
Step-by-step explanation:
I found this proof by induction that all people in canada are the same height, i was wondering what is the incorrect step?
Step 1: In any group that consists of just one person, everybody in the group has the same age, because after all there is only one person!
Step 2: Therefore, statement S(1) is true.
Step 3: The next stage in the induction argument is to prove that, whenever S(n) is true for one number (say n=k), it is also true for the next number (that is, n = k+1).
Step 4: We can do this by (1) assuming that, in every group of k people, everyone has the same age; then (2) deducing from it that, in every group of k+1 people, everyone has the same age.
Step 5: Let G be an arbitrary group of k+1 people; we just need to show that every member of G has the same age.
Step 6: To do this, we just need to show that, if P and Q are any members of G, then they have the same age.
Step 7: Consider everybody in G except P. These people form a group of k people, so they must all have the same age (since we are assuming that, in any group of k people, everyone has the same age).
Step 8: Consider everybody in G except Q. Again, they form a group of k people, so they must all have the same age.
Step 9: Let R be someone else in G other than P or Q.
Step 10: Since Q and R each belong to the group considered in step 7, they are the same age.
Step 11: Since P and R each belong to the group considered in step 8, they are the same age.
Step 12: Since Q and R are the same age, and P and R are the same age, it follows that P and Q are the same age.
Step 13: We have now seen that, if we consider any two people P and Q in G, they have the same age. It follows that everyone in G has the same age.
Step 14: The proof is now complete: we have shown that the statement is true for n=1, and we have shown that whenever it is true for n=k it is also true for n=k+1, so by induction it is true for all n.
Answers
The incorrect step in the induction that all people in Canada are the same height is; Step 9
How to prove Mathematical Induction?The principle of mathematical induction as follows:
For example, we have a set of natural numbers. Now, suppose that 1 is in the set. Now, we assume that anytime n is in the set, n + 1 is also in the set. Therefore we can say that every natural number is in the set.
The wrong step in the given mathematical Induction is Step 9. This is because;
We might not be to see anyone else in the arbitrary group G other than groups P or Q!
Recall that G is a group of k + 1 people. Thus, provided that k > 1, k + 1 > 2 and that a third person R in G does not exist, then the rest of the proof will work.
The steps above proves that;
S(k) = S(k + 1), for every k > 1.
Thus, we can also say that if S(2) is true, then it equally means S(3) is true and so on till infinity.
From our induction process written so far, we have see that S(1) was true. However, our induction step in the question does not show us that that S(1) = S(2) = true.
So: Thus, from the induction I have done It shows that S(1) not imply S(2) and as a result the proof is fallacious.
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Use the equation to complete an algebraic proof that proves the answer is x = 7/6. Write your proof in your journal and upload your answer. You will be awarded 5 points for the statements and 5 points for the reasons.
I need the algebraic proofs please!!!
Answers
Using the algebraic equation, (2x + 6)/5 = 4x - 3, it has been proved that x = 7/6
Algebraic Proof for the Given Algebraic Equation
The given algebraic equation is,
(2x + 6)/5 = 4x - 3
2x + 6 = 5(4x - 3)
2x + 6 = 20x - 15
20x - 15 = 2x + 6
This algebraic equation can be written as,
20x - 2x - 15 = 6
18x = 15 + 6
18x = 21
x = 21/18
x = 7/6
Hence, using the given algebraic equation, it has been proved that the value of x is 7/6.
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What are the zeros of the polynomial function: f(x) = x^3 - x^2 – 6x ?
Answers
Answer:
x=0, x=3, x=-2
Step-by-step explanation:
factor the equation
x(x^2-x-6)
factor more
x(x-3)(x+2)
set it equal to 0
x(x-3)(x+2)=0
plug in numbers for x that would result in the answer being 0
0(0-3)(0+2)=0
3(3-3)(3+2)=0
-2(-2-3)(-2+2)=0
Please Solve the following #6 and #7. Answer: C, A
Answers
6) For the inverse to be a function, f(x) needs to be one to one. To accomplish this, restrict the domain to one side of the axis of symmetry
7) The y-intercept of the inverse is when x=0. This means we want to find when f(x)=0.
[tex]4(1/3)^x = 16 \\ \\ (1/3)^x= 4 \\ \\ x=\log_{1/3}(4) \approx -1.26[/tex]