The table of x, y and t for the given parametric equations is
The Table is as follows:
t -4 -2 0 2 4
x 16 4 0 4 16
y 0 2 4 6 8
The parametric equations are given:
x = t², y = t + 4; -4 ≤ t ≤ 4
if t = -4
x = (-4)² = 16
y = -4 + 4 = 0
if t = -2
x = (-2)² = 4
y = -2 + 4 = 2
if t = 0
x = (0)² = 0
y = 0 + 4 = 4
if t = 2
x = (2)² = 2
y = 2 + 4 = 6
if t = 4
x = (4)² = 16
y = 4 + 4 = 8
The Table is as follows:
t -4 -2 0 2 4
x 16 4 0 4 16
y 0 2 4 6 8
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At the point of tangency, a tangent to a circle is to the radius.
At the point of tangency, a tangent to a circle is perpendicular to the radius.
What is tangent of circle?A tangent is a line that extends from a point on the circle to two points that are eternally close to one another. To put it another way, we can say that tangents are lines that precisely cross a circle at a certain location. Where the tangent touches the circle is known as the point of tangency. An angle is tangent to the radius at the point of tangency. This is a key component of geometric constructions and proofs, and as such, it is related to a number of theorems. One by one, we will examine them.
Theorem: 1
By connecting the center with the point of tangency, a radius is produced. A circle's tangent at a given location is perpendicular to its radius. Simply adhere to the diagram below: Here AB⊥OP
Theorem:2
According to this theorem, two tangents traced to a circle from a single exterior point have equal numbers of tangent segments. Line connecting the exterior point and the point of tangency is referred to as a tangent segment.
Hence the theorem of the tangent of circle mentioned above.
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Complete question:
At the point of tangency, a tangent to a circle is ______ to the radius.
Find the distance from (-4, 7) to the line y = 2x
Answer:
Step-by-step explanation:
y=mx+c
7=2*-4+c
7=-8+c
7+8=c
15=c
Build a VI to compute the variance of an array x. The variance sigma is defined as: sigma = 1/N sigma^N_j = 1 (x_j - mu)^2 where mu denotes the average of the array x. For x, use all the integers from 1 to 1000.
There are 4 steps to build a VI to compute the variance of an array x.
Here is a VI in LabVIEW to compute the variance of an array x:
Create a new VI and add a 1D array constant to the front panel. Connect it to a For Loop.Inside the For Loop, subtract the average of the array x from each element and square the result. Accumulate the result in a shift register.After the For Loop, divide the accumulated result by the number of elements in the array to find the variance.Add a control to the front panel to display the result.To learn more about variance here:
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For each strategy which recent decisions have been made in that manner and which factors influenced the decisions to use that strategy.
Ask questions such as :
Which strategies do you use more than others ?
What is the hardest part of the decision making process for you ?
Am there be It’s than one solution to a problem?
Spontaneity :
Choosing the first alternative that comes to mind without thinking about the consequences.
Compliance :
Going along with what your family, teachers, or friends expect you to do.
Strategies CONT:
Procrastination: Waiting to act on a decision for so long that your choices become limited .
Agonizing: Gathering so much information that analyzing the choices becomes overwhelming
Desire: Choosing an option that achieves a wanted result but may involve risk
Avoidance: Choosing an option that prevents an unpleasant result
Security: Choosing an option that does not upset people or involve risk
Synthesis: Choosing an option that will probably be successful and which you like the best.
Step-by-step explanation:
It's difficult for me to determine which recent decisions have been made using these strategies without more context about the specific situation. However, I can provide general information about how each strategy may be used and what factors may influence the decision-making process.
Spontaneity: This strategy may be used in situations where time is of the essence, and there is not enough time to weigh all options. The individual may also be impulsive or lack the ability to plan ahead.
Compliance: This strategy may be used in situations where the individual values the opinions of others over their own, or they may not want to upset their family, teachers, or friends.
Procrastination: This strategy may be used when the individual is overwhelmed by the decision-making process, and they are unsure of what choice to make. They may also be afraid of making the wrong choice.
Agonizing: This strategy may be used when the individual wants to make sure that they are making the best decision, and they want to gather as much information as possible. This can lead to paralysis by analysis, and they may not make a decision at all.
Desire: This strategy may be used when the individual wants to achieve a specific outcome, and they are willing to take a risk to do so. They may also be motivated by a sense of adventure.
Avoidance: This strategy may be used when the individual wants to avoid a negative outcome, and they are willing to make a decision based on that.
Security: This strategy may be used when the individual wants to make a decision that will not upset others or involve risk. They may also be motivated by a sense of stability.
Synthesis: This strategy may be used when the individual wants to choose an option that will probably be successful and which they like the best. They may also have a good sense of what they want and what is best for them.
These are general information, the hardest part of the decision-making process for an individual may vary depending on the situation, the options available, and their personal preferences. Furthermore, there may be more than one solution to a problem, and the best one depends on the individual's preferences, resources, and the context of the problem.
▸ The rules of the Witches Guild are very strict. Black hats must be worn in public at all times. Broomsticks are to be replaced yearly and goblin gowns must not contain any patches. On Halloween, each witch must scare 13 people-no more and no less. Each goblin must scare 33 people, and each ghost must scare 19 people. How many people were scared by a group of 135 ghosts and 273 witches?
At the haunted mansion, 6114 people were scared by a group of 135 ghosts and 273 witches.
How do equations work?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
According to the question each ghost must scare 19 people that means 135 ghost will scare:
135 ghosts x 19 people = 2,565 people......................(i)
And each witch must scare 13 people-no more and no less i.e 273 witches will scare:
273 witches x 13 people = 3,549 people.....................(ii)
Adding (i) and (ii) we get;
2,565 + 3,549 = 6114 people
Therefore, 6114 people were scared by a group of 135 ghosts and 273 witches.
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Aaron arrives at school late because his car broke down, and therefore, has only 45 minutes to complete a history exam. The exam has two open-ended questions and 30 multiple-choice questions. Each correct open-ended question is worth 20 points, and each multiple-choice question is worth 2 points. He knows that it usually takes him 15 minutes to answer an open-ended question and only 1 minute to answer a multiple-choice question. Assume that for each question Aaron answers, he receives full credit. How many of each type of question should he answer to get maximum possible points?
Aaron should answer 3 open-ended questions and 0 multiple-choice questions to get a maximum of 3 * 20 points/question = 60 points
How to calculate the amount of time it would take AaronAaron has 45 minutes to answer the questions, so he has 45 minutes / 15 minutes/question = 3 open-ended questions that he can answer.
For the remaining questions, he has 45 minutes - (3 * 15 minutes) = 45 minutes - 45 minutes = 0 minutes.
So he cannot answer any more open-ended questions.
He can answer 0 minutes / 1 minute/question = 0 multiple-choice questions.
Therefore, Aaron should answer 3 open-ended questions and 0 multiple-choice questions to get a maximum of 3 * 20 points/question = 60 points.
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while on vacation, michelle and her family visit mount rushmore in south dakota. they watch a movie in the visitor center for 14 of an hour. this accounts for 15 of the total time they spend at mount rushmore.which equation can you use to find the total amount of time t michelle's family spends at mount rushmore?
The total amount of time Michelle's family spends at Mount Rushmore is 93.38 minutes, which is equivalent to 1 hour and 33.38 minutes.
The time Michelle and her family spend watching the movie in the visitor center is 14/60 of an hour or 14 minutes. We are told that this accounts for 15% of the total time they spend at Mount Rushmore, so to find the total amount of time they spent at Mount Rushmore, we need to divide the time spent watching the movie (14 minutes) by the percentage of the total time this accounts for (15%). This gives us the equation:
time = 14 / (15/100)
time = 14 × (100/15)
time = 14 × (6.67)
time = 93.38 minutes or 1 hour and 33.38 minutes.
So the total amount of time Michelle's family spends at Mount Rushmore is 93.38 minutes, which is equivalent to 1 hour and 33.38 minutes.
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a hospital is trying to implement a new patient assessment form. they want to first test the usability and efficacy of the form.when determining sample size for the first test, it is most important to:
When determining sample size for the first test, it is most important to Weigh the potential consequences of a test that does not lead to improvement against the belief in success.
When evaluating a patient, a patient assessment form is used to evaluate the patient's potential diagnosis and the appropriate course of therapy. To prevent misdiagnosis and ensure that the right therapy is given, it is crucial to gather relevant data. In order to register patients for operations provided by medical institutions, patient registration forms are utilised. Our free patient registration forms will efficiently capture patient information online, streamlining the registration and onboarding process whether you need to register new patients for your hospital, clinic, health centre, or private practise. Usability testing may find and support data-driven design decisions that have been drawn from practitioner usage of the system in a hectic office setting. Health care safety may be improved by using human factors understanding of HCI design and its effects on human performance.
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Describe the pattern, Write the next term, and write a rule for the nth term of the sequence
15. 1, 6, 11, 16, ...
Step-by-step explanation:
it is a arithematuc sequence because it has a common difference of 5
so the general term is Tn = 1 + (n-1)5
also the 5th term is T(5) = 1 + (5-1)5 = 21
Does anybody know this?
They sold 400 student tickets and 200 student tickets.
And at a certain performance, they sold 100 adult tickets and 200 student tickets.
What is a linear equation?An equation of degree one is known as a linear equation.
A linear equation of two variables can be represented by ax + by = c.
Given, Let 'x' represents the number of adult tickets and 'y' represent the number of student tickets.
So, The two equations can be formed as,
x + y = 600 and 7.5x + 4.5y = 3300.
Multiplying equation 1 by 7.5x we have 7.5x + 7.5y = 4500 and subtracting it from equation 2 we have,
- 3y = - 1200.
y = 400 and hence x = 200.
At a certain performance, they sold twice as many student tickets as adult tickets.
y = 2x.
x + y = 300.
x + 2x = 300.
3x = 300
x = 100 and hence y = 200.
100×7.5 + 200×4.5 = 750 + 900 = 1650.
So, they were 3300 - 1650 = $1650 short.
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Find g(x), where g(x) is the reflection across the y-axis of f(x) = x + 5. Write your answer in the form mx + b, where m and b are integers.
Considering the Question G(x) = -x + 5 is the equation for such reflections at f(x) = x + 5 from across y-axis.
What does the y-axis stand for?Similar to a vertical ruler is the y-axis. It displays the location of an object on a two-dimensional Cartesian graph with in y (vertical) plane. On a graph, it serves as the starting point, or "zero," from which to calculate how far a tip is from right or left (horizontally).
The sign of the x-coordinate is altered by reflection across the y-axis, while the y-coordinate remains constant. By changing the sign of x, we may represent f(x) = x + 5 from across y-axis as g(x) = -x + 5. G(x) = -x + 5 is the equation for the reflections for f(x) = x + 5 from across y-axis.
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how much consumer surplus will there be if the price is $40?
If the price paid for a certain item is $40 and the consumer surplus is $4, then the maximum buying price for that item is $44 .
The Consumer's Surplus is defined as the difference between the maximum price a consumer is willing to pay for an item and the actual price paid for the item.
If the price paid for the item is $40 and the consumer's surplus is $4, then the maximum buying price for that item can be calculated as :
⇒ Maximum buying price = Price paid + Consumer's surplus
Substituting the values of Price paid and consumer surplus ,
we get ;
⇒ $40 + $4
⇒ $44
Therefore , the maximum buying price for that item is $44 .
The given question is incomplete , the complete question is
If the price paid for a certain item is $40 and the consumer surplus is $4, then what is the maximum buying price for that item ?
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select all the shapes below which are an enlargement of x by scale factor -1
Shapes A and B are enlargements of x by a scale factor of -1 because they are mirror images of x. Shape C is not an enlargement of x by scale factor -1 because it is not a mirror image of x. Therefore, the option is A and B.
An enlargement by a scale factor of -1 means that the image is flipped and has the same size as the original.
Therefore, any shape that is a mirror image of x is an enlargement of x by scale factor -1. Looking at the shapes, we can see that shapes A and B are mirror images of x, so they are enlargements of x by scale factor -1.
Shape C is not a mirror image of x, so it is not an enlargement of x by scale factor -1. Therefore, the answer is A and B.
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15-28i=3l+(4m)i
(find the values of l and m)
Step-by-step explanation: To find the values of l and m, we need to solve the equation 15 - 28i = 3l + (4m)i for l and m.
First, we can move all the terms with i to one side of the equation:
15 = 3l + 4mi
-28i = 4mi
To solve for m, we can divide both sides by 4i:
-28i/4i = m
m = -7
Now that we know the value of m, we can substitute it back into the equation to solve for l:
15 = 3l + 4(-7)i
15 = 3l - 28i
3l = 15 + 28i
To solve for l, we can divide both sides by 3:
l = (15 + 28i)/3
So the values of l and m are l = (15 + 28i)/3 and m = -7
Answer:15
Step-by-step explanation:
Determine the coordinates of the image of point 8 of quadrilateral ABCD after the translation of 5 units to the left and 3 units down.
The coordinates of the image of point B of quadrilateral ABCD after the translation of 5 units to the left and 3 units down are B'(-14, -11).
What is a translation?In Mathematics, the translation of a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image.
On the other hand, the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate of the pre-image.
By translating the pre-image of quadrilateral ABCD vertically down by 3 units and horizontally left by 5 units, the coordinates of B in triangle A'B'C' include the following:
(x, y) → (x - 5, y - 3)
Coordinate B = (-9, -8) → Coordinate B' = (-9 - 5, -8 - 3) = (-14, -11)
In conclusion, the coordinates of B' are (-14, -11).
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Complete Question:
Determine the coordinates of the image of point B of quadrilateral ABCD after the translation of 5 units to the left and 3 units down.
Please answer this question with a decent explanation ty.
The measure of angle R is 16.1°
What is the law of sine?Law of Sines In trigonometry, an equation relating the lengths of the sides of any triangle to the sines of its angles.
Given that, a triangle RST, with one angle S = 39° and RT = 25, ST = 11
We need to measure the angle R,
Using law of sine,
Sin R / TS = Sin T / RS = Sin S / RT
Sin R / 11 = sin 39° / 25
Sin R = 11 × sin 39° / 25
Sin R = 0.2769
R = sin⁻¹(0.2769)
R = 16.1
Hence, the measure of angle R is 16.1°
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convert the repeating decimal into a fraction 2.916666666666
Answer:2 45833333333/50000000000
Order these numbers from least to greatest.
5.9, 5.64, 5.604, 7.71
1b. Hailey's plane climbed 1,004.7 feet in 59.1 seconds. How fast did her plane climb every second?
Answer:
:)
Step-by-step explanation:
Just divide 1,004.7 by 59.1
Reducing each ratio to its lowest form 250:400 math
Answer: 5:8
Step-by-step explanation:
to reduce 250:400, simply start with common factors. Right now, it looks like both numbers have 10 in common, so we can divide 10 from both numbers, which will result in 25:40.
We still need to simplify, and now it looks like both numbers have 5 in common, so we can divide 5 from both numbers, resulting in 5:8.
I hope this helps!
what is the domain and range of the mapping diagram ?
Answer:
Below
Step-by-step explanation:
Domain is the 'x' values a function can have for this one {1,3,4,5}
Range is the 'y' values a function has {6,8,10}
Sum up the series 2/3+5/9+8/27+11/81+..... to n terms
AP GP CLASS 11 ISC QUESTION FIRST ONE TO GIVE RIGHT ANSWER I WILL paytm3000 thanks
Answer:
Sn = (7 -(6n +7)3^-n)/4
Step-by-step explanation:
You want the sum of n terms of the series 2/3 +5/9 +8/27 +11/81 +....
Partial sumsThe sums of n terms for n = 1 .. 5 are ...
2/3, 11/9, 41/27, 134/81, 416/243
We recognize the denominators as powers of 3. The numerator sequence is ...
2, 11, 41, 134, 416, ...
Differences are ...
9, 30, 93, 282
And second differences are ...
21, 63, 189
We note that these have a common ratio of 3, leading us to speculate that the numerator sequence can be written as the sum of a linear expression and a power of 3.
CoefficientsAssuming the sequence of numerator terms is of the form ...
a·3^n +bn +c
We can write equations for a, b, c:
a·3 +b·1 +c = 2 . . . . . . for n = 1
a·9 +b·2 +c = 11 . . . . . .for n = 2
a·27 +b·3 +c = 41 . . . . for n = 3
These equations can be solved for a, b, c using any of your favorite techniques. The attached calculator output shows the values to be ...
a = 1.75 = 7/4
b = -1.5 = -6/4
c = -1.75 = -7/4
Nth sumThen the sum of n terms can be written as ...
[tex]\boxed{S_n=\dfrac{7\cdot3^n -6n-7}{4\cdot3^n}}[/tex]
__
Additional comment
The n-th term of the series is (3n-1)/3^n. This can be decomposed into two sums: 3(n/3^n) -1/3^n. The latter is the well-known sum of a geometric series. The sum of the first term is less well-known: ∑(k/3^k) = (3(3^n-1)-2n)/(4·3^n).
a car depreciates ( loses value ) at a rate of 4.5% annually . greg purchased a car for 12,500. which equation can be used to determine the value of the car ,v, after 5 years
The equation used to determine the value of the car ,v, after 5 years is V= 12500*4.5*5/100-D.
What does it mean to solve an equation?An equation represents equality of two or more mathematical expression.
When someone asks you to solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).
Solutions to an equation are those values of the variables involved in that equation for which the equation is true.
Given;
A car depreciates ( loses value ) at a rate of 4.5% annually
Greg purchased a car for 12,500
Time= 5years
Here, the depreciation is equal to the simple interest but in depreciation
So, Let the depreciation be D
D=P*R*T/100
D=12500*4.5*5/100
=2812.5
Now, value of car v;
V= 12500*4.5*5/100-D
Therefore, the equation will be V= 12500*4.5*5/100-D
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suppose that the general solution of a system of m linear equations in n variables contains k free variables. how many basic variables does it have? explain your answer.
It has n-k basic variables. The basic variables are the variables that are not free variables, and they are the ones that can be solved for as part of the general solution.
The general solution of a system of m linear equations in n variables contains k free variables. This means that there are k variables that have no restrictions and can take on any value. The remaining n-k variables are the basic variables, which are the ones that can be solved for as part of the general solution. The basic variables are the ones that have restrictions and need to be solved for in order to determine the solution of the system. In other words, the number of basic variables is equal to the number of variables minus the number of free variables. Thus, the general solution of the system has n-k basic variables.
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P varies inversely as Q and P = 6 when Q = 24. find
a. Q when P = 8
b. P when Q=16
Answer:
Step-by-step explanation:
P = k/Q where k is a constant.
P is 6 when Q is 24, so:
6 = k / 24
k = 6*24 = 144
so, the relation is P = 144/Q.
a. When P = 8,
8 = 144/Q
8Q = 144
Q = 144/8 = 18
b. When Q = 16
P = 144/16
= 9.
Paul wins 1500 metres in 4,67minute (a) Estimate his average speed in metres per minute (b) Use calculator to find his actual average speed in metres per minutes
Answer: See below
Step-by-step explanation:
A) The best way to estimate average speed is to make sure that each number is a whole number (with no decimals). This will make division much easier. The number of meters is already a whole number, but to make the number of minutes a whole number, we must round. Because the number after the decimal is greater than 5, that means we will round up, making the value of minutes 5. Now we can estimate 1500 metres/5 minutes = 300 metres/minute
As a little rounding tip, you can use this mnemonic: 4 and below, let it go (round down). 5 and above, give it a shove (round up)!
B) To do this part, we can simply plug the following into the calculator:
1500 metres/4.67 minutes = 321.2 metres per minute
Hope this helps!
Draw a triangle ABC if BC = 8 cm, ∠B = 60°and ∠C = 70°.
If BC = 8 cm, ∠B = 60°and ∠C = 70° then the triangle is an acute triangle and the value of ∠A is 50.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
BC = 8 cm
∠B = 60° and ∠C = 70°.
Now,
The sum of all the angles is 180.
This means,
∠A + ∠B + ∠C = 180
∠A = 180 - 130
∠A = 50
Now,
The triangle is an acute triangle since all the angles are acute.
i.e less than 90.
Thus,
The triangle is an acute triangle.
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Maay I please get some help?
The complementary angle is 19 degrees and the supplementary angle is 109 degrees.
What are complementary angles?Complementary angles can be defined as the angles whose sum is 90 degrees.
The ‘c’ in complementary angle can be used to form 9 in 90 degrees. Supplementary angles are angles whose sum is 180 degrees. The ‘s’ in supplementary angle can be used to form 8 in 180 degrees
If the intersection of P and Q creates a 71 degree angle,
then 90 – 71 = 19 degrees is its complementary angle. Its supplementary angle is 180 – 71 = 109 degrees.
Therefore, The complementary angle is 19 degrees and the supplementary angle is 109 degrees.
So, The answer is D)
The complementary angle is 19 degrees and the supplementary angle is 109 degrees.
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Three ballet dancers are positioned on stage.Ann is 3 feet straight behind Elena and 2 feet directly left of Rob.When the music Begins,Ann twirls to robs position,then leaps to Elena’s position,and finally walks back to her original position.How far did Ann travel? If necessary,round to the nearest tenth.
The distance that Ann travelled is; 3.61 ft
How to use Pythagoras theorem?Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.
Ann and Elena form the vertical leg of a right angle triangle of length = 3ft. Elena and Rob form the opposite side of the right angle triangle of length = 2 ft.
Using the Pythagorean theorem to find the distance that Anna traveled which is the length of the hypotenuse of the right angle triangle; let that length be x. Then:
x = √(3² + 2²)
x = √ 13
x = 3.61 ft
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can someone pls solve this for me?(and pls make sure its the right answer I really need to get this right.)
The surface area of the right triangular prism is 108 ft²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The surface area of a three dimensional figure is gotten by individually adding each of their respective areas of the surfaces.
From the net and the diagram shown:
A = 5 feet, B = 4 feet, D = 3 feet and C = 8 feet
Surface area = area of triangle 1 + area of triangle 2 + area of rectangle 1 + area of rectangle 2 + area of rectangle 3
Surface area = (0.5 * B * D) + (0.5 * B * D) + (A * C) + (C * B) + (D * C)
Substituting:
Surface area = (0.5 * 4 * 3) + (0.5 * 4 * 3) + (5 * 8) + (4 * 8) + (3 * 8) = 108 ft²
The surface area is 108 ft²
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