CALC HELP!!! WILL MARK BRAINLIEST
Consider the parametric equations below.
x = t2 − 2, y = t + 1, −3 ≤ t ≤ 3
(a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.
(b) Eliminate the parameter to find a Cartesian equation of the curve. for −2 ≤ y ≤ 4
Answers
Answer:
(a) In attachment
(b) x = y² - 2y - 1, −2 ≤ y ≤ 4
Step-by-step explanation:
(a)
The graph of the given parametric equation is given in the attachment.
The direction in which the curve is traced as t increases, is indicated by black arrows.
(b)
To eleminate the parameter t, we simultaneously solve both the equations.
So, we have the equations:
x = t² - 2 ----- equation (1)
y = t + 1 ----- equation (2)
So, from equation (2), we have:
t = y - 1
Substituting this in equation (1), we get:
x = (y - 1)² - 2
x = y² - 2y + 1 - 2
x = y² - 2y - 1
Now, for limits of y, we use equation (2)
For initial limit, t = -3
y = - 3 + 1 = - 2
For final limit, t = 3
y = 3 + 1 = 4
Therefore, the final relation after eliminating t is:
x = y² - 2y - 1, −2 ≤ y ≤ 4
The Cartesian equation of the curve after eliminating the parameter t is expressed below.
[tex]x=y^2-2y-1[/tex]
For, the y values of, [tex]-2 \leq y \leq 4[/tex]
What is a parametric equation?The parametric equation is the type of equation in which the variable which is in depended on on is known as parameter. The dependent function in this equation is defined as the continuous function of that variable.
The first equation given in the problem is,
[tex]x = t^2 - 2 \\t^2=x+2[/tex]
The second equation given in the problem is,
[tex]y = t + 1\\t=y-1[/tex]
Put the values of t in the modified first equation as,
[tex](y-1)^2=x+2\\y^2+1-2y-2=x\\x=y^2-2y-1[/tex]
The values of t are between -3 to 3.
[tex]-3 \leq t \leq 3[/tex]
The value of t is -3 then the value of y will be -2 and when the value of t is 4 then the value of y will be 4 from equation 2.
Hence, the Cartesian equation of the curve after eliminating the parameter t is expressed below.
[tex]x=y^2-2y-1[/tex]
For, the y values of, [tex]-2 \leq y \leq 4[/tex]
Learn more about the parametric equation here;
https://brainly.com/question/21845570
Related Questions
"Eat For 10 Hours. Fast For 14. This Daily Habit Prompts Weight Loss, Study Finds"
This is the title of an NPR article about a 2019 study that recruited 19 overweight adults diagnosed with metabolic syndrome (elevated blood sugar, elevated cholesterol levels, high blood pressure). Participants were asked to restrict any eating to a period of just 10 hours each day. The study found a statistically significant reduction in body weight after 12 weeks of this eating pattern.
1. To be able to conclude that a time-restricted eating pattern causes a weight loss in this population on average, we would need to ___________.
O use a much larger sample than what this study used
O collect weight-loss data on all adults, not just adults with metabolic syndrome
O find a significant weight-loss difference for participants that would be randomly assigned to time-restricted eating or regular eating
O collect weight-loss data on the entire population of adults with metabolic syndrome
O make sure that the study found a very small P-value and check that the conditions for inference were all met
Answers
Answer:
Option A
Step-by-step explanation:
To conclude that a time-restricted eating pattern causes a weight loss in this population on average, we would need to use a much larger sample than the 19 actually used in the study to get an unbiased conclusion and to also ensure that the sample itself and whatever result produced is a true representation of this particular population itself.
Sherri hikes on the Pacific Coast trail. She plans to hike 3.72 miles. If she hikes at an average speed of 1.2 miles per hour, how long will she hike?
Answers
Answer:
3.1 hours
Step-by-step explanation:
Average Speed=Distance Traveled ÷ Time Taken
Sherri plans to hike 3.72 miles at an average speed of 1.2 miles per hour.
Average Speed=1.2 miles per hour.Distance =3.72 milesTherefore:
1.2 miles per hour=3.72 miles ÷ Time
1.2 miles per hour X Time=3.72 miles
Time = 3.72 ÷ 1.2 hours
Time taken by Sherri=3.1 hours
Sherri will hike for 3.1 hours.
what is the number that has the same value as l6l
Answers
Answer:6
Step-by-step explanation: Moving two bars to the edge of 6 will result in 6.
in the year 2005 a company made $6.6 million in profit for each consecutive year after that their profit increase by 9% how much would a companies profit be in the year 2009 to the nearest 10th of $1 million
Answers
Answer:
$9.3 million
Step-by-step explanation:
Given that the company profit increases by 9% yearly from 2005.
Using the exponential growth formula;
A = P(1+r)^(t) .....1
Where;
A = final amount/value of profit
P = initial amount/value = $6.6 million
r = growth rate yearly = 9% = 0.09
t = time of growth in years = 2009 - 2005 = 4 years
Substituting the values;
A = 6.6(1+0.09)^(4)
A = 6.6(1.09)^(4)
A = 9.3164386 million
A = $9.3 million
The companies profit in the year 2009 to the nearest 10th of $1 million is $9.3 million
5lb 7oz -11oz need help quick
Answers
Answer:
76 ounces
Step-by-step explanation:
I'm assuming you meant:
5lb+7oz-11oz=
16 ounces in a pound
5lb+7oz-11oz=
80+7-11=
87-11=
76 ounces
Add. Enter your answer in scientific notation.
2.25 x
108 +3.50 x 108 +2.25 x 108 =
Answers
Answer:
8×10⁸
Step-by-step explanation:
2.25×10⁸ +3.50×10⁸ +2.25×10⁸ = (2.25 +3.50 +2.25)×10⁸ = 8×10⁸
__
Your calculator can do this for you and display the result in scientific notation.
The percent markup on a video game is known to be 108% based on cost. If the seller paid $35 for one, then what would be the corresponding percent markup based on the sale price? (Round to the nearest tenth percent)
Answers
Answer: 48.1%
Step-by-step explanation:
The percent markup is defined as:
PM = (gross benefit/cost per unit.)*100%
We know that the cost per unit is $35
then we have:
108% = (gross benefit/$35)*100%
gross benefit = (108%/100%)*$35 = $37.8
This means that a game is selled by $35 + $37.8 = $72.8
Now we have:
Markup percent = (gross benefit/selling price)*100% = ($35/$72.8)*100% = 48.1%
Please Help With problem 1
Answers
Answer:
60
Step-by-step explanation:
To find the volume of a rectangular prism you need to use the formula Base times height or in this case length times-width times height so multiply 5 x 4 x 3 to get your answer
Write a division word problem for 31 divided by 4 that requires to round up
Answers
Answer:
31/4 is 7.75 so you could round up to 7.8 or 4/31 which is. 0.129... and you could round up to 0.13
Word problem:
Mark has 31 Starburst and wants to give them all to his 4 friends. About how many starburst will each friend have. Be sure to round your answer.
Answer:
This is just going to be a word problem so Imma just give you one you can use.
Step-by-step explanation:
Stacy has 31 cookies that she wants to divide for herself and her three other siblings. About how much cookies did each person get?
The ages of Rohit and James are in the ratio 2 : 5. In 9 years, the ratio of their ages will be 5 : 8. Find their present ages.
Answers
Answer:
Step-by-step explanation:
I don't say you have to mark my ans as brainliest but if you think it has really helped you then plz don't forget to thank me...
Answer:
Rohit is 6 years old
James is 15 years old
Step-by-step explanation:
Rohit : James 2 : 5
the difference between their units is 3
Now we add the 9 years
5 : 8the difference between their units should be 3 because they both age every year. the question was nice enough to give to same amount of units
Now we subtract James's original 'unit age' from his new one
8u - 5u = 3 uWe also need to make sure the difference between Rohit's original 'unit age' is 3
5u - 2u = 3uthis 3 units represent the 9 years that have passed
3 units = 9 yearsTo find James's age all we ahve to find is their original unit number
James (5 units) -> 3 × 5 = 15same for Rohit
Rohit (3 units) -> 3×3 = 9hence, Rohit's and James's ages are 9 and 15 respectivelya cartographer used a scale of 1 inch :300 meters for the heights of different mountains if the actual height of one of those mountains is 3700 meters high. what is the height on the map?
Answers
Answer:
[tex]12\frac{1}{3}[/tex] inches
Step-by-step explanation:
So to go from 300 to 3700 you have to multiply by [tex]12\frac{1}{3}[/tex]
The diagram above shows
circle ABCD
with Centre E Quadrilateral EADC is a rhombus.
<BAE =<ECB=n and <ABC=m.
find
i) m
ii) n
Answers
Answer:
m = 60°n = 30°Step-by-step explanation:
Opposite angles D and E in the rhombus are congruent. The measure of arc ADC is the same as the measure of central angle AEC. The measure of arc ABC is twice the measure of angle AEC, so the measure of arc ABC is twice the measure of arc ADC.
This means that short arcs AB, BC and CA are all 120°. Inscribed angle ABC (angle m) is half that value, or 60°.
Likewise, the angle BAC is 60°. We know that angle EAD is supplementary to angle AEC, so is 180° -120° = 60°. Segment AC bisects this angle, so angle n is 60°/2 = 30° less than angle BAC.
angle m is 60°, angle n is 30°
An above-ground swimming pool is 5 feet long, 4 feet wide, and 3 feet deep and is shaped like a rectangular prism. A rectangular prism has a length of 5 feet, height of 3 feet, and width of feet. If you use a net to find the amount of material used to make the pool, what faces are included in the calculation?
Answers
Answer:
the faces representing the sides and bottom of the pool are included
Step-by-step explanation:
Obviously, there is no pool material covering the top of the pool. Rather, it is "an open-top box", so the area of the faces of the box does not include the area of the top. The five faces other than the top face are included.
Answer:
First answer is 1
Second is 2
Third is 2
Please help.
Best answer will get brainliest.
Answers
Answer:
59.1 for the mean
Step-by-step explanation:
You add all the numbers together and divde it by the amount of numbers there are.
Answer:
Mean= 59.1
Median= 58
Range= 11
Step-by-step explanation:
Mean= Total data/Number of given datas
= 60+58+54+56+63+65+62+59+56+58/10
Mean = 591/10= 59.1
Median= Middle value
= 65, 63, 62, 60, 59, 58, 58, 56, 56, 54
Median= 58
Range= Highest value- Lowest value
= 65-54
Range= 11
b. David and Andrew are traveling to a Mathematics conference. David travels 110 miles in the same time that Andrew travels 140 miles. Andrew travels 15 miles per hour faster than David. Find the average rate of each person.
Answers
Answer:
Its 14 and 19
Step-by-step explanation:
Answer:
b. About 15 miles
Step-by-step explanation:
got it right on edge
PLEASE HELP me with the magic square
Answers
Fill in each slot in the square with variables a, b, c, d, and e, in order from left-to-right, top-to-bottom. In a magic square, the sums across rows, columns, and diagonals all add up to the same number called the magic sum.
The magic sum is -3.9, since "diagonal 2" (bottom left to top right) has all the information we need:
3 + (-1.3) + (-5.6) = -3.9
Use this to find the remaining elements
row 1:a + b + (-5.6) = -3.9
row 2:c + (-1.3) + d = -3.9
row 3:3 + e + 0.02 = -3.9
column 1:a + c + 3 = -3.9
column 2:b + (-1.3) + e = -3.9
column 3:(-5.6) + d + 0.02 = -3.9
diagonal 1 (top left to bottom right):a + (-1.3) + 0.02 = -3.9
You will find
a = -2.62
b = 4.32
c = -4.28
d = 1.68
e = -6.92
Which statement is true? Question 10 options: A) |13| = – 13 B) – |13| = 13 C) |–13| = 13 D) – |–13| = 13
Answers
Answer:
The answer is C
Step-by-step explanation:
Every negative or positive number in the modulus while be positive at the end
The true statement is C) |–13| = 13, indicating that the absolute value of -13 is 13, representing the distance of -13 from zero on the number line.
How to Solve Absolute Value Equations?The true statement is: C) |–13| = 13, as explained below.
The expression |–13| represents the absolute value of -13, which is the distance of -13 from zero on the number line, always resulting in a non-negative value.
|–13| = 13, because the absolute value of -13 is 13, meaning it is 13 units away from zero on the number line. So, the correct option is C) |–13| = 13.
Learn more about Absolute Value on:
https://brainly.com/question/12928519
#SPJ6
A fenced enclosure consists of a rectangle (length L and width 2R) attached to a semicircle with a radius R as pictured below. Note: there is fencing between the rectangular and semi-circular portions. The enclosure is to be built to have a total area (the entire shaded region), A, of 2000 ft2. The cost of the fence is $20/ft for curved sections and $30/ft for straight sections. Analytically (show all of your steps using algebra and calculus in the write up), find the minimum cost to build the fence and the dimensions of the enclosure. Show all equations that you derive and use. This part should be done entirely in the write-up: no coding. It is fine to do this by hand and include a high-resolution picture in the writeup rather than using Equation Editor. Hint: you will need to use two equations in order to find the cost as a function of only R or L. Construct a plot to graphically determine the values of R and L (x-axis) that minimize the total cost (y-axis) of the fence. Using the MIN function, determine the R and L that minimize cost and what that cost is Do your answers in A, B and C all agree? Why or why not?
Answers
Answer:
A. $ 6053.44
B. From the graph, R = 21.027 ft and C = $ 5700.005, L = 31.043 ft
The values in A and B do not all agree. This could be due to error in approximations. Their values are close though.
Step-by-step explanation:
A. The area A of the enclosure equals, A = 2RL + πR²/2.
The total cost C = 20 × length of curved section + 30 × length of straight section
C = 20πR + 30[2(L + 2R)]
= 20πR + 60L + 120R
Making L subject of the formula from A,
L = A/2R - πR/4
Substituting L into C, we have
C = 20πR + 60(A/2R - πR/4) + 120R
= 20πR + 30A/R - 15πR + 120R
= 5πR + 30A/R + 120R
We now differentiate C with respect to R to find the value of R for minimum cost
dC/dR = 5π - 60A/R² +120
Equating dC/dR to zero, we have
5π - 60A/R² + 120 = 0
So, R = ±√[60A/(5π + 120)]
substituting A = 2000 ft²
R = ±√[60 × 2000/(5π + 120)] = ±29.74 ft
We take the positive answer, R = 29.74 ft since R cannot be negative.
To determine if this is a minimum point, we differentiate dC/dR with respect to R.
So d²C/dR² = 120A/R³
Since d²C/dR² = 120A/R³ > 0 for positive R, it is a minimum point.
Substituting the value of R into C we have
C = 5πR + 30A/R + 120R
= 5π(29.74) + 30 × 2000/29.74 + 120(29.74)
= 467.155 + 2017.485 + 3568.8
= $ 6053.44
and L = A/2R - πR/4
= 2000/2(29.74) - π(29.74)/4
= 33.625 - 23.356
= 10.269
≅ 10.27 ft
B. From the graph, R = 21.027 ft and C = $ 5700.005, L = 31.043 ft
The values in A and B do not all agree. This could be due to error in approximations. Their values are close though.
In Prof. Smith's class, the 11 students had the following scores on the last midterm.
73, 77, 78, 82, 83, 85, 86, 89, 95, 95, 188
Identify all values that are outliers.
If there is more than one outlier, separate them with commas.
If there are no outliers, click on "None".
Answers
Answer:
There are no values that are outliers.
The mean temperature for the first 7 days in January was 4 °C.
The temperature on the 8th day was 4 °C.
What is the mean temperature for the first 8 days in January?
Answers
Answer:
4 degrees Celsius
Step-by-step explanation:
Since the mean is (total/amount), we can remake this to get That mean*amount=total. For the first 7 days, 4*7=28 for our total, and add that to the 8th day to get 32 for our total. 32/8=4 for our mean for the first 8 days of january
Answer:
Answer:
4 degrees Celsius
Step-by-step explanation:
Since the mean is (total/amount), we can remake this to get That mean*amount=total. For the first 7 days, 4*7=28 for our total, and add that to the 8th day to get 32 for our total. 32/8=4 for our mean for the first 8 days of january
ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answers
Answer:
x > 5
Step-by-step explanation:
Subtract 7 from both sides, like so:
x + 7 > 12
- 7 - 7
________
x > 5
A television is 28.5 inches wide and 16 inches long.
Using the Pythagorean Theorem, what is the length of the diagonal of the television, rounded to the nearest inch?
Answers
Answer:
33 in
Step-by-step explanation:
The Pythagorean theorem tells you ...
diagonal² = length² +width²
diagonal² = (16 in)² +(28.5 in)² = 1068.25 in²
diagonal = √(1068.25 in²) ≈ 32.684 in
The diagonal of the television is about 33 inches.
Carlo buys $14.40 worth of grapefruit. Each grapefruit costs 0.80. (PLz help and yeett) with steps plz
Answers
Answer:
a) 18 grapefruits
b) 6 grapefruits
Step-by-step explanation:
a) n = 14.4 / 0.80 = 18 grapefruits
b) n = (14.4 / 3) / 0.8 = 6 grapefruits
The amplitude of y= – sin is
b 0
C2
d 1
Answers
Answer:
d. 1
Step-by-step explanation:
The amplitude of such a function is the magnitude of the coefficient of the sine function.
|-1| = 1 . . . . the amplitude . . . matches choice D
find the slope of the line passing through the points (6,9) and (6, -1)
Answers
Answer:
Undefined
Step-by-step explanation:
M=undefined
Slope = y2-y1 /x2- x1
=9 -(-1). / 6-6
= 10/0 = infinity ; undefined
What does X equal?? Please help me out!!
Answers
What is the volume, in cubic cm, of a rectangular prism with a height of 19cm, a
width of 16cm, and a length of 8cm?
Answers
Answer: 2432
19 x 16 x 8 = 2432
Answer: 2,432 cm³
Step-by-step explanation: To find the volume of a rectangular prism or a prism whose base is a rectangle, we use the formula below.
Volume = length × width × height
Since the rectangular prism has a length of 8 centimeters, a width of 16 centimeters, and a height of 19 centimeters,
we can plug this information into the formula to get
(8 cm)(16 cm)(19 cm).
This gives us 2,432 cm³.
So the volume is 2,432 cm³.
avier is considering two options for college. Option A: Complete the first two years of schooling at a community college and then transfer to a university. Option B: Complete all four years of schooling at the university.
Answers
Answer:
kok
Step-by-step explanation:
If you were to roll a six-sided number cube 60 times, about how many times would you expect the number cube to land on a 1?
Answers
Answer:
10
Step-by-step explanation:
Probability is the likeliness of happening of an event.
Probability of any event A can be be defined by
no. of time event A happens/ total no. all possible event that can occur
___________________________________
In the problem
probability of occurrence of 1 on rolling a cube is needed.
A cube has six sides with one written on one sides and rest has 2,3,4,5,6.
No of times 1 can occur on rolling the dice once will be = 1
Since there six sides and and each has different number (1,2,3,4,5,6)
There is chance that each of the number can come.
Thus, total no possible outcome = 6
Probability of occurrence of 1 = No of times 1 occurs on rolling the dice /total no possible outcome = 1/6
_____________________________________________
If dice is rolled 1 time there is 1/6 chance that 1 will be the outcome.
If dice is rolled 1*60 time then there is 1/6*60= 10 chance that 1 will be the outcome
Thus , If you were to roll a six-sided number cube 60 times, about 10 times it is expected that the number cube to land on a 1.
Answer:
20
Step-by-step explanation:
Jamie spent $12 dollars a day on food for 6 days. What was Jamie’s overall change in her bank account for food over the 6days?
Answers
Answer:
-72
Step-by-step explanation:
12 * 6 = 72
Jaime spent 72 dollars for the 12 days
It went down because the money was spent
-72