Find all values of t on the parametric curve where the tangent line is horizontal or vertical. x = t^3 - 3t, y = t^3 - 3t^2
Answers
The values of t on the parametric curve where the tangent line is horizontal or vertical are t = -1, t = 0, t = 1, and t = 2/3.
To find the values of t on the parametric curve where the tangent line is horizontal or vertical, we need to find the derivative of y with respect to x and set it equal to zero to obtain the values of t at which the tangent line is horizontal. We will also need to find the derivative of x with respect to y and set it equal to zero to obtain the values of t at which the tangent line is vertical.
Firstly, let us find dy/dx:dy/dx = dy/dt / dx/dt
We know that x = t³ - 3ty = t³ - 3t²
By differentiating each equation with respect to t we get the following:
dx/dt = 3t² - 3dy/dt = 3t² - 6t
Therefore,dy/dx = (3t² - 6t) / (3t² - 3)
Now, let's set dy/dx equal to zero and solve for t:
(3t² - 6t) / (3t² - 3) = 0
3t² - 6t = 0
t(3t - 6) = 0
t = 0 or t = 2/3
Thus, the values of t at which the tangent line is horizontal are t = 0 and t = 2/3.
Now, let's find dx/dy:dx/dy = dx/dt / dy/dt
We know that x = t³ - 3ty = t³ - 3t²
By differentiating each equation with respect to t we get the following:
dx/dt = 3t² - 3dy/dt = 3t² - 6t
Therefore,
dx/dy = (3t² - 3) / (3t² - 6t)
Now, let's set dx/dy equal to zero and solve for t:
(3t² - 3) / (3t² - 6t) = 03t² - 3 = 0t² - 1 = 0t = ±1
Thus, the values of t at which the tangent line is vertical are t = -1 and t = 1.
Therefore, the values of t on the parametric curve where the tangent line is horizontal or vertical are t = -1, t = 0, t = 1, and t = 2/3.
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Related Questions
SOMEBODY HELP ME I NEED THE ANSWER AND DONT GIVE ME A LINK DOES THE LINK IS FAKE !!!!
Answers
Answer:
c
Step-by-step explanation:
Answer:
A. C. and D.Step-by-step explanation:
Now I can not be 100% sure since I can not see the chart, but I can go off of logic. So let´s get started
First we can eliminate answer B. Answer B does not make ANY sense. Why would the number 3 make a difference.
Now answer A and D. These answers are basically the same. So if one is true, the other is as well. For D, if it were the same number, just negative and positive, the sum would be 0.
So this makes A and D true
Answer C is backed up by answer D as well. They can only be the same distance if one is positive and the other is negative
please help ASAP i will give brainliest.
Select all the points that are on the graph of the line 2x+4y=20.
A=(1,2)
B=(10,0)
C=(5,0)
D=(1,4)
E=(0,5)
F=(0,10)
Answers
Answer:
i am sure there is B and E
.
..
.
Answer:
(0,5) and (10,0)
Step-by-step explanation:
The equation of the straight line is given by 2x + 4y = 20 .......... (1)
Now, point (0,5) satisfies the equation (1) as putting x = 0, we will get y = 5.
Now, point (0,10) does not satisfy the equation (1) as putiing x = 0, we get y = 5 ≠ 10
Again, point (1,2) does not satisfy the equation (1) as putiing x = 1, we get y = 4.5 ≠ 2
Now, point (1,4) does not satisfy the equation (1) as putiing x = 1, we get y = 4.5 ≠ 4
Again, point (5,0) does not satisfy the equation (1) as putiing y = 0, we get x = 10 ≠ 5
Finally, point (10,0) satisfies the equation (1) as putiing y = 0, we get x = 10 .
Therefore, only points (0,5) and (10,0) are on the graph of the line 2x + 4y = 20 (Answer)
there you go have a wonderful day!
Please help I need 1, 2, 5, and 6!
Answers
Step-by-step explanation:
1. 21√n/2
2. 2/3 3√x
(3) - 5/2b 7/2
4. (10m) 6/5
4 units right
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11. Translate the figure 2 units left
and 4 units down. What are the
coordinates of the image?
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If so
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23.
B
3
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-4-3-2
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Answers
When Q > K, the amount of products must _____ and the amount of reactants must _____ for equilibrium to be established. Thus, when Q > K, the reaction will proceed toward the _____ to establish equilibrium.
Answers
When Q > K, the amount of products must decrease and the amount of reactants must increase for equilibrium to be established. Therefore, the reaction will proceed in the reverse direction to establish equilibrium.
When discussing chemical reactions and equilibrium, the reaction quotient (Q) and equilibrium constant (K) play important roles.
The reaction quotient is calculated in the same way as the equilibrium constant, but it can be evaluated at any point during the reaction, not just at equilibrium.
If the reaction quotient, Q, is greater than the equilibrium constant, K (Q > K), it indicates that the system has an excess of products compared to what is required at equilibrium.
To establish equilibrium, the reaction needs to shift in the reverse direction to reduce the concentration of products and increase the concentration of reactants.
This shift occurs because the system seeks to minimize the imbalance caused by the excess of products.
By proceeding in the reverse direction, the reaction consumes some of the excess products and forms more reactants.
As reactants are consumed, their concentration increases, bringing the system closer to equilibrium. The reaction will continue to proceed in the reverse direction until Q becomes equal to K, indicating that the system has reached equilibrium.
In summary, when Q > K, the reaction will proceed toward the reverse direction to establish equilibrium by reducing the concentration of products and increasing the concentration of reactants.
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Discrete Math
Two student council representatives are chosen at random from a group of 7 girls and 3 boys. Let G denote the distribution over the number of girls chosen.
a. What is the range of G?
b. Give the distribution over the random variable G.
Answers
Answer:
Step-by-step explanation:
a. The range of G is the set of possible values that G can take. G represents the distribution over the number of girls chosen, so G can take any value between 0 and 2, inclusive. That is, the range of G is {0, 1, 2}.
b. To give the distribution over the random variable G, we need to determine the probability of each possible value of G.
Let's consider each possible value of G in turn:
If no girls are chosen (G=0), then both representatives must be boys. The probability of choosing a boy on the first draw is 3/10, and the probability of choosing another boy on the second draw is 2/9 (since there are only 2 boys left). Therefore, the probability of G=0 is (3/10) * (2/9) = 1/15.
If one girl is chosen (G=1), then one representative must be a girl and the other must be a boy. There are two ways this can happen: either the girl is chosen first and then the boy, or the boy is chosen first and then the girl. The probability of choosing a girl on the first draw is 7/10, and the probability of choosing a boy on the second draw is 3/9 (since there are 3 boys left). The probability of choosing a boy on the first draw is 3/10, and the probability of choosing a girl on the second draw is 7/9 (since there are 7 girls left). Therefore, the probability of G=1 is (7/10) * (3/9) + (3/10) * (7/9) = 14/45.
If two girls are chosen (G=2), then both representatives must be girls. The probability of choosing a girl on the first draw is 7/10, and the probability of choosing another girl on the second draw is 6/9 (since there are 6 girls left). Therefore, the probability of G=2 is (7/10) * (6/9) = 7/15.
Therefore, the distribution over the random variable G is:
G=0 with probability 1/15
G=1 with probability 14/45
G=2 with probability 7/15
find the derivative, r'(t), of the vector function. r(t) = tan(3t), sec(4t), 1 t3
Answers
The derivative of the vector function r(t) is:
r'(t) = (3sec^2(3t), 4sec(4t)tan(4t), 3t^2)
To find the derivative of the vector function r(t) = (tan(3t), sec(4t), t^3), we need to take the derivative of each component function separately with respect to t.
Using the chain rule, we have:
r'(t) = (d/dt) (tan(3t), sec(4t), t^3)
= (d/dt) tan(3t), (d/dt) sec(4t), (d/dt) t^3
= 3sec^2(3t), 4sec(4t)tan(4t), 3t^2
Therefore, the derivative of the vector function r(t) is:
r'(t) = (3sec^2(3t), 4sec(4t)tan(4t), 3t^2)
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What is the factored form of b3 − 1,000?
Answers
The factorization of the polynomial b³-1000 is (b-10)(b²+10b+100).
What is factorization?The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.
The given expression is b³-1000.
Here, b³-1000=b³-10³
Using a³-b³=(a – b)(a² + ab + b²), we get
(b-10)(b²+10b+100)
Therefore, the factorization of the polynomial b³-1000 is (b-10)(b²+10b+100).
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An analysis of variances produces dftotal = 29 and dfwithin = 27. for this analysis, what is dfbetween?
a. 1
b. cannot be determined without additional information
c. 3
d. 2
Answers
The value of dfbetween in the analysis of variances is 2. Thus option D is correct option.
According to the statement
we have given that the df total = 29 and df within = 27. And we have to find the value of the df between.
So, For this purpose, we know that the
Analysis of variance (ANOVA) is an analysis tool used in statistics that splits an observed aggregate variability found inside a data set into two parts.
So, Df between values are the values between the value of dftotal and dfwithin.
Here df total = 29 and df within = 27
So, df between = df total - df within
Substitute the values in it then
df between = df total - df within
df between = 29 - 27
df between = 2.
So, The value of dfbetween in the analysis of variances is 2. Thus option D is correct option.
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Joe has read 30% of a book. He has 14 more pages to finish. How many pages are there in the book?
Answers
Since Joe has read 30% of the book, that means that 14 pages is 70% of the book. That means that two pages equals 10%. Therefore, the book has 20 pages.
70% = 14
so 30% = 6
total pages = 14+6=20
Lily buys some of her clothes from the mall. If 100% of her shirts are from the mall and she owns 86 shirts, how many of Lily's shirts are from the mall?
Answers
Answer:
the answer is 86
Step-by-step explanation:
the answer is 86 because if all of her shirts are from the mall and she has 86 of them, 100% of 86 is 86
Sofia has planted a total of 40 plants in her new garden. 18 of these are pink geraniums. What percentage of the plants are pink geraniums?
Answers
Answer:
45%
Step-by-step explanation:
18 divided 40 =
18/40 =
9/20 = .45
.45 <- move the decimal to 2 spaces to the right =
45%
Geometry: Transformations
The point (-4, -1), is the bottom of a triangle. Which point would it map to if the triangle was translated right 5 units and reflected about the x-axis.
A) (2, 1)
B) (1, 1)
C) (-4, -4)
D) (-9, 1)
Answers
Answer: Ur answer will be A.
How many 1/3 of a hour to make a hour?
Answers
Answer: 3
Step-by-step explanation:
\(\frac{1}{3}\) × 3 = 1
Melanie’s family drove for 5 hours on the main highway and 3 hours on a smaller highway, and traveled a total of 456 miles. Their average speed was 8 miles per hour faster on the main highway than on the smaller highway. What was their average speed on the smaller highway?
Answers
Answer:52 miles per hour
Step-by-step explanation:
Determine whether ABCD is a parallelogram if AB = 6, BC = 12, CD = 6, and DA = 12. Justify your answer
A/ Yes; Opposite sides are congruent to each other.
B/ Yes; Opposite sides are parallel to each other.
C/ Yes; Opposite angles are congruent to each other.
D/ No
Answers
Two-Variable Statistics:Question 2
You obtain a correlation value of r = -0.744 when you
analyze the relationship between the time it takes
someone to swim a mile and her heart rate at the end of
the swim. Choose the word completes this interpretation
of the correlation value: The correlation between the time
it takes to swim and heart rate is ___ and ___
Answers
Dilate the triangle by a scale factor of 1/2
pls
pls
Answers
Consider Juan Soto's wins above replacement statistics for the four seasons in the table. In which season did he have the greatest value to his team?
Answers
Answer: 2021
Step-by-step explanation:
Find the distance between (1, 3) and (5, 6)
a) 3
b) 4
c) 5
d) 6
Answers
Reason: cause
The answer the problem
Answers
Answer:
The answers 528
put 2 and 5
Answer:
528
Step-by-step explanation:
:)
Eric owns and operates the hot ham food truck. the expression 3.25 b 2 h 3.25b 2h3, point, 25, b, plus, 2, h gives the cost of b bb burgers and h hh hot dogs. what is the cost of 4 44 burgers and 6 66 hot dogs?
Answers
Using the algebraic expression that models the cost of burgers and hotdogs, the cost of 4 burgers and 6 hot dogs is $25.
An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An algebraic equation is the equality of expressions.
If the expression 3.25b + 2h gives the cost of b burgers and h hotdogs, and we want to determine the cost of 4 burgers and 6 hot dogs, then plug in the values and solve the equation.
cost = 3.25b + 2h
cost = 3.25(4) + 2(6)
cost = 13 + 12
cost = 25
Hence, the cost of 4 burgers and 6 hot dogs is $25.
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A shirt is discounted by 20%. The discounted prices is $32. What was the original price of the shirt?
Answers
Answer:
160
Step-by-step explanation:
the original price of the shirt is
\(\frac{32}{20}.100=160\)
please help !! write an expression that can be used to determine the total change
Answers
Answer:
y = 125x + 775
Step-by-step explanation:
you can make coordinate points (x, y) from the graph
x = Number of hours
y = Total Charge
(1, 800) and (2, 925)
slope from 2 points = y2-y1/x2-x1
x1 = 1
y1 = 800
x2 = 2
y2 = 925
925 - 800/2-1 = 125/1
m = 125
using y = mx + b, where m = 125, and 1 of the coordinate points you can find the y intercept
multiply 125 times 2
925 = 250 + b
subtract 250 from both sides
b = 675
y = 125x + 675
randy wants to attach a 20 foot string of lights to the top of the 19 foot mast of his sailboat. how far from the base of the mast should he attach the end of the light string? round your answer to two decimal places.
Answers
The distance between the base of the string and the base of the mast of the sailboat is 6.24.
Here we have to find the distance from the base of the mast that should be attached to the end of the light string.
Data given:
length of the string = 20 foot
length of the mast of the sailboat = 19 foot
Distance between the base of the mast and the light string = \(\sqrt{20^{2} - 19^{2} }\)
= \(\sqrt{400 - 361}\)
= √39
= 6.245
Therefore the distance between the string and the mast is 6.24.
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Lei presold 323232 carnations for a fundraiser, then she sold ccc more carnations on the day of the fundraiser. She earned 0.250.250, point, 25 dollars for each carnation she sold.
The expression 8+ 0.25c8+0.25c8, plus, 0, point, 25, c describes how much money Lei earned for the fundraiser. We can also use the expression 0.25(32+c)0.25(32+c)0, point, 25, left parenthesis, 32, plus, c, right parenthesis to represent the same quantity.
Match each amount in the situation with the expression that represents it.
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Sale before fundraiser = 32
Sale on the day of fundraiser = c
Cost of each carnation sold = 0.25
(Cost * sale before fundraiser) + cost * sale on day of fundraiser
(0.25 * 32) + 0.25 * c
8 + 0.25c
Or
Total carnation sold * cost per carnation
(sale before fundraiser + sale on day of fundraiser) * cost per carnation
(32 + c) * 0.25
Which of the following is equivalent to
the expression (i + 5)(3 + 4i)?
Answers
Answer: 11+23i
Step-by-step explanation:
(i+5)(3+4i)
First foil
3i+4i^2 +15+20i
Then combine like terms
23i+15+4i^2
i^2 = -1 so,
23i+15+4(-1)
11+23i
RIGHT ANSWER GETS BRAINLIEST POINTS AND 15 POINTS. Fill in the blanks with greater or less
Answers
Answer: The mean of data set K is greater than the mean of data set L.
The median of data set K is greater than the median of data set L
Step-by-step explanation:
we need to calculate the mean (average) of each data set and compare them.
Mean of data set K = (28 + 145 + 112 + 57 + 130) / 5 = 112.4
Mean of data set L = (141 + 171 + 68 + 124 + 43) / 5 = 109.4
'Arranging the values in data set K in ascending order, we get:
28, 57, 112, 130, 145
The median of data set K is the middle value, which is 112.
The mean of data set L is 109.4.
Help please me thanks
Answers
Answer:
option 1:a+12
Step-by-step explanation:
add 12 to a
Identify the domain of the function shown in the graph.
A. X>0
B. 0≤x≤8
C. -6≤x≤6
D. x is all real numbers.
Answers
Answer:
d
Step-by-step explanation: