Find an equation of the tangent to the curve at the given point by both eliminating the parameter and without eliminating the parameter.
x = 3 + ln t, y = t^2 + 3, (3, 4)
y =
Answers
y = 2x - 2, This is the equation of the tangent to the curve at the point (3, 4) after eliminating the parameter.
How y = 2x - 2 is the equation of the tangent to the curve at the point (3, 4) after eliminating the parameter?To find the equation of the tangent to the curve at the point (3, 4), we need to first find the derivative of the parametric equations with respect to t and evaluate it at t such that x = 3. Then, we can use the derivative to find the slope of the tangent and the point (3, 4) to write the equation of the tangent.
Find the derivative of the parametric equations with respect to t.\(dx/dt = 1/t\)
\(dy/dt = 2t\)
Evaluate the derivative at t such that x = 3.\(x = 3 + ln(t) -- > ln(t) = x - 3 -- > t = e^(x-3)\)
\(dx/dt = 1/t = 1/e^(x-3)\)
\(dy/dt = 2t = 2e^(x-3)\)
When x = 3, t = 1 and \(dx/dt = 1/e^0\)\(= 1\), \(dy/dt = 2(1) = 2\).
Therefore, the slope of the tangent at (3, 4) is:
\(m = dy/dx = (dy/dt) / (dx/dt) = 2/1 = 2\)
Use the point-slope form of the equation of a line to write the equation of the tangent.\(y - y1 = m(x - x1)\)
Substituting the values of\((x1, y1)\)= \((3, 4)\)and\(m = 2\), we get:
\(y - 4 = 2(x - 3)\)
Simplifying, we get:
\(y = 2x - 2\)
This is the equation of the tangent to the curve at the point (3, 4) without eliminating the parameter.
To eliminate the parameter, we can solve for t in terms of x in the first parametric equation and substitute the resulting expression into the second parametric equation. Then, we can find the derivative of y with respect to x and use it to write the equation of the tangent.
\(x = 3 + ln(t) -- > ln(t) = x - 3 -- > t = e^(x-3)\)
Substituting into the second parametric equation, we get:
\(y = e^(2(x-3)) + 3\)
Taking the derivative of y with respect to x, we get:
\(dy/dx = 2e^(2(x-3))\)
When\(x = 3, t = 1\) and\(dy/dx = 2e^0 = 2.\)
Therefore, the slope of the tangent at (3, 4) is:
\(m = 2\)
Using the point-slope form of the equation of a line and the point (3, 4), we get:
\(y - 4 = 2(x - 3)\)
Simplifying, we get:
\(y = 2x - 2\)
This is the equation of the tangent to the curve at the point (3, 4) after eliminating the parameter.
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Related Questions
Choose
1. Identify the slope of the line with the given equation. y = 3x + 12 *
A) x
B) y
C) 3
D) 12
Answers
a triangle has sides measuring 31 in 18in and 25 in what is the perimeter of the triangle
Answers
44) 93
O 2 remainder of 6
2 remainder of 7
2 remainder of 4
2 remainder of 5
Answers
PLEASE ANSWER QUICK
Evaluate the expression when n = 3:
−|−4n|
Answers
Answer:
12
Step-by-step explanation:
-4 X 3 =-12
=-(-12)
=12
Cos 0 = 4/5 and sin 0 < 0. Identify the quadrant of the terminal side of 0 and
find sin 0
Answers
Answer:
sinθ = -3/5, Quadrant IV (Option B)
Step-by-step explanation:
Let's first find the sine
cosθ = adj./hyp.
Pythagorean theorem (in terms of right triangle trig) = (opp)^2 + (adj)^2 = (hyp)^2
Plug in the adjacent and hypotenuse
(opp.)^2 + 16 = 25
solve for the opposite side
opp. = 3
To find the quadrant, recall the sin <0, so the sin has to be negative.
So, your sine value is -3/5.
Sine is negative at Quadrants III and IV, so eliminate C and D.
Since your cosine value is positive, it is at Quadrant IV (Cosine is positive at the first and fourth quadrants.)
Therefore, Option B is correct.
A car rental agency charges $15 a day for driving a car 200 miles or less. If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven. Which of the following functions represents the cost to drive a car from this agency miles x a day?
Answers
The function which represents the cost to drive a car from this agency miles x a day is :
C(x) = 15, if 0 ≤ x ≤ 200
= 15 + 0.05x, if x > 200
Given that,
A car rental agency charges $15 a day for driving a car 200 miles or less.
The function can be written as,
C(x) = 15 if 0 ≤ x ≤ 200
If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.
C(x) = 15 + 0.05x, if x > 200
Hence the correct option is D.
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Which of the following is something not impacted by the Coriolis Effect?
Question 4 options:
A. Student running across a gym
B. Hurricane Sandy moving across the coast of the United States
C. global wind patterns
D. a plane moving in a curved path from Los Angeles to New York City.
Answers
Answer: it would be A lad :)
Step-by-step explanation:
i hope this helps
have a great day :D
Option D is will not have the Coriolis effect.
Coriolis effectWhen an object has a linear motion on a rotating body then it has Coriolis effect.
How to get info on the Coriolis effect?The airplane will not feel the Coriolis effect because it is not in contact with the rotating body.
Thus, option D is will not have the Coriolis effect.
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i need to know how many solutions to this problem there are
Answers
EXPLANATION
Given the equation:
-4x -5 = 6 -11x
Adding +11x to both sides:
11x -4x -5 = 6
Adding+5 to both sides:
11x -4x = 6+5
Adding similar terms;
7x = 11
Now, we can see that there is only one solution that is 11/7.
The coordinate grid shows points A through K. What point is a solution to the system of inequalities? y > −2x + 10 y > 1/2x − 2 coordinate grid with plotted ordered pairs, point A at negative 5, 4 point B at 4, 7 point C at negative 2, 7 point D at negative 7, 1 point E at 4, negative 2 point F at 1, negative 6 point G at negative 3, negative 10 point H at negative 4, negative 4 point I at 9, 3 point J at 7, negative 4 and point K at 2, 3
answer:
a) E
b) K
c) B
d) D
Answers
Based on the analysis, point D at (-7, 1) is the only solution to the system of inequalities y > -2x + 10 and y > (1/2)x - 2. Therefore, the correct answer is option d) D.
To determine which point is a solution to the system of inequalities y > -2x + 10 and y > (1/2)x - 2, we can test each point to see if it satisfies both inequalities.
a) Point E at (4, -2):
Substituting the coordinates into the inequalities:
-2 > -2(4) + 10 -> -2 > -8 + 10 -> -2 > 2 (False)
-2 > (1/2)(4) - 2 -> -2 > 2 - 2 -> -2 > 0 (False)
b) Point K at (2, 3):
Substituting the coordinates into the inequalities:
3 > -2(2) + 10 -> 3 > -4 + 10 -> 3 > 6 (False)
3 > (1/2)(2) - 2 -> 3 > 1 - 2 -> 3 > -1 (True)
c) Point B at (4, 7):
Substituting the coordinates into the inequalities:
7 > -2(4) + 10 -> 7 > -8 + 10 -> 7 > 2 (True)
7 > (1/2)(4) - 2 -> 7 > 2 - 2 -> 7 > 0 (True)
d) Point D at (-7, 1):
Substituting the coordinates into the inequalities:
1 > -2(-7) + 10 -> 1 > 14 + 10 -> 1 > 24 (False)
1 > (1/2)(-7) - 2 -> 1 > -3.5 - 2 -> 1 > -5.5 (True)
Based on the analysis, point D at (-7, 1) is the only solution to the system of inequalities y > -2x + 10 and y > (1/2)x - 2. Therefore, the correct answer is option d) D.
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1. f(x)=0.5x-1.5x +1I 4x<-1-1sx53 x>3
Answers
Answer:
sorry dont know
Step-by-step explanation:
good luck tho
\
f(x) = 0.5x-1.5x+1
4x<-1
-1 ≤ x ≤ 3
x < 3
Problem Solving
Find all of the solutions for the following equation.
tan theta= 4 tan theta - square 3
Answers
Answer:
A) \(\theta=30^\circ+180n^\circ\)
Step-by-step explanation:
\(tan\theta=4tan\theta-\sqrt{3}\\\\-3tan\theta=-\sqrt{3}\\\\9tan^2\theta=3\\\\tan^2\theta=\frac{3}{9}\\ \\tan^2\theta=\frac{1}{3}\\ \\\frac{1-cos(2\theta)}{1+cos(2\theta)}=\frac{1}{3}\\ \\ 3-3cos(2\theta)=1+cos(2\theta)\\\\2-3cos(2\theta)=cos(2\theta)\\\\2=4cos(2\theta)\\\\\frac{2}{4}=cos(2\theta)\\ \\\frac{1}{2}=cos(2\theta)\\ \\2\theta=60^\circ+360n^\circ\\\\\theta=30^\circ+180n^\circ\)
Recall the identity \(tan^2(\theta)=\frac{1-cos(2\theta)}{1+cos(2\theta)}\)
Pls Help me I need the answer really fast A.S.A.P
Answers
Answer:
15 or 15.4!!!!!!!!!! I hope this helps
Answer:
15
Step-by-step explanation:
9.2 + 6.2 is 15.4
we are rounding to the nearest whole
15.4 goes to 15
What kind of angle is each of the following: 37°, 105°, 76°, 147°, 169°, 89°, 15°,
179°, 180°, 205°, 360°, 90°?
Answers
Answer:
Down below
Step-by-step explanation:
37 degrees is an acute angle, 105 degrees is an obtuse angle, 76 degrees is an acute angle, 147 degrees is an obtuse angle, 169 degrees is an obtuse angle, 89 degrees is an acute angle, 15 degrees is an acute angle, 179 degrees is an obtuse angle, 180 degrees is a straight angle, 205 degrees is a reflex angle, 360 degrees is a full circle, and 90 degrees is a right angle.
Hope this helps! :)
a store buys 120 baseball hats at 0.50 each including tax.the store sells the hats at Markup of 50% they sell all of the hats during the season for the selling price.How much money do they receive for the sales of all the hats
Answers
Answer:
R90
Step-by-step explanation:
120 hats sold and each = $0.50
0.50 × 120 = R60 (all the baseball hats cost)
50% of 0.50 = 0.25
0.25 × 120 = 30 (markup price)
60 + 30 = 90 ( total received for the sales)
A survey on a sample of 35 new cars b eing sold at a lo cal auto dealer was conducted to see which of three p opular options: Air-conditioning (A), Blueto oth (B), and Rear Camera (C), were already installed. The survey found: 18 had A, 13 had B, 12 had C,5 had A and B, 8 had A and C, 6 had B and C, 4 had all three options.
Find the numb er of cars that had:
(a) A and B but not C,
(b) A and C but not B,
(c) B and C but not A;
(d) only one of the options;
(e) at least one option;
(f ) exactly two options;
(g) none of the options.
Answers
Gianelli earns $4.50 per hour. If she works 8 hours per day and 5 days a week, how much will she earn in one week?
$32.40
$36.00
$162.00
$180.00
Answers
Answer:
$180
Step-by-step explanation:
because 4.50 x 8 = 36 then 36 times 5 = 180
WILL GIVE BRAINLIEST! What is 24 written as a percent?
Answers
Answer:
24%
Step-by-step explanation:You divide it by a hundred percent and overall it equals 24% since 24 out of one hundred (24/100) it would be 24% of that.
Now you owe me brainly. Thanks.(:
Will give
BRAINLY AND FIVE STARS and A THANKS
Answers
Answer:
k = 12h
Step-by-step explanation:
Since each of the inputs of h can be mutiplied by 12 to get the output k, the equation is k = 12h
Hope this helps :)
If n is a negative number and p is a positive
number, which of the following is the greatest?
A. n-p
B. np
C. np^2
D. p-n
E. pn^3
Answers
Answer:
The answer is n-p
Please mark me brainalist !
Tell the next two terms in the sequence: 40, 10, 5/2, 5/8
Answers
Answer:
5/32 & 5/128
Step-by-step explanation:
find the slope of each line
y = 2x - 2
y = 7/3x + 2
2x + y = -5
4x - 5y = -20
Answers
Answer: first one is 2 second one is not linear the 3rd one is -2 and the 4th one is 4/3
Step-by-step explanation: use the equation y=mx + b u dont have to find anything the slope is already given to you
Un celular cuesta $ 3 360, ya con el 60% de descuento aplicado. ¿Cuánto cuesta el celular sin el descuento?
a) $ 5 600 b) $ 5 500 c) $ 5 650 d) $ 2 016
24.-Una laptop cuesta $ 12500, pero tiene un descuento del 25%, ¿Cuánto cuesta la laptop con el descuento incluido?
a) $ 9 573 b) $ 9 753 c) $ 9 375 d) $ 9 703
25.- En Copel hay un refrigerador que cuesta $18 270 con el IVA incluido. ¿cuál es el costo del refrigerador sin el IVA?
a) $ 15 750 b) $ 15 570 c) $ 15 705 d) $ 15 507
26.- En el salón de 6to. "C" de la Esc. Juan Escutia, 5 alumnos estaban comparando sus estaturas. Joaquín midió 1.6 m., Adriana un metro con sesenta y cuatro centímetros, Beto 1 metro 2/4, Maximiliano 168 centímetros y Eduardo 100 centímetros más 3/5 de metro, ¿quiénes tienen la misma estatura?
a) Maximiliano y Adriana. b) Joaquín y Maximiliano. c) Beto y Eduardo. d) Eduardo y Joaquín.
Answers
Answer:
b
Step-by-step explanation:
plato
PLEASE HELP ASAPPP:( i’ll mark brainlest
Answers
Answer:
480
Step-by-step explanation:
in this type of question you would multiply the amount of ounces in 1 pound to the amount of how many pounds there is.
Can someone please tell me what letter c equals? The answer choices are , 48, 58, 138, and 148
Answers
Answer:
Step-by-step explanation:
B= 42
C= 48
Answer:148 the percent of the top pieces or c the bottom c answer
Step-by-step explanation:
how many meters are their in centimeter
Answers
Answer:
You mean how many centimerters are in a meter?
In that case 100.
Step-by-step explanation:
i need help please
find b
Answers
Answer:
12
Step-by-step explanation:
This triangle is a 3-4-5 Pythagorean Triple. 9 is 3*3, 15 is 5*3, so b is 4*3, which is 12. Alternatively, you could use the Pythagorean Theorem's converse, sqrt(15^2-9^2), and get 12.
NORMAL distribution is what shape?
how many in 1st deviation
2nd deviation
3rd deviation
Answers
A NORMAL distribution is a symmetrical probability distribution with a bell-shaped curve. It is also called a Gaussian distribution or a normal curve. This distribution is often used in statistics to represent a large number of natural phenomena, such as the distribution of height, weight, or IQ scores in a population.
The first deviation of a NORMAL distribution includes 68.2% of the data. This means that if we were to take a random sample of data from a normally distributed population, about 68.2% of the data would be within one standard deviation of the mean.
The second deviation includes 95.4% of the data. This means that about 95.4% of the data would be within two standard deviations of the mean.
The third deviation includes 99.7% of the data. This means that about 99.7% of the data would be within three standard deviations of the mean.
It is important to note that while these percentages hold true for a NORMAL distribution, they may not apply to other types of distributions.
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Two boys together have $12. One of them has $10 more than the other. How much money does each of them have
Answers
Which function could be used to represent the sequence 8, 20, 50,
125, 312.5...., given that a, = 8?
(1) a, = 4,- 1 ta
(3) 4, = 4, + 1.5(, -1)
(2) a. = 2.5(
4-1) (4) 4 = (a), -1)
Answers
Answer: a = 2.5 (an-1)
Step-by-step explanation: trust me;)
The function which is used to represent the geometric progression 8, 20, 50, 125, 312.5, ... is \(a_{n} = 8(2.5)^{n-1}\).
What is geometric progression?sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is as a geometric sequence of numbers.
Formula for nth term of geometric progression\(a_{n} =ar^{n-1}\)
Where,
\(a_{n}\) is the nth term of the sequence or geometric progression
n is the total number of terms
r is the common ratio
and a is the first term
According to the given question
We have
A geometric progression
8, 20, 50, 125, 312.5
Now the common ratio for the above progression is given by
\(r = \frac{20}{8} = 2.5\)
And the first term is
a = 8
Therefore, the function which is used to represent the above sequence is given by
\(a_{n} = 8(2.5)^{n-1}\)
Hence, the function which is used to represent the geometric progression 8, 20, 50, 125, 312.5, ... is \(a_{n} = 8(2.5)^{n-1}\).
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what number is 10 times greater then 44,660
Answers
The number which is 10 times greater than 44,660 as required to be determined in the task content is; 446,600.
What number is 10 times as great as 44,600?It follows from the task content that the number which is 10 times as great as the given number 44,660 is to be determined.
It follows from arithmetic operations that the required number is given by the product of 10 and 44,660.
Consequently the number is; 10 × 44,660
= 446,600.
Ultimately, the number which is 10 times as great as 44,660 is; 446,600.
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