To find the equation for the line tangent to the parametric curve at the point where t=3, we need to find the values of x and y at t=3 and the corresponding slopes.
Given the parametric equations: x=t^3−9t and y=9t^2−t^4.
At t=3, we have:
x = (3)^3 - 9(3) = 0
y = 9(3)^2 - (3)^4 = 54
To find the slope at t=3, we need to find dy/dx:
dy/dt = 18t - 4t^3
dx/dt = 3t^2 - 9
dy/dx = (dy/dt) / (dx/dt)
= (18t - 4t^3) / (3t^2 - 9)
At t=3, we have:
dy/dx = (18(3) - 4(3)^3) / (3(3)^2 - 9)
= -6
Therefore, the slope of the tangent line at t=3 is -6. To find the equation of the tangent line, we use the point-slope form- y - 54 = (-6)(x - 0)
Simplifying y = -6x + 54
So the equation of the tangent line at t=3 is y = -6x + 54x
For t=-3, we can repeat the same process to find the equation of the tangent line. However, since the curve is symmetric about the y-axis, the tangent line at t=-3 will have the same equation as the tangent line at t=3, except reflected across the y-axis. Therefore, the equation of the tangent line at t=-3 is y = 6x + 54.
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Sarah is conducting a science experiment where she initially has a population of 4 fruit flies. Every week the population triples. She writes the function f(x)=4(3)x to predict the population growth. Which rule can also model the function?
Answer and explanation:
Given that initial population of fruit flies = 4
And population of fruit flies triple every week
If population of fruit flies triple every week then let x represent number if weeks
Therefore function can be modelled thus :
f(x)= 4 + 3x
To demonstrate that the function is correct, we use an example. Now assume population grows for two weeks, using the function:
f(2)= 4+3×2
f(2)= 10
Therefore population grows to 10 fruit flies in 2 weeks based on our function
A submarine travels 12 km due West from its base and then turns and travels due South for 14.8 km. How far away is the submarine from its base? .
Answer:
the submarine travels 26.8 km. from its base
Answer:
The answer is 19.1
Step-by-step explanation:
[tex]z = \sqrt{ {x}^{2} + {y}^{2} } = \sqrt{ {12}^{2} + {14.8}^{2} } = 19.1[/tex]
geometry, write statement and reason
sebuah kantong berisi 20 kelereng merah dan 15 kelereng putih.toni memiliki 3 kantong yang berisi kelereng dengan jumlah yang sama. jika Toni memberikan 45 kelereng kepada adiknya, sisa kelereng Toni adalah
Answer:
60
Step-by-step explanation:
The computation of the rest of the marbles is given below:
Since there is 20 red and 15 white marbles
Also the 3 bags contains same marbles
So if he gives 45 marbles, so the remaining would be
= (20 + 15) × 3 - 45
= 35 × 3 - 45
= 105 - 45
= 60
What is the answer to 2 + n = 16
Answer:
Original Equation: 2+n=16
Subtract 2 from both sides: 2+n-2=16-2
Simplify: n=14
Hope this helps!
d-1/2=5/12 what is d??
Answer:
d = [tex]\frac{11}{12}[/tex]
Step-by-step explanation:
1) To solve for d, isolate it in the equation. So, to get rid of the [tex]-\frac{1}{2}[/tex] with the d, add [tex]\frac{1}{2}[/tex] to both sides.
[tex]d-\frac{1}{2} = \frac{5}{12} \\d - \frac{1}{2} +\frac{1}{2} = \frac{5}{12} + \frac{6}{12} \\d = \frac{11}{12}[/tex]
Thus, d = [tex]\frac{11}{12}[/tex].
COULD I GET GET SOME HELP PLZ? REWARD BRAINLIEST
Answer:
1. D) -4/3 or 4/3
2. A) -6 or 8
Step-by-step explanation:
Answer:
x=4/3 or -4/3
x=8,-6
Step-by-step explanation:
A coupon book has a coupon for 40% off of a lift ticket at Mt. Woodstock. A lift ticket usually costs $70. How much would a skier save?
Answer:
The Skier would save $28 dollars
Step-by-step explanation:
The answer is 28 because 40% of 70 is 28.
Hope this helps! :)
Answer:
The skier would spend $48 and save $28
Step-by-step explanation: In the attachment
If 8 model airplanes cost $24, what is the unit price of the model airplanes? The unit price of the model airplane.
Answer:
3 dollars per airplane
Step-by-step explanation:
24/8 is 3, where 8 is airplanes and 24 is cost in total
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Lesson 2 Review...
< Exit
Topic 5 Assessment
IMPLAYER
Drag each expression to its equivalent expression. Each expression may be used only once.
+ 1
4
1
X +
+1
3
Expression
Equivalent Expression
-
3
4
1
4
+
3
+
3
4
See
pls help this is due soon check 2 that apply
Answer:
I am pretty sure it is option a and c
Sorry if i am wrong
The length of an alligator in a zoo is 14 5/6 feet. The Everglades National Park lists the longest alligator ever recorded in Florida at 17 5/12 feet. Which is the difference in their lengths? a 2 3/4 feet b 2 7/12 feet c 3 5/8 feet d 3 5/6 feet
9514 1404 393
Answer:
b) 2 7/12 ft
Step-by-step explanation:
The difference is ...
(17 5/12 ft) - (14 5/6 ft) = (17 -14) ft + (5/12 -5/6) ft
= 3 ft + (5/12 -10/12) ft = 3 ft - 5/12 ft
= 2 7/12 ft
Can you plz help me!
7x-3=12 help me please
Answer:
x=15/7
Step-by-step explanation:
7x-3=12
+3=+3
7x=15
/7=/7
x=15/7
n the diagram, the measure of angle 9 is 85°.
4 lines intersect to form 16 angles. The angles created, clockwise from top left are 1, 2, 3, 4; 5, 6, 7, 8; 9, 10, 11, 12; 13, 14, 15, 16.
Which angle must also measure 85°?
Angle2
Angle5
Angle11
Angle12
Answer:
The real answer is angle 5
Step-by-step explanation:
The angle 11 must measure the angle 85. The correct option is C.
What are lines and angles?An infinitely long row of evenly spaced dots that extends in both directions makes up a line. Its length is the only dimension it has. An illustration of a line is a horizontal mark made on a piece of paper. A figure made by two rays that intersect at the same endpoint is referred to as an angle.
Given that in the diagram, the measure of angle 9 is 85°. 4 lines intersect to form 16 angles. The angles created, clockwise from the top left are 1, 2, 3, 4; 5, 6, 7, 8; 9, 10, 11, 12; 13, 14, 15, 16.
The measure of angle 9 is equal to the measure of angle 11. it means that angle 9 and angle 11 are equal to 85 degrees. The image is attached with the answer below. Shows the angle 9 and angle 11 are vertically opposite angles.
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Find the values of the variables and the lengths of the sides of this kite.
Answer:
option D
Step-by-step explanation:
option D is the correct answer of this question .
plz mark my answer as brainlist.
hope this will be helpful to you.
Answer:
D
Step-by-step explanation:
The weights of four puppies are shown in pounds
9.5 9
9.125 9
Which list shows these weights in order from greatest to least?
Answer:
9.125 9, 9.59
Step-by-step explanation:
Help meh ill mark you all 4 plz if you can
Answer:
Step-by-step explanation:
5+ 1 7/8 = 6 7/8
3 - 1 3/4 = 1 1/4
7 3/4 + 4 = 11 3/4
4- 2 3/7 = 1 4/7
Is my answer correct???
Answer:
Yes! Great job!
Hope that helps!
If y = 3x - 5 and x = 3y - 5, then what are x and y?
Answer:
2?
Step-by-step explanation:
Answer:
x nang iwan at y naman ganon
Solve the quadratic equation x^2- 11x = 12 using any method. Describe the method you chose and why you chose it.
Answer:
12, -1 its the answer
Step-by-step explanation:
1. subtract 12 from both sides
2. simplify which looks like this x^2- 11x - 12=0
3.solve with the quadratic formula
4.separate the solutions
and there you go
please help asap!!!!
Answer:
primeter 34.ft
area.30 ft
Step-by-step explanation:
I did this myself, but I kept getting negative numbers can someone else try and do this and see what you get
Answer:
6
Step-by-step explanation:
Answer:
67
Step-by-step explanation:
4x = 2x + 12
4x - 2x = 2x - 2x + 12
2x = 12
2x ÷ 2 = 12 ÷ 2
X = 6
Plug into HI
9 × 6 + 13 = 67
(3x - 2)³=
gives the solution pls.
Answer:
27x^3 - 54x^2 + 36x - 8
Step-by-step explanation:
(3x - 2)^3
= (3x - 2) (3x - 2) (3x - 2)
= 27x^3 - 54x^2 + 36x - 8
Hope this helps :)
Let me know if there are any mistakes!!
Answer:
1x
Step-by-step explanation:
Please help me again!
Answer:
144
Step-by-step explanation:
First subtract 180 from 20% of 180.
180 - (20/100 x 180) = 180-36 = 144
Solve for x. 3 - √x = 0
Answer:
x = 9
Step-by-step explanation:
3 - √x = 0
Subtract 3 from both sides of the equation
3 - 3 - √x = 0 - 3
-√x = -3
Divide both sides by -1
-√x / -1 = -3 / -1
√x = 3
Take the square of both sides
(√x) ² = 3²
X = 9
Solve for xxx. Your answer must be simplified. x/3 ≥ −33
Answer:
x ≥ -99
Step-by-step explanation:
Its on khan academy
what special name is given to the domain in a linear programming problem
Answer:
Mathematics
Step-by-step explanation:
Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).
Is this a right triangle?
Answer:
No, one of the angles has to be 90º for it to be a right triangle
Step-by-step explanation:
Answer:
no. it doesn't have a right angle.
please help! I will give brainlist
Answer:
A= Yes, it's the equation
B= it's what the problem equals
Step-by-step explanation:
I think this is right I'm not to sure but I think it is
hope this helps :)
Step-by-step explanation:
the process shown in the picture.