find the points on the curve x = t^3 - 3t, y = t^3 - 3t^2 where the tangent line is horizontal or vertical/

Answers

Answer 1

The only point where the tangent line is vertical is (0, 0)..

To find the points on the curve where the tangent line is horizontal or vertical, we need to find where the slope of the tangent line is zero (for a horizontal tangent line) or undefined (for a vertical tangent line). The slope of the tangent line is given by the derivative of y with respect to x, dy/dx:

dy/dx = (dy/dt)/(dx/dt) = (3t^2 - 6t)/(3t^2 - 3)

Setting the numerator equal to zero, we get:

3t^2 - 6t = 0

Factorizing, we get:

3t(t - 2) = 0

So the critical points are t = 0 and t = 2.

At t = 0, we have x = 0 and y = 0, so the point is (0, 0).

At t = 2, we have x = 2 and y = -8, so the point is (2, -8).

To determine if the tangent line is vertical or horizontal at each point, we need to look at the derivative dx/dt:

dx/dt = 3t^2 - 3

At t = 0, dx/dt = -3, which means the tangent line is vertical.

At t = 2, dx/dt = 9, which means the tangent line is not vertical.

To find out if the tangent line is horizontal at t = 2, we can look at the derivative of dy/dt:

dy/dt = 9t^2 - 6t

At t = 2, dy/dt = 24, which means the tangent line is not horizontal.

Therefore, the only point where the tangent line is vertical is (0, 0).

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Related Questions

Hello brainly people, can someone please explain how I do this? I really need help...

Answers

Well to find the slope you go y1-y2/x1-x2
In this case you have 9/-17 now the y intercept is when x is 0 what is why which is 4

Your answer is y=-9/17x+4

convert the decimal into a reduce fraction.

Answers

Answer:

hey i dont really know, but look up calculator soup, it has a ton of different calculators and may be able to help u

Step-by-step explanation:

/

what is 41x plus 21x​

Answers

The answer to that question is 62x ()//‘’::;;

Write an explicit and recursive rule for the geometric sequence -5, 10, -20, 40… and use it to find the 12th

Answers

Answer:

See solutions below

Step-by-step explanation:

Given the sequence -5, 10, -20, 40...

The nth term of the GP is expressed as;

Tn = ar^n-1

a is the first term

r is the common ratio

n is the number of terms

From the sequence, a = -5

r = 10/-5 = -20/10 = -2

Substitute

Tn = -5(-2)^n-1

This gives the explicit formula

For recursive;

a1 = -5

a2 = 10 = -2(-5) = -2a1

a3 = -20 = -2(10) = -2a2

From the shown sequence, we can see that;

an = -2an-1

This gives the recursive formula

Get the 12th term;

Using the explicit formula

T12 = -5(-2)^12-1

T12 = -5(-2)^11

T12 = -5(-2048)

T12 = 10240

Hence the 12th term is 10240

find the value and add them together

Huey is reading a book that is 697 pages long.
He tells a friend that he is about 3/4 of the way done.

About how many more pages must Huey read before he finishes the book?

Answers

Answer:

700 books huey finish he your answer

Answer:

175 pages

Step-by-step explanation:

Answer:

. 175

Step-by-step explanation:

There are 2 ways that we can find the answer to this question:

1. Take 1/4 of 697

2. Take 3/4 of 697 and minus the product from 697.

Let's do it both ways:

If we are doing it the first way it would look like this:

(1/4)(697) = 175

Note that we get 1/4 because Huey already read 3/4 of the book so he has 1/4 left.

The second way would look like this:

(3/4)(697) = 523

679 - 523 = 174 (roughly 175)

Therefore, the answer to your question would be . 175. pls mark brainliest

1. Um prêmio em dinheiro foi dividido entre 3
pessoas: a primeira recebeu 1/4 do valor do
prêmio a segunda recebeu 1/3 e a terceira
ganhou R$ 1000,00. Então, o valor desse prêmio,
em reais, era de:
a) 2400,00
b) 2200,00
c) 2100,00
d) 1800,00​

Answers

I think the answer is b

Write a system of linear inequalities so the points,(1,2) and (4,-3) are solutions of the system, but the point (-2,8) is not a solution of the system.

Answers

Answer:

The sample system is:

y < 5y > x - 8

see the attached

The points (1, 2) and (4, -3) are in the intersected region but the point (-2, 8) is outside

Work out, giving your answer in its simplest form:
4/7 divided by 2 1 / 3

Answers

Step-by-step explanation:

4/7÷21/3

=4/7*3/21

=12/147

Answer:

[tex]\frac{12}{49}[/tex]

Step-by-step explanation:

Given

[tex]\frac{4}{7}[/tex] ÷ 2 [tex]\frac{1}{3}[/tex] ← change mixed number to improper fraction

= [tex]\frac{4}{7}[/tex] ÷ [tex]\frac{7}{3}[/tex]

To perform the division

Leave the first fraction. change division to multiplication and turn the second fraction upside down.

= [tex]\frac{4}{7}[/tex] × [tex]\frac{3}{7}[/tex] ← multiply numerators/ denominators together

= [tex]\frac{4(3)}{7(7)}[/tex]

= [tex]\frac{12}{49}[/tex]

A object falls at 16t^2 feet in t seconds you drop a rock from a bridge that is 906 what is the hight in feet after the rock is droped

Answers

Answer:

824 feet

Step-by-step explanation:

Given

[tex]h(t) = 16t^2[/tex]

[tex]H = 906[/tex] -- Initial Height

Required

Calculate the height after 2 seconds --- missing from the question

First, we calculate the distance moved in 2 seconds

[tex]h(t) = 16t^2[/tex]

[tex]h(2) = 16*2^2[/tex]

[tex]h(2) = 16*4[/tex]

[tex]h(2) = 64[/tex]

This means that the object covered 64feet

The object current height is then calculated as:

[tex]Height = H - h(t)[/tex]

t = 2. So, the equation becomes

[tex]Height = H - h(2)[/tex]

Substitute values for H and h(2)

[tex]Height = 906- 64[/tex]

[tex]Height = 824[/tex]

The square table top has an area of 369 square
inches. The length of one side of the table top is
between which two measurements?

Answers

Answer:

19 in. and 20 in.

Step-by-step explanation:

18^2 = 18 * 18 = 324

19^2 = 19 * 19 = 361

20^2 = 20 * 20 = 400

369 is between 361 and 400, so the side of the table is between 19 in. and 20 in.

Answer:

19 in. and 20 in.

Step-by-step explanation:

18^2 = 18 * 18 = 324

19^2 = 19 * 19 = 361

20^2 = 20 * 20 = 400

369 is between 361 and 400, so the side of the table is between 19 in. and 20 in.

There are 20 animals in the barn. There are chickens and sheep in the barn. If there are
a total of 62 legs, how many of each animal are there? *

Answers

Answer: Nope I was wrong

There are 11 sheep, and nine chickens.

PLZZZZZ HELP ME!
It’s math btw

Answers

Answer:

1. 9/10

2. 15/16

4. 3/5

5. 3/5

Step-by-step explanation:

1. 7/10 + 2/10 = 9/10

2. 13/16 + 2/16 = 15/16

4. 7/15 + 2/15 = 9/15 = 3/5

5. 9/20 + 3/20 = 12/20 = 3/5

Answer: 1 r1 for second

Step-by-step explanation: 13/16+2/16=15/16 divide 15/16 gets 1 r1

Calculate the amount of work done if you use a 150N force to push a 50kg box 5m across the kitchen floor.

Answers

Answer:

750 J

Step-by-step explanation:

PLEASE HELP 50 POINTS Which terms can be combined in the expression below? Select three options.

StartFraction 5 over 6 EndFraction a minus 2 b minus 16.3 + StartFraction b over 12 EndFraction + c minus 0.9 b
StartFraction 5 over 6 EndFraction a
–2b
–16.3
StartFraction b over 12 EndFraction
–0.9b

Answers

Answer:

it -16.3

Step-by-step explanation:

Answer:

Answer:

Option 2nd , 4th and 6th correct

2,4 and 6

Step-by-step explanation:

Like terms are those terms which have same variable to the same power.

Combine like terms

Simplify:

Therefore, the  term can be combined in the given expression is,

2, 4 and 6Barinliest?

Find the slope of the line

Answers

Answer:

-1

Step-by-step explanation:

Using rise over run for the two points

4 - 0/ -1 - 3 = -1

Answer:

We found 2 coordinates

1. ( 0 ,3)

2.(3,0)

Now slope = tan theta = 3/3 = 1

Answer is 1

Mark it as brainlist answer

Step-by-step explanation:

the original pattern for dress is 33 3/4 inches long. kimmy needs her dress to be 32 1/2 inches long how much shorter than the pattern does kimmy need to make her dress​

Answers

Answer: 1 1/4

Step-by-step explanation: 32 1/2 is the same as 32 2/4 so all you have to do is subtract 32 2/4 from 33 3/4 which leaves you with 1 1/4

what iis the answer to this question
1/5x40

Answers

Answer:

8

Step-by-step explanation:

Answer:

1/5 x 40 = 8

(Hope this helps! Btw, I am the first to answer.)

Find the distance between (2, 8) and (−6, 2).

The distance is ( ) units.

Answers

Answer:

✓100 = 10

Step-by-step explanation:

2= x1

8= x2

-6= y1

2= y2

Then you apply your distance formula to solve.

Hope it helps

Write the equation of a line in slope intercept form.
(-3,-9 ) and (2,6)

Answers

Answer:

y = 3x

Step-by-step explanation:

Find the slope of the line passing through the points (-7, 4) & (-7, -8)

Answers

Answer:

Undefined

Step-by-step explanation:

The equation for finding the slope is:

y2 - y1

------------

x2 - x1

--------------------------------------------------------------------------------------------------------

4 - (-8)

----------

-7 - (-7)

-----------------------------------------------------------------------------------------------------------

4 + 8

--------

-7 +7

---------------------------------------------------------------------------------------------------------

12

----

0

---------------------------------------------------------------------------------------------------------

The slope is Undefined, so there is no answer

Help me please!!!!!!

Answers

Answer:

(2,8)

Step-by-step explanation:

I'm not so sure but if I were answering I would have picked (2,8)

Factor completely
x^2 - 8x + 16

Answers

Answer:

(x - 4)^2

Step-by-step explanation:

Find the maeasure of the exterior angle in the figure

Answers

Answer:

the answer would be 5b as the exterior angle is subdivided with the co efficient

Step-by-step explanation:

Cual es el 5% de 80?

Answers

4 porque...
.05*80=4

in estimating the body temperature of a person, what difficulties did you encounter?Explain​

Answers

Answer:

In general , While estimating a bodies temperature that temperature is not the same for long, the temperature of the body is not at homeostasis, the temperature constantly has bumps and drops in the temperature this causes in accuracy thats why the thermometer takes 10-20 seconds because it takes the average of all the temperature's so it is accurate, that is a difficulty when estimating temperature because estimates are not good and the temperature keeps having ups and downs.

I dont really understand this question, can anyone help me out?

Answers

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Angles.

Complementary angles sum up together to become 90°.

Supplementary Angles sum up together to become 180°.

hence,

1.) Ans ==>Angle ABC and Angle NMP

2.) Ans ==> angle ABC and angle EFG

Complementary angles add up to 90 degrees while supplementary angles will add up to 180 degrees.

1) ABC & NMP
2) EFG & RST

f(x)= 10x find the inverse of the function

Answers

This is the answer I got.

someone help me with this answer please !!

Answers

Answer:

-27

Step-by-step explanation:

I didn't mean to click an answer but please help me out

Answers

Answer:

135

Step-by-step explanation:

135+45=180, and supplementary angles always equal 180

Answer:

The answer is 135

Step-by-step explanation:

Definition of supplementary angles: either of two angles whose sum is 180°, so 180 - 45 = 135!

Please mark as brainliest.

How many LaTeX: \frac{1}{3}1 3 inch cubes does it take to fill a box with width LaTeX: 2\frac{2}{3}2 2 3 inches, length LaTeX: 3\frac{1}{3}3 1 3 inches, and height LaTeX: 2\frac{1}{3}2 1 3 inches?

Answers

Answer:

186.7 cubes

Step-by-step explanation:

How many LaTeX: \frac{1}{3}1 3 inch cubes does it take to fill a box with width LaTeX: 2\frac{2}{3}2 2 3 inches, length LaTeX: 3\frac{1}{3}3 1 3 inches, and height LaTeX: 2\frac{1}{3}2 1 3 inches?

Step 1

We find the volume of the box

= Length × Width × Height

Length = 3 1/3 inches = 10/3 inches

Width = 2 2/3 inches = 8/3 inches

Height = 2 1/3 inches = 7/3 inches

The volume of the box =

10/3 inches × 8/3 inches × 7/3 inches

= 560/9 cubic Inches

= 62 2/9 cubic inches

Step 2

How many 1/3 inch cubes would fill the box.

This is calculated as:= 62 2/9 cubic inches/ 1/3 inches

= 560/9 ÷ 1/3

= 560/9 × 3/1

= 186.66666667 cubes

Approximately = 186.7 cubes

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