help with 5 please( question tuped below too).

Prove that y=x+2 is a tangent to the locous P(2t²,4t).

find the point of contact of this tangent to this locous and hence find the equation of normal at the point.


thanks

Help With 5 Please( Question Tuped Below Too). Prove That Y=x+2 Is A Tangent To The Locous P(2t,4t).find

Answers

Answer 1

9514 1404 393

Answer:

tangent point: (2, 4)normal: y = -x +6

Step-by-step explanation:

The derivative of P with respect to t is ...

  P' = (x', y') = (4t, 4)

so the slope of the curve for some value of t is ...

  dy/dx = y'/x' = 4/(4t) = 1/t

The line we want to be a tangent is y = x +2, which has a slope of 1. The curve will have a slope of 1 where ...

  1/t = 1   ⇒   t = 1

At t=1, the point P is (2·1², 4·1) = (2, 4). For x=2, the point on the desired tangent is y = x +2 = 2 +2 = 4, or (x, y) = (2, 4).

The curve and the given line both have a slope of 1 at the point (2, 4), so that is the tangent point.

__

The normal to the curve at (2, 4) will have a slope that is the opposite reciprocal of the slope of the tangent: -1/1 = -1. Then point-slope form of the equation of the normal line is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -4 = -1(x -2) . . . . . . line with slope -1 through point (2, 4)

  y = -x +6 . . . . . . . . equation of the normal line in slope-intercept form

Help With 5 Please( Question Tuped Below Too). Prove That Y=x+2 Is A Tangent To The Locous P(2t,4t).find

Related Questions

What are the ratio of 1:6 and 3:8, 2:14and 3:42

Answers

The ratio of 1:6 is 1/6

The ratio of 3:8 is 3/8

The ratio of 2:14 is 1/7

The ratio of 3:42 is 1/14

Please mark brainliest if that helped!

Find the sum of the geometric sequence.
1, 1/2, 1/4, 1/8, 1/16.

Answers

Answer:

2

Step-by-step explanation:

a1= 1

r= a2/a1

r= (1/2)/1

r=0.5

s= a1/1-r

s= 1/1-0.5

s=2

find the product of 3 and 1/2 and 1.6

Answers

Answer:

5.6

Step-by-step explanation:

3.5 x 1.6

It all depends on where the parentheses are in the question.

(3) · (1/2) · (1.6)  =  2.4

or

(3-1/2) · (1.6)  =  5.6

Circle A has an area of 500 in? The diameter of circle B is three times the diameter of circle A. Estimate the area of circle B. !I will give brainlest!​

Answers

Step-by-step explanation:

circle has an area of 500 inches if we multiply it by 3 we get 1500 inches

How many degrees must the flyswatter pass through before it is horizontal?

Answers

Answer:

90°

Step-by-step explanation:

assuming it's upright and you swat it down it will go down by 90°

802.4 divided 1.7

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Answers

The answer to this equation is 472.

Answer:

472

Step-by-step explanation:

First we make both numbers into wholes by moving the decimal point one place behind.Then divide normally.

8024 ÷ 17 = 472

I hope this helps :)

Help!! Please photo art attached below

Answers

Answer:

C

Step-by-step explanation:

180 degrees + 30 =210 degrees

210 degrees equals 7π/6

Three times the sum of a number and eight is four more than the number. find the number

Answers

Answer:

3(x+8)=4+x

distribute the 3 by multiplying it with the x and the 8

3x+24=4+x

subtract x from both sides

2x+24=4

subtract 24 from both sides

2x=4-24

2x=-20

divide each side by 2

leaving the variable isolated

x=-10

Step-by-step explanation:

It is important to balance each side by doing the same to both sides such as at the end divide both sides by 2.

The unknown number will be equal to 10.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that three times, the sum of a number and eight is four more than the number.

The equation will be written as,

3(x+8)=4+x

Distribute the 3 by multiplying it with the x and the 8,

3x+24=4+x

Subtract x from both sides,

2x+24=4

Subtract 24 from both sides,

2x=4-24

2x=-20

Divide each side by 2.

x=-10

Therefore, the unknown number will be equal to 10.

To know more about an expression follow

https://brainly.com/question/25968875

#SPJ2

The area of a triangle is 24 square inches. What is the height of the triangle if the base length is 4 inches?
6 inches
8 inches
12 inches
20 inches

Answers

Answer:

[tex]\boxed {\boxed { \sf 12 \ inches}}[/tex]

Step-by-step explanation:

The area of a triangle can be calculated using the following formula.

[tex]a=\frac{1}{2} bh[/tex]

The area of the triangle is 24 square inches and the base is 4 inches long.

a= 24 in² b= 4 in

Substitute the values into the formula.

[tex]24 \ in^2 = \frac {1}{2} * 4 \ in * h[/tex]

Multiply on the right side of the equation.

[tex]24 \ in ^2 = ( \frac{1}{2} * 4 \ in ) * h[/tex]

[tex]24 \ in ^2 =2 \ in *h[/tex]

We are solving for the height of the triangle, so we must isolate the variable h. It is being multiplied by 2 inches. The inverse of multiplication is division, so we divide both sides by 2 inches.

[tex]\frac { 24 \ in ^2 }{2 \ in }= \frac{ 2 \ in *h}{ 2 \ in}[/tex]

[tex]\frac { 24 \ in ^2 }{2 \ in }= h[/tex]

[tex]12 \ in = h[/tex]

The height of the triangle is 12 inches.

A plumber charges $65 for a diagnostic check. After the check, it is $85 per hour for the work. With $320 in your wallet, how many hours of Work can you afford?​

Answers

Answer:

3 hours

Step-by-step explanation:

first, you subtract 65 from 320 to cover the diagnostic check.

Then, you subtract 85 from the remaining cash three times and you'll get 0

Geometry please help me!!!!

Answers

Answer:

Step-by-step explanation:

What is the "least common denominator" of the following two fractions:

1/6 and 1/2

Answers

Answer:

it is 6

Step-by-step explanation:

2 and 6 are the denominators and the least common denominator is the number in which 2 & 6 can go in without leaving a remender and 6 is that number

Answer:

The LCD of the fractions 1/6 and 1/2 is 6

Step-by-step explanation:

The LCD of 2 or more fractions is the least common multiple of the denominators.

The given fractions are 1/2 and 1/6. The denominators are 2 and 6

List the multiples of each denominator:

Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, …

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, ..

The least common multiple that the two share is 6.

So the LCD of 1/2 and 1/6 is 6.

Finding Perimeter Practice Pages continued Name: 3 A rectangular garden has a width of 90 feet. The perimeter is 500 feet. What is the length of the garden? 500 = (2x) + .......... .........) 500 = 2€ + = 20 = 2 = = € The length of the garden is ................. feet. inchor lona Tell w​

Answers

Step-by-step explanation:

After putting the values:-

A 3-gallon jug of water costs $15.00. What is the price per quart?

Answers

5 Bc u divide 15 by 3 to get 5

Answer:

1.25 dollars per quart

Step-by-step explanation:

There are 4 quarts per gallon

3 gallons * 4 quarts/ gallon = 12 quarts

15 dollars/ 12 quarts

1.25 dollars per quart

What I got to do please

Answers

Answer:

4

Step-by-step explanation:

[tex]3 \div \frac{3}{4} \\ = \frac{3}{1} \div \frac{3}{4} \\ = \frac{3}{1} \times \frac{4}{3} \\ = \frac{12}{3} \\ = \frac{4}{1} \\ = 4[/tex]

Answer:

4

Step-by-step explanation:

3÷3/4

3*4/3

12/3

4

Vertical plane R intersects horizontal plane P. Points D, and B are on the line of the intersecting planes. Point F is on the top half of plane R. Point G is on the bottom half of plane G. Point C is on the left half of plane P. Point E is on the right side of plane P. There is a line formed between points C and E. Point H to above and to the right of the planes. Point L is below and to the left of the planes.
The intersection of plane R and plane P is


.

Point
is not on plane P.

Line C E and Line D B intersect at point
.

Answers

Answer:

The intersection of plane R and plane P is line DB

Point H is not on plane P.

CE and DB intersect at point D

Explanation:

got it right on edge 2021 :)

Answer:

there right^

Step-by-step explanation:

edge 22

Instructions: Determine whether the following polygons are
similar. If yes, type in the similarity statement and scale factor. If
no, type 'None' in the blanks.

Answers

Answer:

No they aren't similar different measurements but same angle so they can't be said to be similar

what is 98×63-32×69=

Answers

Answer: plz marl brainilist

3966

Step-by-step explanation:

(98 × 63 - 32 × 69

98 * 63) - (32 * 69)

Answer:

3966

Step-by-step explanation:

98 x 63 - 32 x 69 =

Multiply

6174 - 2208

Subtract

3966

solve for y. identify the slope and y-intercept. then graph the equation.

y=-3x+1

Answers

Answer:

the slope -3, slope meaning rate of change and y intercept is 1.

hope that answers your question

(used desmos to graph, good stuff!!!)

Cyclically each of 3 tanks fires at one of the other 2 until only 1 is left. A hit destroys a tank. A has probability 1 of hitting its target, B has probability 0.8, and C has probability 0.5. What are the best strategies for each of the tanks and what are their survival probabilities

Answers

Answer:

.................................................................

Step-by-step explanation:

..............................................

please help! x^3 +y^3=9

Answers

Step-by-step explanation:

Taking the derivative of both sides with respect to x, we get

[tex]\dfrac{d}{dx}(x^3 + y^3) = \dfrac{d}{dx}(3)[/tex]

[tex]\Rightarrow 3x^2 + 3y^2\dfrac{dy}{dx} = 0[/tex]

Solving for [tex]\frac{dy}{dx}[/tex], we get

[tex]\dfrac{dy}{dx} = -\dfrac{3x^2}{3y^2} = -\dfrac{x^2}{y^2}[/tex]

help fast pleasee




find the unit rate for Dion and Emily who read faster?


Dion: 36 pages in 3 days
emily: 45 pages in 5 days

36 pages
__________= ? pages per day.
3 days



45 pages
_________=? pages per day.
5 days


deon read _____ pages per day than emily.​

Answers

Step-by-step explanation:

36 pages in 3 days, 36/3=12 pages per day.

45 pages in 5 days, 45/5=9 pages per day.

Difference is 3 pages per day

Answer:

Deon read 3 more  pages per day than Emily.

Is the rate of change of the function 5?

Answers

the rate of change is 4-x every y-1 so if you’re asking if is 5 it’s not

Using the graph as your guide, complete the following statement.
The discriminant of the function is ___
A. positive
B. zero
C. negative

Answers

negative gujgdddgnhhhffvvjjjhg

Line A passes through the points (-2, 27) and (1, -9). Line B passes through the points (-1, 15)
and (3,-33).
Which statement is true?
Line A overlaps line B.
Line A does not intersect line B.
Line A intersects line B at exactly one point.

Answers

Answer:

Line A overlaps line B

Step-by-step explanation:

find gradient of both A and B and use it to find the equation of both lines

final answer will reveal that both lines are the same implying that one overlaps the other

Consider the line 9x + 8y = -8.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?

Answers

Answer:

Step-by-step explanation:

The slope of the line is -9/8. The slope of any parallel to the line is also -9/8.

..............................

Answers

Answer:

[tex]x=17[/tex]

Step-by-step explanation:

[tex](6x+10)(x+17)(4x-34)[/tex]

[tex]6x+10+x+17+4x-34=180[/tex]

Add:- [tex]6x+x+4x=11x[/tex]

and [tex]10+17-34=-7[/tex]

So, [tex]11x-7=180[/tex]

Add 7 to both sides:-

[tex]11x=187[/tex]

Divide both sides by 11:-

[tex]\frac{11x}{11}=\frac{187}{11}[/tex]

[tex]x=17[/tex]

OAmalOHopeO

What are all the factors of 618?

Answers

Answer:

1, 2, 3, 6, 103, 206, 309, 618

For the function y=f(x), find f’(a)

Answers

Answer:

-1/4

Step-by-step explanation:

f(x) = 1/(x+1)

f(a) = 1/(a+1)

f'(a) = {(a+1)×d/da (1) - d/da (a+1) × 1}/(a+1)²

f'(a) = {(a+1)×0 - 1×1}/(a+1)²

f'(a) = (0-1)/(a²+2a+1)

f'(a) = -1/(1+2a+a²)

putting a = 1

f'(a) = -1/(1+2+1)

f'(a) = -1/4

Alice, Bob, and Carol play a chess tournament. The first game is played between Alice and Bob. The player who sits out a given game plays next the winner of that game. The tournament ends when some player wins two successive games. Let a tournament history be the list of game winners, so for example ACBAA corresponds to the tournament where Alice won games 1, 4, and 5, Caroll won game 2, and Bob won game 3.

Required:
a. Provide a tree-based sequential description of a sample space where the outcomes are the possible tournament histories.
b. We are told that every possible tournament history that consists of k games has probability 1/2k, and that a tournament history consisting of an infinite number of games has zero prob- ability. Demonstrate that this assignment of probabilities defines a legitimate probability law.
c. Assuming the probability law from part (b) to be correct, find the probability that the tournament lasts no more than 5 games, and the probability for each of Alice, Bob, and Caroll winning the tournament.

Answers

Answer:

I don't know what you think about it is not going to be a great day of school and I don't know what you think about it is not going to be a great day of school

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