Find an equation of the tangent line to the bullet-nose curve y=|x|/sqrt(2−x^2) at the point (1,1) I think that square root is what is confusing me on this question

Answers

Answer 1

[tex]\bf y=\cfrac{|x|}{\sqrt{2-x^2}}\qquad \boxed{|x|=\pm\sqrt{x^2}}\qquad y=\cfrac{\sqrt{x^2}}{\sqrt{2-x^2}}\\\\ -------------------------------\\\\ \cfrac{dy}{dx}=\stackrel{quotient~rule}{\cfrac{\frac{1}{2}(x^2)^{-\frac{1}{2}}\cdot 2x\cdot \sqrt{2-x^2}~~-~~\sqrt{x^2}\cdot \frac{1}{2}(2-x^2)^{-\frac{1}{2}}\cdot -2x}{(\sqrt{2-x^2})^2}}[/tex]

[tex]\bf \cfrac{dy}{dx}=\cfrac{\frac{x\sqrt{2-x^2}}{\sqrt{x^2}}~~+~~\frac{x\sqrt{x^2}}{\sqrt{2-x^2}}}{2-x^2}\implies \cfrac{dy}{dx}=\cfrac{\frac{x(2-x^2)~~+~~x(x^2)}{\sqrt{x^2}\sqrt{2-x^2}}}{2-x^2}\\\\\\ \cfrac{dy}{dx}=\cfrac{\frac{2x\underline{-x^3+x^3}}{\sqrt{x^2}\sqrt{2-x^2}}}{2-x^2}\implies \cfrac{dy}{dx}=\cfrac{\frac{2x}{\sqrt{x^2}\sqrt{2-x^2}}}{2-x^2}[/tex]

[tex]\bf \cfrac{dy}{dx}=\cfrac{2x}{\sqrt{x^2}\sqrt{2-x^2}(2-x^2)} \implies \boxed{\cfrac{dy}{dx}=\cfrac{2x}{|x|\sqrt{2-x^2}(2-x^2)}} \\\\\\ \left. \cfrac{dy}{dx} \right|_{1,1}\implies \cfrac{2(1)}{|1|\cdot \sqrt{2-1^2}(2-1^2)}\implies 2\\\\ -------------------------------\\\\ \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-1=2(x-1)\implies y-1=2x-2 \\\\\\ y=2x-1[/tex]

Related Questions

Can you answer all of these please?!?!

1. Kim's age is twice that of her sister. When you add Kim's age to her sister's age, you get 36. How old is each sister?
(a) Write an equation that represents the situation. Explain any variable used.(1 point)
(b) Solve the equation from Part (a). Show your work. State your solution as a complete sentence. (3 points)
Answer:

2. Solve each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither.
(a) (2 points)
(b) (2 points)
(c) (2 points)
Answer:

3. At a bargain store, Tanya bought 3 items that each cost the same amount. Tony bought 4 items that each cost the same amount, but each was $2.25 less than the items that Tanya bought. Both Tanya and Tony paid the same amount of money. What was the individual cost of each person's items?
(a) Write an equation. Let x represent the cost of one of Tanya's items. (1 point)
(b) Solve the equation. Show your work. (2 points)
(c) Check your solution. Show your work. (1 point)
(d) State the solution in complete sentences. (1 point)
Answer:

Answers

1) sister-x
kim-2x
x+2x=36
3x=36
x=12
2x=24
Kim is 24 years old and her sister is 12 years old.

3) Tanya-3x
Tony-4y
x-2.25=y
3x=4y
3x=4x-9
9=x
6.75 =y

Tanya's was 9 $ and Tony's was 6.75 $

Suppose it costs $ 20 per day and $ 0.12 per mile to rent a car. What is the total bill if the car is rented for 3 days and is driven 140 miles?
The total bill is $_

Answers

20 per day for 3 days = 20 * 3 = 60
0.12 per mile for 140 miles = 0.12(140) = 16.80
for a total cost of : 60 + 16.80 = 76.80 <==

First, rewrite 9/10 and 23/25 so that they have a common denominator.

Then, use
<, =, or > to order 9/10 and 23/25

Answers

the cheap answer is, well, all we do is, grab the denominator of one and multiply the other by it, top and bottom, and grab the denominator of the other, and multiply the first one by that one too, that way, both will have the same denominator, and then you can simply check the numerator to see who's larger, let's do so.

[tex]\bf \cfrac{9}{\boxed{10}}\qquad \qquad \cfrac{23}{\boxed{25}} \\\\\\ \cfrac{9\cdot \boxed{25}}{10\cdot \boxed{25}}\implies \cfrac{225}{250}\qquad \qquad \qquad \cfrac{23\boxed{10}}{25\cdot \boxed{10}}\implies \cfrac{230}{250}\\\\ -------------------------------\\\\ \textit{so, which is larger then?}\qquad \cfrac{225}{250}~or~\cfrac{230}{250}?[/tex]

surely you can tell.

The lowest common multiple of 10 and 25 is 50, so set that as the denominator.

9/10=45/50 (multiply by 5)
23/25=46/50 (multiply by 2)

46/50 > 45/50 therefore
23/25 > 9/10.

Hope this helps :)

Round the decimal to the nearest hundredths 983.625

Answers

983.625
9 = hundreds
8 = tens
3 = ones
6 = tenths
2 = hundredths
5 = thousandths
You want to round to the nearest hundredths
Look at the number on the right, if it's bigger than 5, round up, if it's 4 or lower, round down.
In this case, the number to the right is a 5, so you round the 2 (hundredths) up one so:
983.63

What integer is equivalent to 9 3/2

Answers

Whole # * denominator + numerator over the denominator
Answer: 21/2

I need help please 4x-10=2(2x-5)

Answers

Since the results are equal to each other, there is more than one solution to x

I'll give BRAINIEST

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

Answers

its 0.25. ez. i hope i helped :)

which number produces a rational number when added to 1/5

Answers

-2/3 produces a rational number.

1/5+(-2/3)=
3/15-10/15=
-7/15 (which is rational)

Answer:

We can add any rational number to 1/5 to get a rational number.

Step-by-step explanation:

Given: We have given a rational number 1/5.

To find: We need to find a number which is added to 1/5 gives a rational number.

Solution: We know that,

Rational number + Rational number = Rational Number

Rational number + Irrational Number = Irrational Number

Irrational Number + Irrational Number = Irrational Number.

As we know that given fraction 1/5 is a rational number.

So, when we add any rational number to 1/5 would give a rational number.

Let us we take an example,

[tex]\frac{1}{5} +\frac{2}{3} = \frac{3+10}{15}= \frac{13}{15}[/tex]

We can see in above example that a rational number 2/3 is added to 1/5 gave us 13/15 which is also a rational number.

Therefore, we can add any rational number to 1/5 to get a rational number.

If a bottle rotates through 270 degrees in 3 seconds how many degrees does it rotate in 2 seconds

Answers

The bottle rotates 180 degrees in 2 seconds.

I divided 270 by 3, which was 90. Then, I multiplied 90 by 2. Which was 180.

270 / 3 = 90
90 sec per spin
then you multply by two for two spins

90x2=180

Answer is 180 per sec

How do I solve a-5/5=5

Answers

5/5 = 1

a - 1 = 5

a - 1 (+1) = 5 (+1)

a = 6

if you mean (a-5)/5 = 5

((a - 5)/5) (5) = 5(5)

a - 5 (+5) = 25 + 5

a = 30

hope this helps

Alexandria wants to go hiking on Saturday. She will consider these conditions when she chooses which of several parks to visit:
• She wants to hike for 2 hours.
• She wants to spend no more than 6 hours away from home.
• She can average 50 miles per hour to and from the park.

Write and solve an inequality to find possible distances from Alexandria’s home to a park that satisfies the conditions.

Answers

Answer: 27

i would say 54/2=27

Step-by-step explanation:

What is 2 divided by 126

Answers

126 divided by 2 is 63

2/ 126= 1/63

If your asking what 126/2 = 63

Hope this helps :)

Solve for x. 3.3x = 29.04

Answers

3.3x =29.04

to find x divide both sides by 3.3

x = 29.04 / 3.3

x = 8.8

29.04 divide 3.3 =x
So therefore
x =8.8

Graph y−5=−23(x+9) using the point and slope given in the equation. Use the line tool and select two points on the line.

Answers

maybe try (-9, 6) and (-9,5)
i think it may be correct

Answer here is correct hope this helps :)

A camper attaches a rope to the top of her tent to give it more support. She stakes the rope, which is 8 ft long, to the ground at a distance of 6 feet from the middle of her tent. About how tall is her tent?

Answers

about five feet tall

5 Foot tall I think.

Which would most likely be graphed using a continuous graph? Check all that apply. (Medal for correct answer.

Answers

We need an image to be able to answer this question

Question:

Which would most likely be graphed using a continuous graph? Check all that apply.

Answer:

B. Total cost, c, of buying g pounds of broccoli.

C. Speed of a car, s, as it accelerates over time, t.

E. total distance, d, that has been driven over time, t.

F. decrease in outside temperature, F, one evening over time, t.

Hope this helped!

what percent of 29.5 is 10.03

Answers

so if we take 29.5 to be the 100%, what is 10.03 in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 29.5&100\\ 10.03&p \end{array}\implies \cfrac{29.5}{10.03}=\cfrac{100}{p}\implies p=\cfrac{10.03\cdot 100}{29.5}[/tex]

can whole numbers be rational numbers

Answers

Use this diagram, it might help.

From the inside, whatever that layer is, it can be any of the layers outside of it.

All whole numbers can be a rational number, but not all rational numbers be a whole number.

Kind of like all squares can be rectangles, but not all rectangles can be a square.

The whole number has all the attributes of a rational number, but not all rational numbers have all of the attributes of a whole number.

at the metal-casting company where i work, i must set up a conveyor system to move castings from the furnace to the heat treatment area 55 yards away. the castings cool at the rate of 0.03 degrees fahrehnheit per second and must not be allowed to cool more that 7 degree's fahrenheit before being heat rtreated. what is the minimum speed per second that the conveyor must move?

Answers

Maximum time allowed = 7 deg. / 0.03 deg/s = 233.3 s
Minimum speed = 55 yd * 3 ft/yd / 233.3 s
= 0.707 ft/s

-1/2(7z+4)+1/5(5z-15)

Answers

[tex] \frac{-(5 ( z + 2 ))}{2} [/tex] I am pretty sure this is the answer.

this number is the same as 31 + 880000

Answers

880,000 + 31 = 880,031

hope this helps

The answer to your question is 880031

Kelly wants to buy 5.6 feet of wood for a bookshelf. The wood costs $3.25 per foot. If Kelly has $18.50 to spend, how much change will she receive?

Answers

$3.25x 5.6=$18.20-$18.50= $0.30

$3.25 x 5.6 = 18.20. Subtract $18.50 from 18.20. 18.50-18.20 = .30

When are two angles called complements of one another ?

Answers

When two angles equal 90 degrees then they would be complementary to each other

Answer:

Two angles are said to be complements of one another if: they add up to be 90 degrees.

Step-by-step explanation:

When are two angles called complements of one another ?

Answer : Two angles are said to be complements of one another if: they add up to be 90 degrees.

Like popular combinations are = 60 degrees plus 30 degrees

45 degrees plus 45 degrees.

And many more.

The scores on ms. martin's statistics quiz had a mean of 12 and a standard deviation of 3. ms. martin wants to transform the scores to have a mean of 75 and a standard deviation of 12. what transformations should she apply to each test score? explain.

Answers

Final answer:

To transform the scores to have a mean of 75 and a standard deviation of 12, Ms. Martin needs to subtract the current mean from each test score, divide the result by the current standard deviation, multiply the result by the new standard deviation, and add the new mean to each transformed score.

Explanation:

To transform the scores to have a mean of 75 and a standard deviation of 12, Ms. Martin needs to apply two transformations to each test score:

First, she needs to subtract the current mean of 12 from each test score.Then, she needs to divide the result by the current standard deviation of 3.After applying these transformations to all the scores, she needs to multiply each result by the new standard deviation of 12 and finally add the new mean of 75 to each transformed score.

By following these steps, Ms. Martin will successfully transform the scores to have the desired mean and standard deviation.

Learn more about Transforming scores here:

https://brainly.com/question/33819675

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Evaluate b – 2a – c for a = –7, b = 3, and c = –7

Answers

3-2(-7) -(-7)

3-(-14)-(-7)

3+14+7 = 24

1 Simplify 2\times (-7)2×(−7) to -14−14
3-(-14)-(-7)3−(−14)−(−7)
2 Simplify brackets
3+14+73+14+7
3 Simplify
2424

How does translating a figure using the formal definition of a translation compare to the previous method of translating a figure?

Answers

It is essentially the same process just different notation.

This method is easy to understand and easy to apply to any figure than the other methods.

What is a translation of the figure?

When the figure is moved from one place to another place is called translation of the figure.

When we add in x then the figure will translate toward the left.

And when we subtract in x then the figure will translate toward the right.

If we add in y then the figure will translate downward.

And when we subtract in y then the figure will translate upward.

This method is easy to understand and easy to apply to any figure than the other methods.

More about the translation of the figure link is given below.

https://brainly.com/question/933695

Beth sold half of her comic books and then bought nine more she now has 28 how many did she have to start with

Answers

28 - 9 = 19
19 + 19 = 38
she started with 38 comics

Ernie's favorite movie of the year is now in its fourth week in the theaters. He is gathering data about its earnings each week. He is also interested in knowing how other recently released movies are doing at the box office compared with his favorite movie. The table gives the earnings of the top-five movies during the third week that Ernie’s favorite movie, movie A, was showing in theaters. Movie Earnings Average Ticket Price A $26,088,808.74 $8.35 B $60,394,938.12 $9.72 C $23,659,617.52 $8.12 D $34,311,887.98 $7.57 E $10,505,611.08 $8.46

Answers

Final answer:

To compare the relative success of his favorite movie to others, the student can calculate each movie's ticket sales by dividing its total earnings by the average ticket price. This provides a clearer idea of the viewership each movie had, which can be more informative than simple box office earnings.

Explanation:

The student is interested in the earnings of his favorite movie in relation to other recently released films. To compare these films, one could calculate each movie's ticket sales by dividing its earnings by the average ticket price. For instance, the ticket sales for the movie A would be calculated by dividing its earnings, $26,088,808.74, by its average ticket price, $8.35. This calculation would need to be repeated for each movie to have a clear comparison.

These calculations will help Ernie understand how many people, roughly, saw each movie, since box office earnings alone can be skewed by differing ticket prices. In other words, a movie could have higher earnings than another but still have fewer viewers if its tickets were significantly more expensive.

Learn more about Comparison of Movie Earnings here:

https://brainly.com/question/33342471

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What is
-29=5(2a-1)+2a

Answers

-29= 5 (2a-1) +2a

Start by distributing the terms....

- 29 = 10a - 5 + 2a

Combine like terms...

- 29 = 12a - 5

Add 5 to both sides ....

- 2 4 = 12 a

Divide both sides by 12 to get a by its self...

a = -2

-29 = 5(2a-1) +2a
-29 = 10a-5+2a
-29 = 12a-5
+ 5 +5
-24 =12a
-2 = a

The tank for a car holds
18
18
gallons. The gasoline gauge shows the tank is
1
3

13
full. How much gas is still in the tank? Give your answer as a whole number or as a mixed fraction reduced to lowest terms

Answers

namely, if the tank is 1/3 full, how much is 1/3 of 18? is just their product.

[tex]\bf 18\cdot \cfrac{1}{3}\implies \cfrac{18}{3}\implies \stackrel{gallons}{6}[/tex]

Final answer:

To calculate the amount of gas left in the tank, you should multiply the total capacity of the tank, which is 18 gallons, by the fraction that represents the amount of gas remaining, which is 1/3. Thus, there are 6 gallons of gas still in the tank.

Explanation:

To answer this question, we should multiply the total capacity of the tank, which is 18 gallons, by the fraction that represents the amount of gas remaining, which is 1/3. This will give us the number of gallons of gas left.

Now, apply the multiplication: 18 gallons * 1/3 = 6 gallons.

So, there are 6 gallons of gas still in the tank.

Learn more about multiplication of fractions here:

https://brainly.com/question/9281754

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