21.
Ify= 1+x, find
x
dy.
/
dx

21.Ify= 1+x, Findxdy./dx

Answers

Answer 1

Answer:

  A.  2/(1 -x)²

Step-by-step explanation:

The derivative of a ratio is given by the formula ...

  d(u/v) = (v·du =u·dv)/v²

Here, we have ...

  u = 1+x; du = 1·dx

  v = 1 -x; dv = -1·dx

Then ...

  [tex]dy=\dfrac{(1-x)(dx)-(1 +x)(-dx)}{(1-x)^2}\\\\\dfrac{dy}{dx}=\dfrac{1-x +1+x}{(1-x)^2}=\boxed{\dfrac{2}{(1-x)^2}}[/tex]

__

Additional comment

The formula used above is a combination of the power rule and the product rule.

d(u^-1) = -du·u^-2 = -du/u² . . . . power ruled(uv) = u·dv +v·du . . . . . . . . product rule

Related Questions

PLEASE HELP!!!! Which quadratic equation is part of the solution process for solving this rational equation using the least common denominator?

Answers

Answer: for plato users

A is the correct answer

Step-by-step explanation:

I just took the test had 100%

The correct option is A. [tex]x^{2} -x-10=0[/tex].

Given quadratic equation  [tex]\frac{2}{3x-6} -\frac{1}{3x+6} =\frac{1}{3}[/tex]

On solving,  [tex]\frac{2(3x+6)-1(3x-6)}{(3x-6)(3x+6)} =\frac{1}{3}[/tex]

Further, [tex]\frac{6x+12-3x+6}{9x^{2} -6^{2} } =\frac{1}{3}[/tex]

[tex]\frac{3x+18}{9x^{2} -36} =\frac{1}{3}[/tex]

Taking 3 common from numerator and 9 common from denominator, we have

[tex]\frac{3(x+6)}{9(x^{2} -4)} =\frac{1}{3}[/tex]

[tex]\frac{(x+6)}{3(x^{2} -4)} =\frac{1}{3}[/tex]

[tex]\frac{x+6}{x^{2} -4} =1[/tex]

[tex]x+6=x^{2} -4[/tex]

On rearranging in decreasing powers of x we get,[tex]x^{2} -x-10=0[/tex].

Hence on solving, We get [tex]x^{2} -x-10=0.[/tex]

For more details on Quadratic equation follow the link:

https://brainly.com/question/17177510

g (x) = x2 + 12x-
35

Answers

Answer:

not factorable

Step-by-step explanation:

g(x) = x²+12x-35

Not factorable

i have 120g butter and 150g sugar.

1) what’s the ratio of butter to sugar?

2) what’s the ratio in the form 1:n ?

Answers

Answer:

1) 4 : 5

2) 1 : 5/4

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

The Red Shell's flight path is modeled by the equation:
y = -2x2 + 60x + 350
a) Factor the equation below:
olutions to the equation?

Answers

Answer:

Geometric figure: Straight Line

Slope = 120.000/2.000 = 60.000

x-intercept = 346/-60 = 173/-30 = -5.76667

y-intercept = 346/1 = 346.00000

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

y-(-4+60*x+350)=0

STEP

1

:

Equation of a Straight Line

1.1 Solve y-60x-346 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y-60x-346 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 346/1 so this line "cuts" the y axis at y=346.00000

y-intercept = 346/1 = 346.00000

Calculate the X-Intercept :

When y = 0 the value of x is 173/-30 Our line therefore "cuts" the x axis at x=-5.76667

x-intercept = 346/-60 = 173/-30 = -5.76667

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 346.000 and for x=2.000, the value of y is 466.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 466.000 - 346.000 = 120.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 120.000/2.000 = 60.000

Geometric figure: Straight Line

Slope = 120.000/2.000 = 60.000

x-intercept = 346/-60 = 173/-30 = -5.76667

y-intercept = 346/1 = 346.00000

A triangle has an area of 35 cm squared. The BASE of the triangle is (x-5) cm and the HEIGHT of the triangle is (x-14) cm. Find the measure of the HEIGHT and BASE.

Answers

Try to use this method and see if you get the answer

Step-by-step explanation:

area = b * h / 2 , where b is a base, h - height.

so h = 2 * area / b.

The area in square feet of a rectangular field is
x2 – 120x + 3500. The width, in feet, is x-50. What is the
length, in feet?

Answers

Answer:

Length in feet:  x-70

Step-by-step explanation:

Use factorization to find the length

Area = X^2-120x+3500

Area= length x width.

Area= L x (x-50)= (x-___) (x-50)

To find L we know that in factoring the quadratic equation 50 x __ must be equal to 3500.

(x-70)(x-50) = x^2-120x+3500.

Diane walked 4/10 mile x 5 days this week. How far did Diane walk?

Answers

answer: 2

(4/10) * 5 = 2

she walk 2 miles per day

in which quadrant is the point (4,-2 located

Answers

Answer:

quadrant 4

Step-by-step explanation:

Hope this helped :)

also can you pls rate thanks

Answer:

The point is located in the fourth quadrant.

Step-by-step explanation:

I'm pretty sure it that. Hope its right!

please help me ..............

Answers

Answer: A, C, E

Step-by-step explanation:

An undefined slope means the line is vertical (and thus the x-coordinates are constant).

Figure ABCD is a parallelogram.What is the value of n?3 5 17 25

Answers

Answer:

17

Step-by-step explanation:

∠B = ∠D

2n + 32 = 4n - 2

32 + 2 = 4n - 2n

2n = 34

n = 17

x2-30x+81

Answer (x-27)(x-3)

Answers

The answer is (x-27)(x-3) in factored form. The answer using the quadratic formula is x= 27,3

Solve the following equation.
25z^2+93 = 100z

Answers

Step-by-step explanation:

25z square+93=100z

=25z square+93=10z square

=25z square-10z square=-93

=15z square= -93

a cylinder has an approimate 1357.1 cubic yards. the raduis of the cylinder is 6 yards. what is the height of the cylinder

Answers

Answer:

Step-by-step explanation:

Find the radius and height. ...

Convert inches to yards, convert feet to yards, or convert meters to yards.

Multiply the radius of the cylinder times the radius, e.g. r2

Multiply times π to get the area of the circle.

Multiply times the height of the cylinder to get the volume.

SOMEONE PLEASE HELP ME WITH THIS ILL GIVE YOU BRAINLY IF YOU GET IT RIGHT AND EXPLAIN PLEASE

Answers

Answer:

48 degrees

Step-by-step explanation:

the angle measure doesn't scale of shrink with the dilation of circles. the angle only just extends.

The value of each expression if x=12
3x

Answers

Answer:

3*12=36

hope thats the answer

rearrange so u Rearrange the equation so www is the independent variable.
−2u+6w=9

Answers

6w = 9 + 2u
w = 9 + 2u / 6

Answer:

w=9+2u/6

Step-by-step explanation:

-2u+6w=9

+2u on both sides

6w=9+2u

/6 on both sides

w=9+2u/6

The smaller of the two containers has a capacity of 150 gallons. When it is $\frac{4}{5}$ full, its contents are emptied into a larger container, filling exactly $\frac{2}{3}$ of it. What is the capacity, in gallons of the larger container?

Answers

Answer:

180 gallons

Step-by-step explanation:

The smaller container has 150 gallons.

Now the large container is filled with the 4/5 of the smaller container.

So if the full volume of the small container is 150 gallons so the 4/5 of it can be calculated as, 4/5*150=120 gallons.

Answer:

hoi

Step-by-step explanation:

PLEASE HELP! WILL GIVE BRAINLIEST

Answers

Answer:

b

Step-by-step explanation:

if you put

[tex] \times = 0 \\[/tex]

and check the values

function b gives highest value

Is this scientific notation
42,060=4.206 x 10 to the 4th

Answers

Answer:

yes it is scientific notation

help i give brianlyist and 5 star rating whith heart

Answers

Answer:

26

Step-by-step explanation:

perimeter is sum of all sides

11+7+4+4=perimeter

26

Volume: The base of a pyramid is a rectangle with a length of 3 centimeters and a width of 6 centimeters. If the height of the pyramid is 12 centimeters, what is the volume of the pyramid?​

Answers

Answer:

72 cm³

Step-by-step explanation:

Volume of a pyramid = Area of base * height / 3

= 3 * 6 * 12/3 = 72 cm³

Please help. I’ll mark you as brainliest if correct!

Answers

Answer:

y=1/3x +16/3

Step-by-step explanation:

m=(y2-y1) / (x2-x1)

   =(6-5) (2- -1)

    =1/3

Substitute in m and either point into the point slope form

y=m(x-x1) + y

y=1/3(x- -1) +5

y=1/3(x+1) +5

Now lets distribute the 1/3 to and combine the constants to put the answer in standard form

y=1/3x + 1/3 + 5

y=1/3x +1/3 + 15/3

y=1/3x +16/3

is 3 8/33 equivalent to the decimal 3.24 (repeating)

Answers

Answer:

Yes it is

Step-by-step explanation:

8 ÷ 33 = .242424( infinite )

Add the beginning 3 to it and you get 3.24 (repeating)

Hope this helps.

yes it is equivalent

MATHEMATICAL CONNECTIONS The volume of a cylinder is given by V=pi r^2h, where r is the radius of the base of the cylinder and h is the height of the cylinder. Find the dimensions of the cylinder. the radius is h-3 and the volume is 25h*pi

Answers

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=h-3\\ V=25h\pi \end{cases}\implies 25h\pi =\pi (h-3)^2 h \\\\\\ \cfrac{25h\pi }{\pi h }=(h-3)(h-3)h\implies 25=\stackrel{F~O~I~L}{h^2-6h+9}\implies 0=h^2-6h-16 \\\\\\ 0=(h-8)(h+2)\implies \blacktriangleright h= \begin{cases} 8~~\checkmark\\ -2 \end{cases} \blacktriangleleft ~\hfill \blacktriangleright \underset{radius}{\stackrel{8~~ - ~~3}{5}} \blacktriangleleft[/tex]

notice, we didn't use h = -2, because the height cannot be a negative value.

Four years ago, you invested $1000 in an account that returns 5.1% annually. The table shows the value of your investment
at the end of each year.
Time (in years)
1
2
Value (in dollars)
$1051.00
$1104.60
$1160.94
$1220.14
3
4
Does the data represent a linear function? Why or why not?
a. Yes, it appears on a straight line.
C. Yes, the average rate of change is constant.
b. No, it does not appear on a straight line.
d. There is not enough information to determine
whether this is a linear function,
Please coloct the boot

Answers

Answer:

It B

Step-by-step explanation:

The data provided in the table does not represent a linear pattern option (b) No, it does not appear on a straight line correct.

What is the rate of change?

It is defined as the change in values of a dependent variable with respect to the independent variables.

It is given that:

Four years ago, you invested $1000 in an account that returns 5.1% annually.

The table represents the value of your investment at the end of each year.

Time (in years)            Value (in dollars)

          1                                    $1051.00

          2                                    $1104.60

          3                                    $1160.94

          4                                    $1220.14

Plot the point (x, y) on the coordinate plane:

From the graph, as we can see (1,  $1051.00) does not lie on the line.

Thus, the data provided in the table does not represent a linear pattern option (b) No, it does not appear on a straight line correct.

Learn more about the rate of change here:

brainly.com/question/12786410

#SPJ2


[tex] \tan(x) [/tex]
integrate ... ​

Answers

combine (one thing) with another so that they become a whole.
"transportation planning should be integrated with energy policy"

Write and equivalent expression for 88 + 16x + 8.
X = 4

Answers

Answer:

88+64+8

Step-by-step explanation:

16*4 =64 and you can just replace that with the x.

Please help me with this coordinate geometry homework !!!!

Answers

Answer:

Step-by-step explanation:

a. Gradient of A = 7/-7 = -1.

b. For line B, m = 3/1.5 = 2 and c = y-intercept = 3.

c. The line parallel to B will have the same gradient m = 2.

It also passes through (1, -1) so we use the point-slope form of the straight line

y - y1 = m(x - x1)

Here m = 2 and (x1, y1) = (1, -1) so

y - (-1) = 2(x - 1)

y = 2x - 2 - 1

y = 2x -3.

Sid Upp is four years younger than his brother Tip. Let x stand for Tip's age . Write an equation stating that Sid's age is 32.

Answers

Answer:

x+4=36

Step-by-step explanation:

you would subtract 4 on each side

x+4=36

  -4   -4

x=32

please help, i did 90 - 10 and I got 80. I’m stuck at 80

Answers

Answer:

approx 216

Step-by-step explanation:

well we go to the 10mm mark and we add the columns taht appear before that. Those are two columns : the brown/orangey one and the green one.

if the scale goes up in twenty and each jump has four squares then we can say that one square is equal to 5 up

so we now can read the first two columns

the first one reads 135

the second one reads approximately 81

we add those up and that becomes 216

so the answer is approximately 216

Other Questions
In Lord Byrons Childe Harolds Pilgrimage, the speaker describes the subjects soul as hindered, or A. eloquent. B. impeded. C. meandering. D. sportive. Help ASAP im in 6th so this could be easy for sum of you to answer! okay so click on this question to see the rest please help me! Billy's soccer team won 17 out of the 20 games played. Sam's soccer team lost 3 games of their 12-game season. Which statment is NOT true about the wins and losses for both Billy's and Sam's soccer teams?Group of answer choices: A, Billy's soccer team won 17 games which represents 85% of their games.B, Sam's soccer team won 9 games which represents 3/4 pf their games.C, Both of their teams lost 3 games, so their losing percentage would be the same.D,Sam's soccer team lost 3 games which represents 25% of their games. Consider a situation where a manufacturer from country A and a distributor based in country B are considering a relationship. To serve this market, the firm from A must invest in new equipment, which can be used only for the B market. The two firms transact infrequently, and there is significant uncertainty about the nature of the market demand. Trust between the two firms is low, and country B's legal system to be unsympathetic to foreign firms. How should the manufacturer choose to organize its transactions Cameron wants to buy a new bike that costs $112. He is saving $8 per week. How many weeks will it be until Cameron has all the money he needs to buy thebike plss help me I need it now How did art change in the mid 19th century? a. it did not have to be as realistic. b. there was a new belief that art should record the life of everyday people. c. there was a greater focus on art portraying royalty. d. there was a shift toward black and white paintings. please select the best answer from the choices provided a b c d What were the effects of Spanish exploration and colonization? Find the measure of angle x in the figure.Note: Angles not drawn to scale.Angle x measures= Imagine what your ideal school would be like, describe it in Spanish, and draw it on a big poster. Which act required colonists to pay for the soldiers that had been sent to maintain orderA) Quartering ActB) Quebec ActC) Boston Port ActD) Stamp Act Based on the perspectives of the sociologist, Can you cite two examples of Theoretical perspectives in the society? A fossil of an ancient palm tree found in Alaska is an indication that Alaska once hadwhat kind of climate in its history?Cold winters and hot summerswarm and humid throughout the yeardry and hot throughout the yearCold winters and mild summers 1 (1 point)What is another term used to identify phospholipid bilayer?Cell envelopeCell membraneAll choices represent the phospholipid bilayer.Selectively permeable membrane Help me asp 25 points and will mark A company rented a computer for $800 a month. Five years later the treasurer calculated that if the company had purchased the computer and paid a $100 monthly maintenance charge, the company would have saved $1000. What was the purchase price of the computer? Passage A: Mountain gorillas are large mammals that weigh up to 440 pounds and when standing, reach heights ranging from four to six feet. As their name states, these animals live in forests high in the mountains in the Democratic Republic of Congo, Rwanda, and Uganda. To survive the harsh, cold temperatures of the mountain range, these gorillas have thick, dense fur to help them stay warm. However, as the human population continues to grow, humans are moving into the mountainous and forested areas. This means the gorillas keep moving further up the mountain, where weather and land conditions make it difficult to survive. As a result of human activity, the mountain gorilla is classified as critically endangered. At one point, scientists thought the species might be completely extinct by the 20th century. However, with the implementation of conservation efforts, there are now 880 mountain gorillas. Although they are still critically endangered, there is hope for this species. Passage B: In the thick mountain forests of Central and West Africa, the large and powerful mountain gorilla can be found. In the wild, mountain gorillas travel in families called troops. A troop can consist of up to 30 gorillas, including males, females, and their infants. Within the troop, the gorillas are very playful, gentle, affectionate, and protective. The uniqueness of these animals is one reason why they are classified as a critically endangered species. In the early 20th century, many people flew to Africa to hunt and collect mountain gorillas. Hundreds of mountain gorillas were taken as trophies or for personal collections. Many people who collected gorillas as trophy items wanted baby gorillas. The entire troop of gorillas would protect the baby to the point that they were all wiped out. Additionally, many people hunted gorillas for their meat. As their population became shockingly low, conservation efforts began. With conservationists' hard work and determination, populations are beginning to rise. These efforts ensure the mountain gorillas are happy and protected from harm. Select a detail in Passage B that helps explain why Passage A states that mountain gorillas are endangered because of human activities. O Atroop can consist of up to 30 gorillas, including males, females, and their intants. O In the early 20th century, many people flew to Africa to hunt and collect mountain gorillas. O The uniqueness of these animals is one reason why they are classified as a critically endangered species.O Within the troop,the gorillas are very playful ,gentle ,affectionate, and protective Help!!!!!!! Plsss!! Plsss! A boat sails 6km from a point x on a bearing of 065 and thereafter 13km on a bearing of 136, what is the distance and of the boat from x? Imagery words in caged birds by maya anglou 1. What arguments do Feingold and Heuvel offer in defense of Roosevelt? 2. What does Michael Beschloss mean when he describes Roosevelts response to the Holocaust as a "strange lapse?" 3. Why does David Wyman call it "the worst failure of his presidency"?