Mathematics High School

Find the equation of the tangent to the curve
[tex]y = \frac{4}{x} [/tex]
at
[tex](8. \frac{1}{2} )[/tex]
​

Answers

Answer 1

9514 1404 393

Answer:

  y = -x/16 +1

Step-by-step explanation:

The slope is at any point x is ...

  y' = -4/x^2

so, at x=8, the slope is ...

  m = -4/8^2 = -4/64 = -1/16

The point-slope form of the equation of the line is ...

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

Then the line with slope -1/16 through point (8, 1/2) is ...

  y - 1/2 = -1/16(x -8)

  y = -1/16x +1/2 + 1/2 . . . . . eliminate parentheses, add 1/2

  y = -1/16x +1 . . . . . equation of the tangent line

Find The Equation Of The Tangent To The Curve [tex]y = \frac{4}{x} [/tex]at [tex](8. \frac{1}{2} )[/tex]

Related Questions

Consider the following pair of equations: y = x + 4 y = −5x − 2 Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.

Answers

Answer:

(-1, 3)

Step-by-step explanation:

to solve using substitution, you have to know the value of either x or y. in this example, they gave you the value of y already: y=x+4.

this means you can substitute the y for (x+4). if we substitute y for (x+4) in the equation y=-5x-2, we get this:

(x+4)=-5x-2

then solve for x

6x=-6

so x=-1

since we know the x value, we can solve for y

y=x+4

y=-1+4

y=3

so the final answer is (-1, 3)

Answer:

(- 1, 3 )

Step-by-step explanation:

Given the 2 equations

y = x + 4 → (1)

y = - 5x - 2 → (2)

Substitute y = x + 4 into (2)

x + 4 = - 5x - 2 ( add 5x to both sides )

6x + 4 = - 2 ( subtract 4 from both sides )

6x = - 6 ( divide both sides by 6 )

x = - 1

Substitute x = - 1 into either of the 2 equations and evaluate for y

Substituting into (1)

y = - 1 + 4 = 3

solution is (- 1, 3 )

Which is the equation of the line through the point (−3, 8) that is perpendicular to the line y=14x+12?

Answers

Answer:

y = -1/14x + 109/14

Step-by-step explanation:

If two lines are perpendicular to each other, they have opposite slopes.

The first line is y = 14x + 12. Its slope is 14. A line perpendicular to this one will have a slope of -1/14.

Plug this value (-1/14) into your standard point-slope equation of y = mx + b.

y = -1/14x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (-3, 8). Plug in the x and y values into the x and y of the standard equation.

8 = -1/14(-3) + b

To find b, multiply the slope and the input of x (-3)

8 = 3/14 + b

Now, subtract 3/14 from both sides to isolate b.

8 - 3/14 = b

112/14 - 3/14 = b

109/14 = b

Plug this into your standard equation.

y = -1/14x + 109/14

This equation is parallel/perpendicular to your given equation (y = 14x + 12) and contains point (-3, 8)

Hope this helps!

HELP PLEASE WILL GIVE A BRAINLIST!!!!!

Answers

Answer:

C. opposite sides are parelell

Answer:

It's C bestie! opposite sides are parallel!

The rational number
number ———————
is equal to its negative​

Answers

Zero is equal to its negative

A square box is being cut apart and has the measurements shown below. What is the surface are each square is 3.5 inches and there 6 squares

Answers

Answer:

73.5 in^2

Step-by-step explanation:

Given data

Dimension of square= 3.5 inches

Area= 3.5^2

Area= 12.25 in^2

Number of square= 6

Hence the total area is

=12.25*6

=73.5 in^2

HELP ASAP!!! HELP FAST PLEASE!!

Answers

Answer:

9

Step-by-step explanation:

(08.03 MC) The dot plot below shows the hourly rate of some babysitters in a city: Which statement best describes the shape of the data? (1 point) Question 7 options: 1) It is symmetric and has no gaps. 2) It is not symmetric and has a peak at $5.00. 3) It is a cluster from $1.00 to $5.00 and has gaps. 4) It is a cluster from $1.00 to $5.00 and has a peak at $5.00.

Answers

Answer:

A. It is symmetric and has no gaps.

Step-by-step explanation:

Given

See attachment for dot plot

Required

Select the true statement

From the attached plot, we can see that

The plot is bell shaped (by tracing the number of dots on each dataset) There is no gap between each dataset (from 4 to 7)

Since (1) all bell shaped distribution are symmetric and (2) there is no gap between the dataset, then (a) is correct.

Someone!!!!
I will mark the person who answers with an actual answer brainliest
Please help!!!
Due soon

Answers

Answer: Just use a calculator.

Step-by-step explanation:

The answer is 8 minutes

Find the product of the sum and difference. (Please try to answer all of them If not it's OK!)

Answers

Answer:

[tex]16 {x}^{2} - 9[/tex]

Step-by-step explanation:

Use the F.O.I.L. method

Answer:

1) [tex]81c^{2}[/tex]-1

2) [tex]16x^{2}[/tex]-9

3) [tex]-4y^{2}[/tex]+25

4) [tex]-w^{2}[/tex]+16

Step-by-step explanation:

On a map, 14inch represents 400 miles. How long would a line on a map need to be in order to represent 3200 miles

Answers

112 inchesor9 feet and 4 inchesor3 yards and 4 inches3200 ÷ 400 = 814 x 8 = 112

1-A) 2
B) 3
C) 5

2-A) up
B) left
C) down
D) right

3)A) f(x)-5
B) f(x+5)
C)f(x)+3
D)f(x)+2
E)f(x-2)
F)f(x-3)

Answers

Translated down 6, g(x)= 3x-5

What is the perimeter of a triangle


3
5
6

Answers

Answer:

all above

Step-by-step explanation:

perimeter can any number

Marking brainliest...

Answers

Answer:

i can't really see your information

Step-by-step explanation:

NO LINKS OR FILE PLZ

a line passes the points with coordinates (0,11) and (3,-1). What best would describe the slope of the line. 1/4.-1/4. 4.-4

Answers

Answer:

slope -4

Step-by-step explanation:

m=y2-y1/x2-x1

m=-1-11/3-0

m=-12/3

m=-4

NEED HELP! The wind-speed, in miles per hour (mph), was measured every six hours during a day on the Isles od Scilly.

Answers

Answer:

That’s not a lot of info...

Step-by-step explanation:

If (x,83) is a solution to the equation 2y=1/2(98x+38), find x.

Answers

Answer:

X= 2y/49 - 19/49

Answer:

because (x; 83) is a solution to the equation

2y=1/2(98x+38)

=> 2.83 = 1/2(98x + 38)

<=> 4.83 = 98x + 38

<=> 332 = 98x + 38

<=> 98x = 294

<=> x = 3

HELP! WILL GIVE BRAINLIEST!

Which statement describes the behavior of the graph of the function shown at the vertical asymptotes?
f(x)= -2x^2+14/x^2-49

Answers

Answer:

I Know it is B trust me

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Please find the area and perimeter

Answers

Answer:

        Area:   54 in²        Perimeter:  36 in

Step-by-step explanation:

Area:

A = 6 in · 10 in - 2 in · 3 in = 60 in² - 6 in² = 54 in²

Perimeter:

P = 2·6 in + 10 in + 6 in + 3 in + 1 in + 2·2 in = 12 in + 20 in + 4 in = 36 in

please answer this question the other one was just kinda a notice manhnifa if you an join!

Answers

Answer:

Option B

Step-by-step explanation:

[tex](1/\sqrt{y} )^{-1/5} = \\(y^{-1/2})^{-1/5} = \\y^{(-1/5)(-1/2)} =\\y^{1/10} = \\\sqrt[10]{y}[/tex]

Correct choice is B

Evaluate the expression below when n = 2.4. If needed, answer as a fraction or a decimal.
12n−8

Answers

Answer:

20.8

Step-by-step explanation:

Plug in 2.4 as n in the expression, and simplify:

12n - 8

12(2.4) - 8

28.8 - 8

= 20.8

So, the answer is 20.8

ILL BRAINLIEST YOU AND GIVE YOU 10 EXTRA IF YOU GET IT RIGHT

Answers

Answer:

A(0,2)

B(2,0)

c(0,-2)

D(-2,0)here is your answer

Find the value of each trigonometric ratio.

Answers

Answer:

SinZ=perpendicular/hypotenuse=15/17 is your answer

find the measure of the arc or angle indicated. assume that lines which appear to be diameters are actual diameters just enter the number no degree sign or word

Answers

Answer:

I think D

if wrong correct me plssssssss

have a nice day

And good luck if you have exam

#Captainpower

Which of the following is equivalent to log 9 27?

1.) 3/2

2.) 2/3

3.) 3

4.) 1.452

Answers

Answer:

here is the answer as I believe it is correct

1.) 3/2

OD) A tree is 30 feet tall and casts a shadow that is 25 feet long. At the same time, a man
casts a shadow that is 5 foot long. How tall is the man?
answer choices

Answers

Answer:

6ft

Step-by-step explanation:

What is the surface area of the cube?

Answers

Answer:

150 is the answer

Step-by-step explanation:

5 x 5 = 25

25 x 6 = 150.

Answer: I think the surface area is 150

Step-by-step explanation: sorry if I’m wrong

write each equation in slope intercept form 9x + 35 = -5y. 2y - 6 = -6x. -11 - 7y = -56​

Answers

Answer:

y= -9/5x -7

y= -3x +2

y= 45/7

In 2002, the membership of a club totaled 5 thousand. By 2005, there were 29 thousand members of this club.
a. Write two ordered pairs of the form (x,y), where x is years after 2002 and y is membership in thousands.
b. Assume that the membership is linear between the years 2002 and 2005. Use the ordered pairs from part (a) to write an equation in slope-intercept form of the line
relating year and membership.
c. Use the linear equation from part (b) to predict membership in 2014.

Answers

Answer:

a)

(0, 5)

(3, 29)

b)  y = 8x + 5

c)  101 thousand

Step-by-step explanation:

slope m = (29-5)/(3-0) = 24/3 = 8

y-intercept = (0, b) = (0, 5)

y = mx + b

y = 8x + 5

2014 - 2002 = 12

y = 8(12) +5

y = 96 + 5 = 101

A parabola opening up or down has vertex (0,0) and passes through (12, -18). Write its
equation in vertex form.

Answers

The equation is y= -1/8x^2

I need help, correct answer will get brainliest!

Answers

Answer:

9

Step-by-step explanation:

1/16 square rooted = .25 * 4 = 1 then 10-1=9

Other Questions
Which of these sentences is a run-on sentence? * 10 points Our English teacher gives us a lot of tests, and they're usually difficult. There's a test today, I hope you studied for it. The test is on punctuation, and it's supposed to be difficult. I studied a lot last night, so I think I'll do well. Complete each sentence with the correct preterite or imperfect verb form.____________________ (Llamarse) Barrign porque ____________________ (gustarle) mucho comer. When eleven is added to the product of a number, x and three, the resultis equal to the number that is nine less than five times the same number, x.What is the value of xHelp if you can How did the Black Death spread across Europe and what were its short and long-term effects? 2Which statements about humus are true? Choose more than oneanswerIt forms from dead plantsIt collects in bedrockIt fertilizes soilIt contains carbonIt is only found in topsoilIt erodes the rocks in soil Phase portraits (or phase diagrams) provide a powerful tool to visualize the dynamics of ODE systems.a. Trueb. False When rutherford bombarded thin gold foil with a-particles,he found that some a-particles were deflected through large angles. Which statement explains this deflection? What was the result of the Great Depression, and how did the United States recover? How did we prevent it from happening again? Help pleaseee pretty please I will mark you brainliest. NO LINKS OR I WILL REPORT YOU. PLEASE GIVE EXPLANATION.pretttty pleaseee this TIMED In 1776 and 1777, Cornwallis went after the colonial army of General George Washington. How did Indians perceive the decision by Great Britain to allow Christian missionaries to settle in India?A: The Indians saw it as a way to make their own country as wealthy as Britain.B: The Indians saw it as Britain's willingness to corrupt India's young people.C: The Indians saw it as a secretive plan to reduce the size of their population.D: The Indians saw it as Britain's attempt to destroy their culture. name 3 negative impact in the exploitation of minerals In an Antarctic pelagic community, the primary producers are phytoplankton, which serve as food for the dominant grazing zooplankton, especially krill and copepods, both of which are crustaceans.These zooplankton species are in turn eaten by various carnivores, including other plankton, penguins, seals, fish, and baleen whales. Squids, which are carnivores that feed on fish and zooplankton, are another important link in these food webs, as they are in turn eaten by seals and toothed whales (Figure 1). Figure 1: Arrows follow the transfer of food from the producers (phytoplankton) up through the trophic levels. For simplicity, this diagram omits decomposers.Antarctic krill (Euphausia superba) is an important source of food for whales, seals, squid, fish, and many species of birds. Its abundant biomass is one of the largest on Earth. Figure 2 compares the effects of krill harvesting on species richness within two small sections of the Antarctic region; one section was subject to krill harvesting and the other section was not.Describe how the autotrophs facilitates the flow of energy through the Antarctic ecosystem. In the Antarctic pelagic community, there are three types of seals. The leopard seals eat birds, but the crabeater and elephant seals do not. Explain how the interactions between seals and other species may affect their food sources.Identify the independent variable of the data graphed in Figure 2. Explain one way this variable is affecting the biodiversity of the Antarctic food web.Analyze the change in species richness with or without krill harvesting. Predict how the removal of krill from the Antarctic ecosystem will affect its long-term structure.Justify the claim that the Antarctic krill is a foundation species, not a keystone species. Provide evidence to support your claim. the question is in the picture attached. please help!!! Find the slope of the line that goes through the points (-3, 1) and (-17, 2). 1A: Consider these compounds:A. PbF2B. Ni(CN)2C. FeSD. CaSO4Complete the following statements by entering the letter(s) corresponding to the correct compound(s). (If more than one compound fits the description, include all the relevant compounds by writing your answer as a string of characters without punctuation, e.g, ABC.)Without doing any calculations it is possible to determine that magnesium hydroxide is more soluble than __________, and magnesium hydroxide is less soluble than _______.It is not possible to determine whether magnesium hydroxide is more or less soluble than_______ by simply comparing Ksp values.1B: For each of the salts on the left, match the salts on the right that can be compared directly, using Ksp values, to estimate solubilities.(If more than one salt on the right can be directly compared, include all the relevant salts by writing your answer as a string of characters without punctuation, e.g, ABC.)1. nickel(II) hydroxide A. Fe(OH)22. silver chloride B. PbSC. AlPO4D. MnSWrite the expression for K in terms of the solubility, s, for each salt, when dissolved in water.nickel(II) hydroxidesilver chlorideKsp=_______Ksp=________Note: Multiply out any number and put it first in the Ksp expression. Combine all exponents for s. If the audience for your research report is a group of second graders, how would you need to write your report?using only picturesusing shorter sentences and simpler wordsusing scientific languageusing lots of specialized vocabulary help ill give brainiest Reggie lost 2 spaceships in level 3 of a video game. He lost 30 points for each spaceship. When he completed level 3, he earned a bonus of 350 points. By how much did his score change? how many nickels are in a quarter