1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ahat [919]
3 years ago
9

To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equati

on of the tangent line at the point (4, 2), we know that (4, 2) is a point on the line. So we just need to find its slope. The slope of a tangent line to f(x) at x = a can be found using the formula
Mathematics
1 answer:
murzikaleks [220]3 years ago
8 0

Answer:

x-4y+4=0

f(x)=\sqrt x and x=4

Step-by-step explanation:

We are given that a curve

y=\sqrt x

We have to find the equation of tangent at point (4,2) on the given curve.

Let y=f(x)

Differentiate w.r.t x

f'(x)=\frac{dy}{dx}=\frac{1}{2\sqrt x}

By using the formula \frac{d(\sqrt x)}{dx}=\frac{1}{2\sqrt x}

Substitute x=4

Slope of tangent

m=f'(x)=\frac{1}{2\sqrt 4}=\frac{1}{2\times 2}=\frac{1}{4}

In given question

m=\lim_{x\rightarrow a}\frac{f(x)-f(a)}{x-a}

\frac{1}{4}=\lim_{x\rightarrow 4}\frac{f(x)-f(4)}{x-4}

By comparing we get a=4

Point-slope form

y-y_1=m(x-x_1)

Using the formula

The equation of tangent at point (4,2)

y-2=\frac{1}{4}(x-4)

4y-8=x-4

x-4y-4+8=0

x-4y+4=0

You might be interested in
El precio de un ordenador portátil ha aumentado un 25% y posteriormente fue rebajado un cierto porcentaje.Calcule que porcentaje
ZanzabumX [31]

Answer:

Se requiere un 20 por ciento de descuento.

Step-by-step explanation:

(This exercise has been presented in Spanish and for that reason explanation will be held in the same language)

Sea p_{o} el precio original del computador portatil, el nuevo precio es:

p_{1} =\left(\frac{100\,\% + 25\,\%}{100\,\%} \right)\cdot p_{o}

p_{1} = 1.25\cdot p_{o}

Si p_{2} = p_{o}, entonces el porcentaje requerido para recuperar el precio original es:

r = \left(1-\frac{p_{2}}{p_{1}} \right)\times 100\,\%

r = \left(1-\frac{p_{o}}{1.25\cdot p_{o}} \right)\times 100\,\%

r = \left(1-\frac{1}{1.25} \right)\times 100\,\%

r = 20\,\%

Se requiere un 20 por ciento de descuento.

5 0
2 years ago
What is 5 (3x + 2y) -2 (3x + 2y) ?
Law Incorporation [45]

Answer:

9x+6y is your simplified answer

Step-by-step explanation:

Your welcome

4 0
3 years ago
In a fruit cocktail, for every 20 ml of orange juice you need 45 ml of apple juice and 100 ml of coconut milk. What is the ratio
Anni [7]

the ratio of apple juice to coconut milk to orange juice is:

45:100:20 = 9:20:4

4 0
2 years ago
Berto has $12 to put gas in his car. If gas costs $3.75 per gallon, which ordered pair relating number of gallons of gas, x, to
Nastasia [14]
Berto can purchase 12/3.75 gallons, this is 3.2 gallons of gas. So the coordinate on this line would be (3.2, 12).
Good Luck! :D

6 0
3 years ago
Read 2 more answers
Connie bought 172 tulip bulbs. She wants to plant an equal number of bulbs in each of 4 flower beds. How many bulbs should Conni
Levart [38]

Answer:

43

Step-by-step explanation:

172/4= 43

4 0
3 years ago
Other questions:
  • Find the distance between the points (4,10) and (0,0) the answer must be a whole number
    7·2 answers
  • Which of the following represents the factorization of the trinomial below?<br>x^2-12x+20​
    13·2 answers
  • A and b share a the cost in a ratio of 3:2 the cost is £85, how much does a pay?
    13·2 answers
  • A soil supplement that weighs 19 lb contains iron, potassium, and mulch. The supplement contains sixteen times as much mulch as
    6·1 answer
  • Which values have exactly three significant figures? Check all that apply.
    8·2 answers
  • 5(2к)<br> What expression is equivalent
    11·1 answer
  • Choose the vector has a magnitude of √2 and a direction of θ = 135°.
    10·2 answers
  • Solve for x.<br> 10<br> 2<br> 98
    8·1 answer
  • I need some help on this.
    8·2 answers
  • Please help i will give brainliest
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!