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
What are the solutions of the quadratic equation 4x^2-8x-12=0
Wewaii [24]

Answer:

<h3>          x₁ = -1,   x₂ = 3</h3>

Step-by-step explanation:

4x^2-8x-12=0\\{}\qquad\qquad^{\div4\qquad\div4}\\x^2-2x-3=0\\\\x^2+x-3x-3=0\\\\x(x+1)-3(x+1)=0\\\\(x+1)(x-3)=0\\\\x+1=0\quad\vee\quad x-3=0\\\\x=-1\quad\vee\quad x=3

6 0
3 years ago
The equation h(t)=−16t2+19t+110 gives the height of a rock, in feet, t seconds after it is thrown from a cliff. What is the init
Gwar [14]
Did you ever get this answer?? I really need it

4 0
3 years ago
Read 2 more answers
Which measure is of an angle that is conterminal with a 95 degree angle
timofeeve [1]

Answer: Choice B

95 - 1080n for any integer n

=================================================

Explanation:

Notice how 1080 is a multiple of 360 since 360*3 = 1080. The other values 1450, 780 and 340 are not multiples of 360. For example 1450/360 = 4.02777 approximately. We need a whole number result to show it is a multiple.

Therefore, choice B shows subtracting off a multiple of 360 from the original angle 95. In my opinion, it would be better to write 95+360n or 95-360n to make it more clear we are adding or subtracting multiples of 360.

Choice B will find coterminal angles, but there will be missing gaps. One missing coterminal angle is 95-360 = -265 degrees. So again, 95-360n is a more complete picture. I can see what your teacher is going for though.

8 0
3 years ago
Form the quadratic equation whose one root is 2 + 2^(1/2)​
Oksanka [162]

9514 1404 393

Answer:

  x^2 -4x +2 = 0

Step-by-step explanation:

The other root is the conjugate of the given one, so is 2-√2. The quadratic equation in factored form is then ...

  (x -2-√2)(x -2+√2) = 0

Expanding this, we get ...

  (x -2)^2 -(√2)^2 = 0

  x^2 -4x +4 -2 = 0

  x^2 -4x +2 = 0 . . . . the equation you're looking for

4 0
3 years ago
Really need help ASAP
Kipish [7]
The third and fourth charts represent functions
4 0
3 years ago
Other questions:
  • If f(x)=-3x+4 and g(x)=2 solve for the value of x for which f(x) = g(x) is true
    15·1 answer
  • 7c-2c=45 plz help I'm bad at math
    7·2 answers
  • The canopy of a parachute is a semicircle with a radius of 13 feet. A company that is making parachutes for a Fourth of July cel
    14·2 answers
  • What is the result of subtracting the second equation from the first? \begin{aligned} -7x-y &amp;= 0 \\\\ 7x+8y &amp;= -6 \end{a
    14·1 answer
  • John is cooking 234 pounds of chicken. He is making a dinner for 8 people, including himself. If everyone gets an equal amount,
    13·1 answer
  • The rubbing alcohol in hand sanitizer has a half-life of 5 seconds. If there are 36 ounces initially,
    7·1 answer
  • The diagonal of a rectangular swimming pool measures 29 yards. If the length of the pool is 25 yards, which measurement is close
    13·1 answer
  • Puzzles are packaged in groups of 3. If the store has 183 nature puzzles and 165 animal puzzles, how many packages of puzzles ar
    14·1 answer
  • 4096<br> Write down the name of each of these shapes.
    7·1 answer
  • Jeremy has 6 apples cut into 1/8 pieces. How many pieces does he have?
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!