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
viktelen [127]
3 years ago
5

Find the equation of the tangent line and normal line to the curve y=(6+4x)2 at the point (6,900). Write the equations of the li

nes in the form y=mx+b. Tangent line: y= equation editor Equation Editor Normal line: y=
Mathematics
1 answer:
Ksenya-84 [330]3 years ago
8 0

Answer:

Equation of the tangent to the curve

y = 240x - 215994

Equation of the normal

y = (-1/240)x + 9.75 = - 0.00417x + 9.75

Step-by-step explanation:

y = (6 + 4x)² = 36 + 48x + 16x² = 16x² + 48x + 36

dy/dx = 32x + 48

At the point (6,900),

dy/dx = 32(6) + 48 = 240

Equation of the tangent at point (a,b) is

(y - b) = m(x - a)

a = 6, b = 900, m = 240

y - 6 = 240(x - 900)

In the y = mx + b form,

y - 6 = 240x - 216000

y = 240x - 215994

The slope of the normal line = -(1/slope of the tangent line) (since they're both perpenducular to each other)

Slope of the normal line = -1/240

Equation of normal

y - 6 = (-1/240)(x - 900)

y - 6 = (-x/240) + 3.75

y = (-1/240)x + 9.75

y = - 0.00417x + 9.75

You might be interested in
What is the y-intercept of the line?
Amanda [17]

Answer:

The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis.

Step-by-step explanation:

<em> got this answer from (www.Math.com) </em>

<em></em>

<em>Glad I helped! =)</em>

5 0
3 years ago
Select all the statements that are true about standard deviation.
frozen [14]

Answer:

A,B, C

Step-by-step explanation:

hope it helps

7 0
3 years ago
Theresa wants to order her mother flowers for her birthday. She wants to give the delivery person a $6.00 tip. The cost of the f
Illusion [34]

Answer:

8\%

Step-by-step explanation:

Since question already gives the number of dollars she will tip, I'm assuming it's asking for percent tipped.

Because the total is $75 and Theresa is tipping $6, she is tipping \frac{6}{75}=0.08 of the total. To convert this to a percentage, multiply by 100: 0.08\implies 0.08\cdot 100=\boxed{8\%}

7 0
3 years ago
Read 2 more answers
Use the x-intercept method to find all real solutions of the equation.<br> x^3-8x^2+9x+18=0
meriva

Answer:

a. x=-1,3,\:or\:6

Step-by-step explanation:

The given equation is;

x^3-8x^2+9x+18=0

To solve by the x-intercept method we need to graph the corresponding function using a graphing calculator or software.

The corresponding function is

f(x)=x^3-8x^2+9x+18

The solution to x^3-8x^2+9x+18=0 is where the graph touches the x-axis.

We can see from the graph  that; the x-intercepts are;

(-1,0),(3,0) and (6,0).

Therefore the real solutions are:

x=-1,3,\:or\:6

8 0
3 years ago
Read 2 more answers
10th grade geometry <br> Select statements that are true about angles on diagram
Goshia [24]

Answer:

  B, C

Step-by-step explanation:

The only statements that must be true are ones that describe the markings on the diagram:

 NO as an angle bisector

  N is the vertex of a pair of congruent angles

_____

The only other fact that must be true is that segments on the left side of the diagram are proportional to those (corresponding) on the right. (This is a property of the angle bisector.) There is nothing that says the sides must be equal, or that the triangle is isosceles.

3 0
2 years ago
Other questions:
  • Find the product of (a²+b)(2a²-5b)
    14·1 answer
  • 329 ten thousandths<br> is how much greater than 32 thousandths
    5·1 answer
  • what are the angle measures of the triangle? a)30, 60, and 90 b)45, 45, and 90 c)60,60,and 60 d)they cannot be determined.
    7·1 answer
  • A rectangle has length of 5.25 cm and area of 44.625 cm2. What does the length of the rectangle have to be?
    10·1 answer
  • Factor this expression. ab + 2a + 3b + 6.
    13·1 answer
  • Lisa descended 120 feet into a cave. She then climbed up 56 feet. If her starting point was 38 feet below sea level at the mouth
    7·1 answer
  • Don't guess!
    7·1 answer
  • two lines in a system of equations with one solution have slopes that must be the same or different ? ​
    9·1 answer
  • Divide $200 in the ration2:3.what is the results​
    13·1 answer
  • Which property justifies this statement?
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!