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
Elina [12.6K]
2 years ago
14

A tangent line and its normal line have a point of tangency to the function f(x) at (x,y). If the slop of the normal line is m=(

8/7), what are the coordinates of the point of tangency?
Please help, step by step explanation would be great

Mathematics
1 answer:
alekssr [168]2 years ago
5 0

Answer:

\displaystyle \\\left(\frac{49}{900},\frac{3761}{900}\right) or approximately (0.544, 4.179)

Step-by-step explanation:

A function and its tangent lines intersect when their slopes are the same. Find the x-coordinate when the slope of f(x) is equal to 8/7 by taking the derivative of f(x):

\displaystyle\\f(x)=\sqrt{x}-x+4\\f'(x)=\frac{1}{2}\cdot\frac{1}{\sqrt{x}}-1=\frac{1}{2\sqrt{x}}-1

Set f'(x) equal to 8/7 and solve for x:

\displaystyle \\\frac{1}{2\sqrt{x}}-1=\frac{8}{7},\\x=\frac{49}{900}

Therefore, f(x) will intersect at a point of tangency with a line of slope 8/7 at x=49/900. Plug in x=49/900 into f(x) to get the y-coordinate:

\displaystyle\\y=\sqrt{x}-x+4 \vert_{x=49/900}=\frac{3761}{900}

⇒Answer: (49/900, 3761/900) or approximately (0.544, 4.179)

You might be interested in
What is p ÷ 6 = 9 ? I'm not really understanding it
Shalnov [3]
Let's figure this out. Step by step:

P /  6 = 9

P = 6(9)

P = 54 is your answer.

I hope this helps :)
8 0
3 years ago
Read 2 more answers
What is the correct reason for statement 3?
olchik [2.2K]
The answer would be Associative Property.

Hope this helps you =)
4 0
3 years ago
Arnold ran 50 feet. Which equation can be used to determine c Arnold’s total distance in cm if 1 inch is equal to 2.54 centimete
bagirrra123 [75]

Answer:

1,524 centimeters

Step-by-step explanation:

Multiply 50 by 12.   50 * 12 = 600 inches

Multiply 600 by 2.54 to get the number of centimeters.   600 * 2.54 = 1,524

6 0
3 years ago
If You Round 344 and times that by 24 add 4 and take away 12, what would be the answer!! I need this quick!!
nadezda [96]
Well 344 rounded to the nearest hundred is 300 so times 24 its 7,200 add 4 is 7,204 but take away 12 is 7,192 and there's your answer
5 0
3 years ago
Mr. Charles cut fresh roses from his garden and gave 10 roses to his neighborhood. then gave half of what was left to his niece.
Vlad [161]
14+14=28
28+10=38 roses
8 0
3 years ago
Read 2 more answers
Other questions:
  • Explain why the exponents cannot be added in the product 12^3 and<br><br> 11^3
    12·1 answer
  • Pls help ASAP!!!!!!!!!
    10·2 answers
  • Estimate what is 31.75÷8= you have to estimate tho
    8·1 answer
  • E
    5·2 answers
  • Which digit is in the thousandths place?<br><br> 1,356.209
    5·2 answers
  • Ben's Parents give him a 10% raise in his weekly allowance. His new allowance is $22.00. what was his old allowance?
    12·2 answers
  • I want a gf seriously!!!!!​
    7·1 answer
  • Quadrilateral BEST is a parallelogram. If m∠B = (x + 40)° and m∠E = (2x + 20)°, what is the m∠T? Note: no need to write the degr
    15·1 answer
  • Percentage:
    14·1 answer
  • What is the five number summary for the data 0,2,2,4,5,5,5,5,7,11
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!