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
Question 1 WRONG With what number must 3.475817 be multiplied in order to obtain the number 34,758.17? A 100 1,000 10,000 D 100,
lbvjy [14]

Answer:

1 - Option C - 10,000

2 - 3x+5 will be 12 more than 3x-7.

Step-by-step explanation:

1) To find : With what number must 3.475817 be multiplied in order to obtain the number 34,758.17?

Solution :

The number 3.475817 is multiplied by number to obtain 34,758.17.

As we see that, the decimal is moved four places to the right.

Which means the number is multiplied by 10000.

i.e. 3.475817\times 10000=34,758.17

Therefore, option C is correct.

2) To find : How much greater is the value of 3x+5 than the value of 3x−7?

Solution ;

Assuming that x is the same value in each equation,

In order to determine the difference between the two values,

We ignore the 3x part as it is the same on both of the equations.

So, from 5 to -7 i.e. 7+5=12.

Therefore, 3x+5 will be 12 more than 3x-7.

5 0
3 years ago
The volume of the cone shown is 5 cubic inches. What is the height of a cone with the same base diameter but a volume of 10 cubi
Alisiya [41]

Answer:

The height of the big cone is double the one in the small cone

h2 = 2h1

Step-by-step explanation:

Given that:

  • The volume of the small cone: 5 cubic inches
  • The volume of the big cone: 10 cubic inches

As we know, the volume of a cone is as following:

V = (1/3)*area of the base*height

If the base diameter are unchanged => area of the base of the two cones are  unchanged and from the given information, the volume of the big cone is double the volume of the small cone. So the height of the big cone is double the one in the small cone

<=> h2 = 2h1

3 0
3 years ago
Jenny has been saving quarters in a piggy bank since she was born. She currently has 192 quarters in her piggy bank. She wants t
Aleksandr [31]

<span>She needs to save an additional 108 quarters.</span>
5 0
3 years ago
Read 2 more answers
Solve pls brainliest
oee [108]

Answer:

mixed no. 51/10

Improper fraction 5/1/10

3 0
2 years ago
POSSIBLE
Levart [38]
I believe the answer is supplementary
7 0
3 years ago
Other questions:
  • What is the mathmatical definition of decomposing
    5·2 answers
  • The last time Dior made tacos for her family,she spent $5.33 on 1 1/2 pounds of ground beef. She's heading back to the store aga
    13·1 answer
  • 12 points for!
    7·1 answer
  • Find the EXACT area AND circumference of the following circle.
    15·1 answer
  • Belinda's family goes through 572 gallons of milk in a year. How many gallons of milk does her family drink every week? (There a
    5·1 answer
  • How to solve -4{1-2x}-1=7x
    15·2 answers
  • What is the missing value?
    12·2 answers
  • Can someone help me PLZ<br> (125n^9) ^ -2/3
    10·2 answers
  • Pls help me :v<br> Mxjgzjgkxgkxmhykx
    12·1 answer
  • A bouncy ball is dropped such that the height of its first bounce is 3.25 feet and each successive bounce is 71% of the previous
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!