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
Round to the nearest hundred thousand 894,659
ipn [44]

Answer:

900,000

because you look to the second place next to it and if 5 and over its goes up if 4 and under it stays the same

3 0
2 years ago
A business uses straight-line depreciation to determine the value y of an automobile over a 5-year period. Suppose the original
Elena-2011 [213]

For this problem. it is found that:

a) The automobile has depreciated 75% in 5 years.

b) The value of the automobile was reduced by $10,500 in five years.

c) The linear function is: s(t) = 14,500 - 2,100t.

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = ax + b

In which:

  • a is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

From the problem, we have that:

a) The automobile has depreciated 75% in 5 years, as 4000/14500 = 0.25, and 100% - 25% = 75%.

b) The value of the automobile was reduced by $10,500 in five years, as 14500 - 4000 = $10,500.

For the linear function, we have that:

  • The initial value is b = 14500.
  • The slope is of a = -10500/5 = -2100.

Hence the linear function is: s(t) = 14,500 - 2,100t.

More can be learned about linear functions at brainly.com/question/24808124

#SPJ1

6 0
1 year ago
Solve for n.<br> 2n - 3<br> 5<br> =<br> = 5<br> Enter your answer in the box.<br> n =
Zina [86]

Answer:

2n - 35 = 5 \\ 2n = 5 + 35 \\ 2n = 40 \\ n = 40 \div 2 \\ n = 20

4 0
2 years ago
Read 2 more answers
J is 14 less than 22 as an equation<br> with what j=
Olegator [25]
22 - 14 = 8 

so i think j = 8
4 0
3 years ago
Rachel is 40 cm taller than Lucy. Rachel is 25 percent taller than Lucy. How tall is Lucy? Explain
tatyana61 [14]
What is 40cm 25% of?
The answer is 160cm.

Rachel is 160cm. 160 - 40 = 120.

Lucy is 120cm tall.
5 0
2 years ago
Other questions:
  • Find the greatest common factor of these monomials <br><br> 34a^2 b 24a^5 b^2
    9·1 answer
  • 9/10 miles in 5 minutes At this rate how many miles can he in in one minute
    12·1 answer
  • The population of bees has been decreasing at a rate of 10% per year in 2012 there were 6000 bees in particular hive how many be
    9·1 answer
  • Write a formula for the general term or nth term for the sequence. Then find the indicated term. five halves comma five fourths
    6·1 answer
  • If there are 18 boxes with 12 caculators in each box how many caculators are there in total
    12·1 answer
  • 9 bowls of soup contain 837 calories. How many calories in each bowl of soup?
    6·2 answers
  • Plz explain
    9·2 answers
  • Hope this makes you day
    7·1 answer
  • Phone chargers in a store are priced $19, $18, $15, $17, $19, $12, $19, and $15.
    13·1 answer
  • Two numbers have these properties.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!