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
zheka24 [161]
3 years ago
14

A curve has a gradient function

Mathematics
1 answer:
zvonat [6]3 years ago
8 0

Answer:

The answer I came up with here brings to question how I solved it.  To double check the wording of the question though, the tangent to the curve is indeed perpendicular to that line and not parallel?

The answer I found is 5i√(1/6), which makes me think I made a mistake at one point.

Step-by-step explanation:

First we need to know the slope of the tangent at point p.  This is perpendicular to the slope of the given line.  So first, let's rearrange that line into the format y = sx + c:

2x - 5y + 3 = 0\\5y = 2x + 3\\y = \frac{2}{5}x + \frac{3}{5}

The line then has a slope of 2/5, meaning that a perpendicular slope would be -5/2.

Next, we can take the derivative of the curve:

y = (2x^3 - 9) / 10\\= x^3/5 - 9/10\\\frac{dy}{dx} = 3x^2/5

Finally, we match that perpendicular slope we found:

-5/2 = 3x^2 / 5\\-25 / 6 = x^2\\x = \sqrt{-25/6}\\x = 5i\sqrt{1/6}\\

The fact that I ended up with an imaginary number makes me think I hit an error there.  I suggest you double check this yourself.  I'm fairly certain that the logic here is correct.

You might be interested in
Kendra has $ 7.35 in nickels and quarters. If she has 15 more quarters than nickels, how many of each coin does she have?
lozanna [386]

x*5 - quarter amount

(x+15)*25- nickels amount

(x*5)+((x+15)*25)=735

5x+25x+375=735

30x=735-375

30x=360

x=360/30=12 - number of nickels

x+15=12+15=27 - number of quarters

CHECK

12*5=60 ¢

27*25=675 ¢

675+60=735 ¢ or $7.35

5 0
4 years ago
I need help on how to do this
Leni [432]

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

a) A system of equations has no solutions when the graphs of those equations do not intersect. If the equations are equations of a line, then the lines must be parallel in order for them not to intersect.

Any parallel line will do.

__

b) There is one solution when the graphs intersect in exactly one point.

Any line that crosses the one shown will do.

__

c) There are infinite solutions when the graphs describe the same curve.

A line overlapping the one shown is the one you want.

5 0
3 years ago
If 10% is RS 1500 then find 90%.​
lapo4ka [179]

Answer:

10%=1500

so 100% = 15000

90%= 100% - 10%

15000-1500=13500

90%=13500

8 0
3 years ago
What is 5/6 - 3/8 ?
topjm [15]

Answer:

D. 11/24

Step-by-step explanation:

→ \frac{5}{6} -\frac{3}{8}

→ \frac{40-18}{48}

→ \frac{22}{48}

→ \frac{11}{24}

5 0
2 years ago
Read 2 more answers
I really need this thank you
a_sh-v [17]

slope intercept form: y=mx+b

y=2x-3

slope is also m

b is the y-intercept

answer:

slope is 2

y-intercept is -3

8 0
3 years ago
Other questions:
  • Which is a valid conclusion that can be drawn from these statements?
    12·1 answer
  • Molly is planting seeds for a pink and white flower garden in her backyard she is planting 1.5 times as many pink flowers as whi
    10·2 answers
  • a scientist was in a submarine, 83.1 feet below sea level, studying ocean life. over the next 10 minutes she ascended 70.8 feet.
    13·1 answer
  • Could someone answer this?
    7·1 answer
  • (10 point's) 10 1/3 + 7/9 =
    8·1 answer
  • Choose the set of equations that best represent the following information:
    10·1 answer
  • What is 35 x 50000000
    11·2 answers
  • Please help... picture is below
    10·1 answer
  • Help me please I need it by tommrow
    14·2 answers
  • Ravi buys some hats to sell at a school fete. He buys 56 hats for a total £120
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!