• The tangent to the curve y^2-xy+9=0 is vertical when?

    Best answer: dy/dx measures the slope of a function. If a tangent to a function has a slope of 0, then dy/dx = 0. If the tangent is undefined, then dy/dx is undefined (in simpler terms, it's some value that's divided by 0). We could then say that dy/dx is undefined when dx/dy is 0. Now let's derive your curve... show more
    Best answer: dy/dx measures the slope of a function. If a tangent to a function has a slope of 0, then dy/dx = 0. If the tangent is undefined, then dy/dx is undefined (in simpler terms, it's some value that's divided by 0). We could then say that dy/dx is undefined when dx/dy is 0.

    Now let's derive your curve implicitly and see when dx/dy = 0

    y^2 - xy + 9 = 0
    2y * dy - (x * dy + y * dx) + 0 = 0
    2y * dy - x * dy - y * dx = 0
    2y * dy - x * dy = y * dx
    (2y - x) * dy = y * dx
    (2y - x) / y = dx/dy

    dx/dy = 0

    (2y - x) / y = 0
    2y - x = 0
    2y = x

    Plug that value for x back into the original equation and solve for y

    y^2 - xy + 9 = 0
    y^2 - (2y) * y + 9 = 0
    y^2 - 2y^2 + 9 = 0
    -y^2 + 9 = 0
    9 = y^2
    -3 , 3 = y

    There it is.
    6 answers · 12 hours ago
  • Solve 117=5+8v?

    10 answers · 3 days ago
  • What’s a 86/100 grade ?

    18 answers · 5 days ago
  • Round off 27.6477?

    7 answers · 2 days ago
  • What is 3(x-4)=10?

    20 answers · 6 days ago
  • Work Problem?

    A tank can be filled by pipe A in half the time pipe B can empty the tank. When both pipes are operating, the tank can be filled in 1 hour and 12 minutes. Determine the time, in hours, for pipe A to fill the tank alone. answer: 0.6 hours
    A tank can be filled by pipe A in half the time pipe B can empty the tank. When both pipes are operating, the tank can be filled in 1 hour and 12 minutes. Determine the time, in hours, for pipe A to fill the tank alone. answer: 0.6 hours
    5 answers · 1 day ago
  • Is 2/3 more,less or equal to half?

    10 answers · 3 days ago
  • What is the 11th term of the sequence 1,2,4,8,16?

    What is the 11th term of the sequence 1,2,4,8,16?

    Best answer: Although 1024 may be the simplest possible answer, there are infinity answers just as valid. For example: If the nth term is (1/24)x^4 - (1/4)x^3 + (23/24)x^2 - (3/4)x + 1, the 11th term is 386. If the nth term is (-59/5040)n^5 + (73/336)n^4 - (1255/1008)n^3 + (1207/336)n^2 - (9973/2520)n + (101/42), the 11th... show more
    Best answer: Although 1024 may be the simplest possible answer, there are infinity answers just as valid. For example:

    If the nth term is (1/24)x^4 - (1/4)x^3 + (23/24)x^2 - (3/4)x + 1, the 11th term is 386.

    If the nth term is (-59/5040)n^5 + (73/336)n^4 - (1255/1008)n^3 + (1207/336)n^2 - (9973/2520)n + (101/42), the 11th term is 32.

    If the nth term is (-97/15120)n^5 + (139/1008)n^4 - (2405/3024)n^3 + (269/112)n^2 - (18959/7560)n + (223/126), the 11th term is 192.

    If the nth term is (277/5040)n^5 - (263/336)n^4 + (4457/1008)n^3 - (3833/336)n^2 + (36059/2520)n - (235/42), the 11th term is 2048.
    6 answers · 2 days ago
  • Can you help me with this math problem?

    2 power 251(mod7)
    2 power 251(mod7)
    4 answers · 1 day ago
  • Is jumping of a bridge easy?

    4 answers · 11 hours ago
  • If 3t-7=5t, then 6t= -21. Can someone please explain to me how that equals -21?

    I googled the question to get the answer, but I need to understand how that even works! I haven’t been to school in 4 years!
    I googled the question to get the answer, but I need to understand how that even works! I haven’t been to school in 4 years!
    6 answers · 2 days ago
  • Why am I good at maths but bad at mental maths?

    Best answer: Perhaps you're not a visual thinker, and are more an audio or kinesthetic thinker. Visual thinkers are often good at mental math because they can "see" the problem written out on any convenient surface in their mind. Where you need paper and pencil, they can use a nearby wall, or the ceiling or even... show more
    Best answer: Perhaps you're not a visual thinker, and are more an audio or kinesthetic thinker.

    Visual thinkers are often good at mental math because they can "see" the problem written out on any convenient surface in their mind. Where you need paper and pencil, they can use a nearby wall, or the ceiling or even the floor. These types of thinkers are also good at spatial apperception - you describe sphere circumscribed by a framework cube, the whole thing tumbling on an axis aligned with a diagonal of the cube, and they can see an image of it in their mind.

    Audio and kinesthetic thinkers can't do that.

    However, everyone is some blend of the three archetype thinkers. This is why practice is often all that is required to develop such a skill. And the further you are from the type of thinker needed to accomplish the task, the harder/longer you will have to work to get there.

    Of course, even if you're a visual thinker and you don't know that's how the other visual thinkers are doing it, you wouldn't think to develop that particular skill.

    I'm reluctant to say that it's strictly because you're dependent on the calculator, because if you are a visual/kinesthetic thinker, you will have a tendency to remember common number/operation combinations that appear on the calculator when you see them. For example, you'll come to remember when you see 1.414... sqrt(2) might be involved - that comes from pressing 2 then sqrt all the time and noticing/remembering the number that appears. Likewise, 0.707... will tend to trigger (1/2) sqrt(2) instead of pi/2 or some other value.

    But again, even if you are a visual/kinesthetic thinker, if you don't think the exercise those skills, you're going to have to do a LOT more practice problems before your brain detects the high frequency patterns and makes the association by itself.

    HTH
    6 answers · 3 days ago
  • Easy ways to die?

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  • How do cows do math?

    4 answers · 23 hours ago