Recent content by Cuisine123

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    Angle of Inclination of Line in Vector Equation

    How do find the solution without having to draw the lines?
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    Angle of Inclination of Line in Vector Equation

    Homework Statement Find the angle of inclination of each of the following lines. i) r = (2,-6) + t(3,-4) ii) r = (6,1) + t(5,1) B) prove that the tangent of the angle of inclination is equal to the slope of the line. Homework Equations N/A The Attempt at a Solution I know...
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    What does this vector equal to?

    Homework Statement Prove that |\vec{A}|2+|\vec{B}|2 equals to \frac{1}{2}(|\vec{A}+\vec {B}|2+|\vec{A}-\vec{B}|2)Homework Equations Perhaps the triangle inequality? I am not sure.The Attempt at a Solution I have no idea how to approach this question. Please help me with clear explanations...
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    Rational Function Application Question

    The questions says, "Determine a rational function that gives the annual cost of a security system as a function of the number of years you own the system. Using this function determine the average annual cost of the security system given above." C(x)=(1500+108n)/n, where n is the number of...
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    Rational Function Application Question

    Homework Statement A home security system costs $9/month in electricity costs (you may assume this is a fixed cost over the duration of the time involved in this question). A new security system costs $1500 to purchase and lasts for 8 years. Determine a rational function that gives the...
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    Curve Sketching for f(x)=6x^2/(x^2-2x-15)

    Will I need to use the values of -15, -3, 0, and 5 for the chart to find intervals of increase and decrease? Also, how do I find the intervals of concave up and concave down and the points of inflection? The second derivative is 12(2x^3+45x^2+225)/(x^2-2x-15)^3. For what values of x do I...
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    Curve Sketching for f(x)=6x^2/(x^2-2x-15)

    Please take a look the edited information that I typed above in my first post. I would appreciate it if you can help me out.
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    Curve Sketching for f(x)=6x^2/(x^2-2x-15)

    Homework Statement Please state the following components of this rational function? f(x)=6x^2/(x^2-2x-15) -intervals of increase/decrease -local maximum and minimum values -intervals of concave up/concave down -points of inflectionHomework Equations N/A The Attempt at a Solution There is a...
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    The derivative of g(x)=R(sqrt(u(x))?

    [\sqrt{u(x)}]' using the chain rule, I get 1/2(\sqrt{}u(x))
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    The derivative of g(x)=R(sqrt(u(x))?

    I am getting even more confused. :cry:
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    How do I find the solution to this derivative problem?

    Is it -2g(x)^-3 x g(x)?
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    The derivative of g(x)=R(sqrt(u(x))?

    I have tried using the chain rule but I don't know how to apply it to this question though.
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    The derivative of g(x)=R(sqrt(u(x))?

    Yes I am. Please tell me how to proceed.
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    How do I find the solution to this derivative problem?

    Homework Statement Two functions f and g are such that f(4)=3, f prime (4)= -2, g(4)=7, and g prime (4)=5. Determine (1/g^2) prime(4). By "prime" I mean when there is something that looks like a little "1" exponent on the letter. Please help and give clear step by step explanations. Thanks...
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    The derivative of g(x)=R(sqrt(u(x))?

    Homework Statement Find the derivative of g(x)=R(sqrt(u(x)). Both R and u are differentiable functions. Homework Equations N/A The Attempt at a Solution I have been told that the solution is R' (sqrt(u(x)) * (1/2)u^(-1/2) * u' but I have no idea why. Please explain how to get to...