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  • Math
    Make a substitution `y = 2x,` then `dy = 2 dx` and the limits of integration for `y` are from `0` to `3.` The integral becomes the table one: `int_0^3 1/(1+y^2) (dy)/2 = 1/2 (tan)^(-1)(y) |_(y=0)^3...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Make a substitution `x = 3y,` then `dx = 3 dy` and the limits of integration for y are from 0 to 1/18. The integral becomes a table one: `int_0^(1/18) (9 dy)/(sqrt(9-9y^2)) = int_0^(1/18) (3...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Hello! It is obvious that there is no linear formula exactly connecting these x's and y's, if we consider the slopes between neighbor points: `(155 - 134)/(31 - 30) = 21,` `(165 - 155)/(33 - 31) =...

    Asked by sd083180 on via web

    1 educator answer.

  • Math
    Hello! Suppose that the two numbers are both >=2 (if one of the numbers is 1, the problem is trivial). Then both have its unique decomposition into prime factors. If we find this decomposition,...

    Asked by user4510571 on via web

    1 educator answer.

  • Math
    Parent functions are the most basic, or "simplest" form of a given function with no transformations placed upon them. For example, `y=4x^2+2x+5` `is a quadratic function. The parent is: ` `y=x^2`...

    Asked by abbeyehrhard on via web

    1 educator answer.

  • Math
    An operation follows the Commutative property if changing the order of the numbers in the operation does not change the outcome. Thus, addition (and multiplication) are commutative (i.e., a+b=b+a...

    Asked by mangomm941 on via web

    1 educator answer.

  • Math
    For a stem and leaf plot, the number to the left of the bar is generally the stem and the numbers to the right of the bar are the leaves. The stem is the first digit(s) and the leaves are the next...

    Asked by user6087133 on via web

    1 educator answer.

  • Math
    To do this, the longest rod would be the diagonal of the box. Now, this is different than the diagonal of one side of the box. I am talking about the diagonal that would go through the middle of...

    Asked by mmfuzz5 on via web

    1 educator answer.

  • Math
    Well, at some point, all subjects can be related. For instance, you could use math quite easily in social sciences, studying peoples and populations, for instance. The "variable" would be how you...

    Asked by carlitobuenaflor on via web

    1 educator answer.

  • Math
    This is a typical problem involving percents. There are a few different way to approach such problems. Recall that percent is a numerator (top) of a fraction with the denominator (bottom) equal to...

    Asked by amandawagner388 on via web

    1 educator answer.

  • Math
    This all depends, on all kinds of factors. For instance, even if each plant is planted separately, away from each other, they may be so far away from each other than one may be more/less sun...

    Asked by yk2011 on via web

    1 educator answer.

  • Math
    In order to factor this expression, first open all parenthesis. The given expression will then become `a^2b + ab^2 + b^2c +bc^2 + ac^2 + a^2c + 3abc` . We need to group these terms in a way so that...

    Asked by user4988197 on via web

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  • Math
    What does the variable n in mathematics usually mean? The variable can mean many things. 1) Maybe the variable is used in an equation only to represent an unknown, such as: `10 = 6n+4` `2) The...

    Asked by aarenill0001 on via web

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  • Math
    `y=3ln(6t+1)` To take the derivative of this, refer to formula: `d/(dx) (ln u) = 1/u * (du)/dx ` Applying that, the derivative of the function will be: `d/(dt)(y) = d/(dt)[3ln(6t+1)]`...

    Asked by movkool14811 on via web

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  • Math
    The general methods are the disk method and the shell method. The disk method adds disks with the radius the height of the representative rectangle from the axis to the curve and height either dx...

    Asked by frogsanchez1 on via web

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  • Math
    Hello! We'll use an identity `a^3 - b^3 = (a - b)(a^2 + ab + b^2)` in the form `a - b = (a^3 - b^3) /(a^2 + ab + b^2)` for `a = root(3)((n+1)^2)` and `b = root(3)((n-1)^2).` This way we...

    Asked by bleardd on via web

    1 educator answer.

  • Math
    The given function is: `h(t) = 20t-5t^2` where h(t) represents the height of the stone above the cliff. Since the cliff is 60m above the sea, when the stone hits the beach, the value of h(t) is...

    Asked by ganga5580 on via web

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  • Math
    In solving trig, or other equations, finding the "roots" means to find the solutions. This also means find the values when "theta" or "x" is zero. Also known as the x-intercepts. Trig equations...

    Asked by richter1 on via web

    1 educator answer.

  • Math
    The area of a right triangle can be found using the formula `A = 1/2 ab` , where a and b are the lengths of the sides that form the right angle. This is an application of a more general formula...

    Asked by uzaifahmad717 on via web

    1 educator answer.

  • Math
    For this one, I always go back to the lines of multiples. For instance, for 6, the line of multiples would be:6, 12, 18, 24, 30, . . .And, you are trying to think of another one where the LCM...

    Asked by raasheed1 on via web

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  • Math
    You would add area of all the sides up. Now, that's literally the formula I like to consider. And, that will work for any non-circular prism, period. Now, special formulas do exist for specific...

    Asked by salar01 on via web

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  • Math
    Hello! Actually, the probability density of the normally distributed random variable is known. The probability in question is the integral of this probability density over the given interval....

    Asked by jenrader66 on via web

    1 educator answer.

  • Math
    The work done by the force field in moving the particle along a path is a circulation, or line integral, of this force field around the path. The circulation is defined as `W = int_C vecF* dvecs`...

    Asked by althunayan91 on via web

    1 educator answer.

  • Math
    Hello! The domain of this function is all real numbers, because `tan^(-1)(x),` and therefore `tan^(-1)(x+1),` is defined for all `x in RR.` By the definition, `tan^(-1)(y)` is the number `w in...

    Asked by sseorder on via web

    1 educator answer.

  • Math
    We have to find the square root of `-1+2i` i.e. `\sqrt{-1+2i}` We will find the square roots of the complex number of the form x+yi , where x and y are real numbers, by the following method: Let...

    Asked by chhatredeepak on via web

    1 educator answer.

  • Math
    Hello! If a surface is given as an image of a scalar function `y=f(x,z),` defined on some region `D` on `(x,z)` plane, then the corresponding surface area is `int int_D sqrt(1+((del f)/(del...

    Asked by althunayan91 on via web

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  • Math
    Green's theorem (1 image)
    Hello! 5b. Green's theorem gives us a possibility to compute the area of a plane region integrating along its boundary. Actually, it can help for more complex tasks then computing area. There are...

    Asked by althunayan91 on via web

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  • Math
    a) A curl is the vector derivative of a vector field. It can be denoted as `vec grad xx vec F` , where `vec F` is the vector field. ` The curl is calculated as three-dimensional determinant: i...

    Asked by althunayan91 on via web

    1 educator answer.

  • Math
    Given `f=x^2z ds` `x=cost, y=2t, z=sint ` for `0<=t<=\pi` We have to find the line integral i.e. `\int_{c} f(x,y,z)ds=\int_{c} x^2z ds` = `\int_{c} f(x(t),y(t),z(t))....

    Asked by althunayan91 on via web

    1 educator answer.

  • Math
    a) Divergence of a vector field is a scalar quantity that represents how the field spreads out, or "diverges", in different directions. It is usually denoted as `vecgrad*vecF` and is calculated as...

    Asked by althunayan91 on via web

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  • Math
    In order to match these two-dimensional vector field with their equations, try to predict how the x- and y- components of each field will vary with the values of x and y, and then check which of...

    Asked by althunayan91 on via web

    1 educator answer.

  • Math
    Hello! Actually, such a situation is typical. If `A` is a subset of `B` and `B` is a subset of `C,` then `A` is a subset of `C` (any element of `A` is an element of `B` and thus is an element of...

    Asked by mymail2abdul on via web

    1 educator answer.

  • Math
    Hello! The original number may be written as `bar(ab),` where `a` and `b` are one-digit natural numbers, `0lt=blt=9,` `1lt=alt=9.` The value of the number `bar(ab)` is obviously `b + 10a.` When we...

    Asked by amitbhati6857 on via web

    1 educator answer.

  • Math
    Hello! When we define the square root function, the function which we start with is a square function `(y=x^2).` We want a function which, given an `y,` would return an `x` such that `x^2=y.` In...

    Asked by tneeraj673 on via web

    1 educator answer.

  • Math
    Hello! The resultant ground velocity of a jet is a vector sum of the jet's air velocity and wind ground velocity. To find its magnitude and direction, we consider the projections on the N-S and W-E...

    Asked by nanduu94 on via web

    1 educator answer.

  • Math
    `F(x) =int_0^(e^(2x)) ln(t+1)dt` `F'(x)=?` Take note that if the function has a form `F(x) = int_a^(u(x)) f(t)dt` its derivative is `F'(x)=f(u(x))*u'(x)` Applying this formula, the derivative of...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `F(x)=int_pi^(lnx) cos(e^t)dt` `F'(x)=?` Take note that if the function has a form `F(x)=int_a^(u(x)) f(t)dt` its derivative is `F'(x)=f(u(x))*u'(x)` Applying this formula, the derivative of the...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Find the derivative if `y=e^(2x)tan(2x) ` : Let u=2x and rewrite as: `y=e^utanu ` Use the product rule noting that `d/(du)e^u=e^udu,d/(du)tanu=sec^2udu ` : `(dy)/(du)=e^udutanu+e^usec^2udu ` Since...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Find the derivative if `y=e^x(sinx+cosx) ` : Use the product rule: `(dy)/(dx)=e^(x)(cosx-sinx)+e^(x)(sinx+cosx) ` `(dy)/(dx)=2e^xcosx `

    Asked by enotes on via web

    1 educator answer.

  • Math
    Find the derivative if `y=(e^(2x))/(e^(2x)+1) ` : Use the quotient rule to get: `(dy)/(dx)=((e^(2x)+1)(2e^(2x))-(e^(2x)*2e^(2x)))/(e^(2x)+1)^2 ` `(dy)/(dx)=(2e^(4x)+2e^(2x)-2e^(4x))/(e^(2x)+1)^2 `...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Find the derivative if ` y=(e^x+1)/(e^x-1) ` : Use the quotient rule to get: `(dy)/(dx)=((e^x-1)(e^x)-(e^x+1)(e^x))/(e^x-1)^2 ` `(dy)/(dx)=(e^(2x)-e^x-e^(2x)-e^x)/(e^x-1)^2 ` `...

    Asked by enotes on via web

    1 educator answer.

  • Math
    We are asked to differentiate `y=(e^x-e^(-x))/2 ` : We use the fact that if f(x), g(x) are differentiable functions of x then `d/(dx)(f(x)+- g(x))=d/(dx)f(x)+-d/(dx)g(x) ` and ` d/(dx)e^u=e^u...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Find the derivative for `y=2/(e^x+e^(-x)) ` : Using the quotient rule we get: `(dy)/(dx)=(-2(e^x-e^(-x)))/(e^x+e^(-x))^2 `

    Asked by enotes on via web

    1 educator answer.

  • Math
    Find the derivative of `y=ln((1+e^x)/(1-e^x)) ` : Use a property of the natural logarithm to rewrite as: `y=ln(1+e^x)-ln(1-e^x) ` If u is a differentiable function of x, then ` d/(dx)ln(u)=(du)/u `...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Find the derivative if ` y=ln(1+e^(2x)) ` : If u is a differentiable function of x then ` d/(dx)lnu=(u')/u, d/(dx)e^(u)=e^u *u' ` so we get: `(dy)/(dx)=(2e^(2x))/(1+e^(2x)) `

    Asked by enotes on via web

    1 educator answer.

  • Math
    Find the derivative if `y=e^(-3/t^2) ` : If u is a differentiable function of x then `d/(dx)e^u=e^u (du)/(dx) ` . Note that `d/(dt) -3/t^2=6/t^3 ` so we get: `(dy)/(dx)=6/t^3e^(-3/t^2) `

    Asked by enotes on via web

    1 educator answer.

  • Math
    Find the derivative if `y=(e^(-t)+e^t))^3 ` : Use the power rule ( `d/(dx)u^n=n*u^(n-1)(du)/(dx) ` where u is a differentiable function of x) to get: `(dy)/(dt)=3(e^(-t)+e^t)^2(-e^(-t)+e^t) `

    Asked by enotes on via web

    1 educator answer.

  • Math
    Find the derivative if ` y=x^2e^(-x)` : Use the product rule to get: `(dy)/(dx)=x^2(-e^(-x))+2xe^(-x) ` `(dy)/(dx)=e^(-x)(2x-x^2) `

    Asked by enotes on via web

    1 educator answer.

  • Math
    Find the derivative if `y=x^3e^x ` : Use the product rule to get: `(dy)/(dx)=x^3e^x+3x^2e^x ` `(dy)/(dx)=e^x(x^3+3x^2) `

    Asked by enotes on via web

    1 educator answer.

  • Math
    Find the derivative if `y=xe^(4x) ` : If u is a differentiable function of x then ` d/(dx)e^u=e^u (du)/(dx) ` , so using the product rule we get: `(dy)/(dx)=x(4)e^(4x)+e^(4x) `...

    Asked by enotes on via web

    1 educator answer.

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