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  • Grammar and speech
    It can sometimes be difficult to discern the differences between informal and formal language, which so often comes down to a single case of word choice or order, small syntactical adjustments,...

    Asked by Peaceful Sthembile on via web

    1 educator answer.

  • Law and Politics
    Thomas Jefferson wrote the Declaration of Independence. In the Declaration of Independence, there are many ideas about the role of government and about the rights the people should have. A big part...

    Asked by stephxniii on via iOS

    1 educator answer.

  • Death, be not proud
    "Death, be not proud" is a sonnet by the iconic English metaphysical poet John Donne. The fourteen-line poem, which is also referred to as "Holy Sonnet X,"deals with the fear of death, overcoming...

    Asked by user3663079 on via web

    1 educator answer.

  • Grammar
    The primary reason this sentence is ambiguous is because of the unclear placement and use of the word "right." In the English language, the word "right" can mean two very different things. The...

    Asked by Peaceful Sthembile on via web

    1 educator answer.

  • Reference
    'Ambiguity' means a lack of clarity or concrete detail, which can make it difficult to discern meaning. In the case of these two sentences, the lack of context and detail make it possible to...

    Asked by Peaceful Sthembile on via web

    1 educator answer.

  • Math
    Given `\frac{dy}{dx}=\frac{1}{\sqrt{4-x^2}}, y(0)=\pi` , we have to find y. So we can write, `dy=\frac{dx}{\sqrt{4-x^2}}` Integrating both sides we have, `y=\int \frac{dx}{\sqrt{4-x^2}}+C` Now...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Complete the square at the denominator: `x^4 + 2x^2 + 2 = (x^2)^2 + 2x^2 + 1 + 1 = (x^2 + 1)^2 + 1.` Now we see the substitution `y = x^2 + 1,` then `dy = 2x dx,` and the integral becomes `int...

    Asked by enotes on via web

    1 educator answer.

  • Math
    By completing the square and making simple substitution, we will reduce this integral to a table one. `-x^2-4x = -(x^2 + 4x + 4) + 4 = -(x+2)^2 + 4 = 4 - (x+2)^2.` Now make a substitution `y =...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Recall that `(arccos(x))' = -1/sqrt(1-x^2)` and make the substitution `y = arccos(x),` then `dy = -1/sqrt(1-x^2).` The limits of integration are from `arccos(0) = pi/2` to `arccos(1/sqrt(2)) =...

    Asked by enotes on via web

    1 educator answer.

  • Math
    We have to evaluate the definite integral: `\int_{0}^{1/\sqrt{2}}\frac{arc sinx}{\sqrt{1-x^2}}dx` Let arc sinx=t Differentiating both sides we get, `\frac{1}{\sqrt{1-x^2}}dx=dt`...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Make the substitution `u = sin(x),` then `du = cos(x) dx.` The integration limits for `u` are from `sin(0) = 0` to `sin(pi/2) = 1,` and the integral becomes `int_0^1 (du)/(1 + u^2) = arctan(1) -...

    Asked by enotes on via web

    1 educator answer.

  • 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
    We have to evaluate the integral : `\int_{0}^{\sqrt{2}}\frac{dx}{\sqrt{4-x^2}}` let `x=2sin t` So, `dx=2cos t dt` When x=0, t=0 `x=\sqrt{2}, t=\pi/4` So we have,...

    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
    We have to evaluate the integral : `\int \frac{sec^2x}{\sqrt{25-tan^2x}}dx` Let `tanx =t` So, `sec^2x dx=dt` Therefore we have, `\int \frac{sec^2x}{\sqrt{25-tan^2x}}dx=\int...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Recall that the indefinite integral is denoted as: `int f(x) dx =F(x)+C` There properties and basic formulas of integration we can apply to simply certain function. For the problem `int...

    Asked by enotes on via web

    1 educator answer.

  • Math
    We have to evaluate `\int \frac{dx}{\sqrt{1-4x^2}}` Let `x=\frac{1}{2} sint ` So, `dx= \frac{1}{2}cost dt` Hence we have, `\int \frac{dx}{\sqrt{1-4x^2}}=\int \frac{\frac{1}{2}cost...

    Asked by enotes on via web

    1 educator answer.

  • Math
    We have to evaluate the integral: `\int \frac{dx}{\sqrt{9-x^2}}` let `x=3sint` So, `dx=3cost dt` Hence we have, `\int \frac{dx}{\sqrt{9-x^2}}=\int \frac{3cost}{\sqrt{9-9sin^2t}}dt`...

    Asked by enotes on via web

    1 educator answer.

  • Math
    First, check that the given point satisfies the equation: `arctan(1 + 0) = 0 + pi/4` is true. The slope of the tangent line is `y'(x)` at the given point. Differentiate the equation with respect to...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Recall that the derivative of a function f at a point x is denoted as f'(x). The given function: `f(x)= arcsin(x)+arccos(x)` has inverse trigonometric terms. We can solve for the derivative of...

    Asked by enotes on via web

    1 educator answer.

  • Math
    We use the product rule, `(uv)' = u'v + uv',` for `u = x^2` and `v = arctan(5x),` and then the chain rule: `h'(x) = 2x*arctan(5x) + x^2 (arctan(5x))' =` `= 2x*arctan(5x) + (5 x^2)/(1 + 25x^2).`

    Asked by enotes on via web

    1 educator answer.

  • Math
    The given function `f(x) = arctan(sqrt(x))` is in a inverse trigonometric form. The basic derivative formula for inverse tangent is: `d/(dx) arctan(u) = ((du)/(dx))/sqrt(1-u^2)` . Using...

    Asked by enotes on via web

    1 educator answer.

  • Math
    The derivative of a function with respect to t is denoted as f'(t). The given function:` f(x) = arcsin(t^2) ` is in a form of a inverse trigonometric function. Using table of derivatives, we have...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `arccos(1)` Let this expression be equal to y. `y = arccos(1)` Rewriting it in terms of cosine function, the equation becomes: `cos(y) = 1` Base on the Unit Circle Chart, cosine is 1 at angles 0...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `arccos(1/2)` Let this expression be equal to y. `y = arccos(1/2)` Rewriting this in terms of cosine function the equation becomes: `cos(y) =1/2` Base on the Unit Circle Chart, cosine is 1/2 at...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `arcsin(0)` Let this expression be equal to y. `y =arcsin(0)` Re-writing this equation in terms of sine function, it becomes: `sin (y) = 0` Base on the Unit Circle Chart (see attached figure), sine...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `arcsin(1/2)` Let this expression be equal to y. `y =arcsin(1/2)` Rewriting it in terms of sine function, the equation becomes: `sin(y) = 1/2` Base on the Unit Circle Chart (see attached figure),...

    Asked by enotes on via web

    1 educator answer.

  • Math
    To evaluate the integral: `int_(-4)^(4) 3^(x/4) dx` , we follow the formula based from the First Fundamental Theorem of Calculus: `int_a^bf(x)dx=F(b)- F(a)` wherein f is a continuous and F is...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Recall the First Fundamental Theorem of Calculus: If f is continuous on closed interval [a,b], we follow: `int_a^bf(x)dx` = F(b) - F(a) where F is the anti-derivative of f on [a,b]. This...

    Asked by enotes on via web

    1 educator answer.

  • Math
    By definition, if the function F(x) is the antiderivative of f(x) then we follow the indefinite integral as `int f(x) dx = F(x)+C` where: f(x) as the integrand F(x) as the...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Indefinite integral are written in the form of` int f(x) dx = F(x) +C` where: f(x) as the integrand F(x) as the anti-derivative function C as the arbitrary constant known...

    Asked by enotes on via web

    1 educator answer.

  • Math
    The point is really on the graph, because `2^(-(-1)) = 2.` The tangent line has the slope of `y'(-1),` and the equation `y - 2 = y'(-1)(x+1).` It is clear that `y'(x) = -2^(-x) ln2` and `y'(-1) =...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Derivative of a function h with respect to t is denoted as h'(t). The given function: `h(t) = log_5(4-t)^2` is in a form of a logarithmic function. From the derivative for logarithmic functions,...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `y= log_3(x^2-3x)` The derivative formula of a logarithm is: `d/(dx) [log_a (u)] = 1/(ln(a) * u) * (du)/(dx)` Applying this formula, the derivative of the function will be: `(dy)/(dx) = d/(dx)...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `y=log_4(5x + 1)` The derivative formula of a logarithm is: `d/(dx) [log_a (u)] = 1/(ln(a) * u) * (du)/(dx)` Applying that formula, the derivative of the function will be: `(dy)/(dx) = d/(dx)[...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `f(t) = 3^(2t)/t` To take the derivative of this function, use the quotient rule `(u/v)'= (v*u' - u*v')/v^2`. Applying that, f'(t) will be: `f'(t) = (t * (3^(2t))' - 3^(2t)*(t)')/t^2` `f'(t) =...

    Asked by enotes on via web

    1 educator answer.

  • Math
    The derivative of a function f at a point x is denoted as y' = f'(x). There are basic properties and formula we can apply to simplify a function such as the Product Rule provides the formula:...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Recall that the derivative of a function f at a point x is denoted as `y' = f'(x)` . There basic properties and formula we can apply to simplify a function. For the problem `y = x(6^(-2x)),` we...

    Asked by enotes on via web

    1 educator answer.

  • Math
    The given function: `f(x)=x9^x ` has two factors since that is the same as `f(x) =x* 9^x` . In this form, we can apply the Product Rule for derivative. Product Rule provides the formula: `f(x) =...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `y=6^(3x-4)` The derivative formula of an exponential function is: `d/(dx) (a^u) = ln(a) * a^u * (du)/dx` Applying this formula, the derivative of a function will be: `(dy)/(dx) = d/(dx)...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `y=5^(-4x)` The derivative formula of an exponential function is: `d/(dx) (a^u) = ln(a) * a^u * (du)/(dx)` Applying this formula, the derivative of the function is: `(dy)/(dx) = d/(dx)(5^(-4x))`...

    Asked by enotes on via web

    1 educator answer.

  • Math
    The derivative of f(x) with respect to x is denoted a f'(x). The given function f(x) = 3^(4x) is in exponential form which means we can apply the basic integration formula: `d/(dx)(a^u) =...

    Asked by enotes on via web

    1 educator answer.

  • Math
    By definition, the derivative of f(x) with respect to x is denoted a f'(x) where `f'(x) = lim (f(x+h) -f(x))/h ` as` h->0` . Instead of using the limit of difference quotient, we may apply the...

    Asked by enotes on via web

    1 educator answer.

  • Math
    To simplify the logarithmic equation: `log_5(sqrt(x-4))=3.2` , recall the logarithm property: `a^((log_(a)(x))) = x` . When a logarithm function is raised by the same base, the log cancels out...

    Asked by enotes on via web

    1 educator answer.

  • Math
    To solve a logarithmic equation, we may simplify or rewrite it using the properties of logarithm. For the given problem `log_(3)(x^2)=4.5` , we may apply the property: `a^((log_(a)(x))) = x` The...

    Asked by enotes on via web

    1 educator answer.

  • Math
    In solving a logarithmic equation, we may simplify using logarithm properties. Recall the logarithm property: `a^((log_(a)(x))) = x` . When we raise the log with the same base, the "log" will...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `log_2 (x-1) =5` To solve, convert the equation to exponential form. Take note that if a logarithmic equation is in the form `y = log_b (x)` its equivalent exponential equation is `x= b^y` So...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Problem:`3(5^(x-1))=86` ` ` To simplify, we divide both sides by 3: `(3(5^(x-1)))/3=(86)/3` `5^(x-1)=(86)/3` ` ` ` ` Take the "log" on both sides to apply the logarithm property:...

    Asked by enotes on via web

    1 educator answer.

  • Math
    For exponential equation:`2^(3-z)=625` , we may apply the logarithm property: `log(x^y) = y * log (x)` . This helps to bring down the exponent value. Taking "log" on both sides:...

    Asked by enotes on via web

    1 educator answer.

  • Math
    For exponential equation: `5^(6x)= 8320` , we may apply the logarithm property: `log(x^y) = y * log (x).` This helps to bring down the exponent value. Taking "log" on both sides:...

    Asked by enotes on via web

    1 educator answer.

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