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  • Math
    `lim_(x->0) (1+(3x)/25))^(1/x)` To solve, let's assign values to x that are approaching zero from the left and from the right. For x values that are approaching zero from the left: `x=-0.1` `y=...

    Asked by user8667928 on via web

    1 educator answer.

  • Math
    In a geometric sequence, the ratio between two consecutive numbers is same. ratio r = `(a2)/(a1)` To find nth term of the sequence we use an formula. `an = a1 . r^(n-1)` 1. 2500, 500, 100,........

    Asked by user6864069 on via web

    2 educator answers.

  • Math
    Hello! Yes, it is not difficult. First, we can open the parentheses using the distributive property: 8*(cos(30°) + i*sin(30°)) = 8*cos(30°) + i*(8*sin(30°)). Formally, this is the answer...

    Asked by user8269967 on via web

    1 educator answer.

  • Math
    Hello! To find a center and a radius of a circle given by its equation, it is desirable to express this equation in the form `(x-a)^2+(y-b)^2=r^2.` Then the center is (a, b) and the radius is r....

    Asked by karagrenzer on via web

    2 educator answers.

  • Math
    Hello! It isn't clear what the problem is. I see two variants: extract some more factors (factor completely) and, to the contrast, open the parentheses (express as a sum of monomials). Let's do...

    Asked by bogardd on via web

    1 educator answer.

  • Math
    Sturges' rule is a way of calculating the number of bins (e.g. categories or classes) of a set of data. It is assumed that the data come from a normally distributed population. Sturges' rule states...

    Asked by cfoster4 on via web

    1 educator answer.

  • Math
    We are given that the population mean mu=12.074, with a population standard deviation sigma=.046. We are asked to find the percentage of the population with the following properties: (a) Find...

    Asked by cfoster4 on via web

    1 educator answer.

  • Math
    A pareto chart consists of a bar chart, with bars in descending order of length, and a line graph representing the cumulative total. Please see the attached graph:

    Asked by cfoster4 on via web

    1 educator answer.

  • Math
    You need to find the length of the given curve, on the interval [1,3], using the formula `int_1^3 ds` , where `ds = sqrt(1+((dy)/(dx))^2).` You need to differentiate the equation of the curve `y =...

    Asked by naruto007 on via web

    1 educator answer.

  • Math
    You need to evaluate the sum of imaginaries of the given powers of complex number z, such that: `Sigma_(m=1)^15 Im(z^(2m-1)) = Im(z^(2*1-1)) + Im(z^(2*2-1)) + Im(z^(2*3-1)) + ... + Im(z^(2*15-1))`...

    Asked by pratha2295 on via web

    1 educator answer.

  • Math
    Hello! mL stands for milliliters. As usual, the prefix "milli" means "one thousandth" of the unit following it. Any quantity contains one thousand of its thousandths. So does liter, 1 L = 1000 mL....

    Asked by charlottehackney on via web

    2 educator answers.

  • Math
    You need to place the number (-3) to numerator and to put the difference -3+12 into brackets, such that: `(-3+12)/4 = 9/4 = 2.25` If you place the number -3 outside the brackets, the evaluation...

    Asked by user6539068 on via web

    1 educator answer.

  • Math
    Fraction of blue paint that Mike mixed `= 1/6` Fraction of green paint that Mike Mixed `= 5/8` Total fraction of paint Mike mixed `= 1/6+5/8` Here we need to get a common denominator to add up...

    Asked by tiannaarne on via web

    1 educator answer.

  • Math
    Probability is the measure of the likelihood that an event occurs. The problem requires you to determine what the probability is of 45 children being born on the same day of the week. There are 7...

    Asked by tonys538 on via web

    1 educator answer.

  • Math
    Hello! Let's find the month interest rate `m,` then the year (simple) interest rate will be `12m.` There are `6` full months elapsed till the end of June. The entire amount deposited is...

    Asked by nehadhillon5 on via web

    1 educator answer.

  • Math
    Hello! Express the function under integral as `(x^2*x)/(1+25x^2),` observe that `x*dx = 1/2 d(x^2)` and make the substitution `x^2=u.` Then `du=2xdx` and the integral becomes `1/2 int (u)/(1+25u)...

    Asked by al-farabi12 on via web

    1 educator answer.

  • Math
    Hello! Summands of the Riemann sum have a form `Delta x_n*f(x_n),` where segments `d_n` of length `Delta x_n` cover the integration segment and each `x_n` is in `d_n.` In our problem all length...

    Asked by user6040956 on via web

    1 educator answer.

  • Math
    1. Construction of angle 105 degree using compass:(Refer attached image) Steps: Draw a line AB and mark point O on it where angle is to be drawn. With O as center draw an arc (semicircle) which...

    Asked by saiabh360 on via web

    1 educator answer.

  • Math
    The reciprocal of `x = 1/x ` The reciprocal of `(-x) = 1/(-x) = - 1/x` So, the reciprocal of `(-5x) = -1/(5x)` `-1/(5x) = -1/5 . 1/x = (-0.2)/x` `therefore` the reciprocal of `(-5x)` is `(-0.2)/x`

    Asked by fluberdoodlez on via web

    2 educator answers.

  • Math
    Hello! If we could split boys and girls into n teams, and b boys and g girls will be in each team, then obviously `nb=48` and `ng=60.` Therefore `n` divides 48 and `n` divides 60, or the same may...

    Asked by gramma635 on via web

    1 educator answer.

  • Math
    You need to use the substitution `-2y = u` , such that: `-2y= u => -2dy = du => dy= -(du)/(2)` Replacing the variable, yields: `int y*e^(-2y) dy = (1/4)int u*e^u du` You need to use the...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int_1^sqrt(3)arctan(1/x)dx` If f(x) and g(x) are differentiable functions, then `intf(x)g'(x)dx=f(x)g(x)-intf'(x)g(x)dx` If we write f(x)=u and g'(x)=v, then `intuvdx=uintvdx-int(u'intvdx)dx`...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int_0^(1/2)cos^(-1)xdx` Let's first evaluate the indefinite integral by using the method of integration by parts, `intcos^(-1)xdx=cos^(-1)x*int1dx-int(d/dx(cos^(-1)x)int1dx)dx`...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int_1^2(ln(x))^2/x^3dx` If f(x) and g(x) are differentiable function, then `intf(x)g'(x)=f(x)g(x)-intf'(x)g(x)dx` If we rewrite f(x)=u and g'(x)=v, them `intuvdx=uintvdx-int(u'intvdx)dx` Using the...

    Asked by enotes on via web

    1 educator answer.

  • Math
    You need to use the substitution `sin x = t,` such that: `sin x = t => cos x dx = dt` Replacing the variable, yields: `int cos x*ln(sin x) dx = int ln t dt` You need to use the integration by...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int_0^1r^3/sqrt(4+r^2)dr` Let's first evaluate the indefinite integral using the method of substitution, Substitute `x=4+r^2, =>r^2=x-4` `=>dx=2rdr`...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int_1^2x^4(ln(x))^2dx` If f(x) and g(x) are differentiable functions, then `intf(x)g'(x)dx=f(x)g(x)-intf'(x)g(x)dx` If we write f(x)=u and ` ` g'(x)=v, then `intuvdx=uintvdx-int(u'intvdx)dx` Using...

    Asked by enotes on via web

    1 educator answer.

  • Math
    You need to use integration by parts, such that: `int udv = uv - int vdu` `u = e^s => du = e^s ds` `dv = sin(t-s) => v = (-cos(t-s))/(-1)` `int e^s sin (t-s) ds = e^s*cos(t-s) - int...

    Asked by enotes on via web

    1 educator answer.

  • Math
    You need to use the following substitution, such that: `sqrt x = t => (dx)/(2sqrt x) = dt => dx = 2tdt` Replacing the variable yields: `int cos sqrt x dx = int (cos t)*(2tdt)` You need to...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `intt^3e^(-t^2)dt` Let `x=t^2` `dx=2tdt` `intt^3e^(-t^2)dt=intxe^(-x)dx/2` `=1/2intxe^(-x)dx` Now apply integration by parts, If f(x) and g(x) are differentiable functions then,...

    Asked by enotes on via web

    1 educator answer.

  • Math
    You need to use the substitution `theta^2= t` , such that: `theta^2 = t => 2theta d theta= dt => theta d theta= (dt)/2` Replacing the variable, yields: `int_(sqrt(pi/2))^(sqrt pi)...

    Asked by enotes on via web

    1 educator answer.

  • Math
    You need to use the substitution `cos t = u` , such that: `cos t = u => -sin t dt = du => sin t dt = -du` Replacing the variable, yields: `int_0^pi e^(cos t)*sin (2t)dt = 2int_0^pi e^(cos...

    Asked by enotes on via web

    1 educator answer.

  • Math
    You need to use the substitution `1+x = t` , such that: `1+x = t => dx = dt` Changing the variable yields: `int x*ln(1+x) dx = int (t-1)*ln t dt = int t*ln t dt - int ln t dt` You need to...

    Asked by enotes on via web

    1 educator answer.

  • Math
    We need to make a substitution then use integration by parts. Let us make the substitution: `ln(x) = t,` so: `x = e^t` therefore `dx = e^t dt` so our equation can be changed. `int sin(ln(x))dx =...

    Asked by enotes on via web

    1 educator answer.

  • Math
    You need to use the substitution `beta*t = u` , such that: `beta*t = u => beta dt = du ` Replacing the variable, yields: `int t^2*sin(beta*t) dt = 1/(beta^3) int u^2*sin u du` You need to use...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int ln (root(3)(x)) dx` To evaluate, apply integration by parts `int udv = uv - int vdu` . So let `u = ln (root(3)(x))=ln (x^(1/3))=1/3ln(x)` and `dv = dx` Then, differentiate u and integrate...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `intsin^-1xdx` If f(x) and g(x) are differentiable functions, then `intf(x)g'(x)dx=f(x)g(x)-intf'(x)g(x)dx` If we write f(x)=u and g'(x)=v, then `intuvdx=uintvdx-int(u'intvdx)dx` Using the above...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `intarctan(4t)dt` If f(x) and g(x) are differentiable functions, then `intf(x)g'(x)dx=f(x)g(x)-intf'(x)g(x)dx` If we write f(x)=u and g'(x)=v, then `intuvdx=uintvdx-int(u'intvdx)dx` Using the above...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int p^5 ln(p) dp` To evaluate, apply integration by parts intu dv = uv -int vdu. So let `u= ln (p)` and `dv = p^5 dp` Then, differentiate u and integrate dv. `du=1/p dp` and `v = int p^5dp =...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `inttsec^2(2t)dt` If f(x) and g(x) are differentiable functions, then `intf(x)g'(x)dx=f(x)g(x)-intf'(x)g(x)dx` If we write f(x)=u and g'(x)=v, then `intuvdx=uintvdx-int(u'intvdx)dx` Now using the...

    Asked by enotes on via web

    1 educator answer.

  • Math
    You need to use the integration by parts such that: `int fdg = fg - int gdf` `f = s => df = ds` `dg = 2^s=> g = (2^s)/(ln 2)` `int s*2^s ds = s* (2^s)/(ln 2) - int (2^s)/(ln 2) ds` `int s*2^s...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int (ln x)^2dx` To evaluate, apply integration by parts `int udv= uv - vdu` . So let `u = (lnx)^2` and `dv = dx` Then, differentiate u and integrate dv. `du = 2lnx * 1/x dx = (2lnx)/x dx` and `v =...

    Asked by enotes on via web

    1 educator answer.

  • Math
    To help you solve this, we consider the the integration by parts: `int u * dv = uv - int v* du` Let `u = t` and `dv = sinh(mt) dt.` based from `int t*sinh(mt) dt` for` int u*dv` In this integral,...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `inte^2thetasin(3theta)d theta` If f(x) and g(x) are differentiable functions, then `intf(x)g'(x)=f(x)g(x)-intf'(x)g(x)dx` If we rewrite f(x)=u and g'(x)=v, then `intuvdx=uintvdx-int(u'intvdx)dx`...

    Asked by enotes on via web

    1 educator answer.

  • Math
    You need to use integration by parts, such that: `int udv = uv - int vdu` `u = e^(-theta) => du =- e^(-theta)d theta` `dv = cos (2theta) => v = (sin 2 theta)/2` `int e^(-theta)cos (2theta) d...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `intz^3e^zdz` If f(x) and g(x) are differentiable functions, then `intf(x)g'(x)=f(x)g(x)-intf'(x)g(x)dx` If we write f(x)=u and g'(x)=v, then `intuvdx=uintvdx-int(u'intvdx)dx` Using the above...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `intxtan^2xdx` Rewrite the integrand using the identity `tan^2x=sec^2x-1` `intxtan^2xdx=intx(sec^2x-1)dx` `=intxsec^2xdx-intxdx` Now let's evaluate `intxsec^2xdx` using integration by parts,...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int(xe^(2x))/(1+2x)^2dx` If f(x) and g(x) are differentiable functions, then `intf(x)g'(x)=f(x)g(x)-intf'(x)g(x)dx` If we rewrite f(x)=u and g'(x)=v, then `intuvdx=uintvdx-int(u'intvdx)dx` Using...

    Asked by enotes on via web

    1 educator answer.

  • Math
    You need to use integration by parts, such that: `int udv = uv - int v du` `u = (arcsin^2(x))=> du = (2arcsin x)/(sqrt(1-x^2))dx` `dv = 1 => v = x` `int (arcsin^2(x)) dx = x*(arcsin^2(x)) -...

    Asked by enotes on via web

    1 educator answer.

  • Math
    You need to solve the integral `int_0^(1/2) (x) cos (pi*x) dx` , hence, you need to use substitution `pi*x = t => pi*dx = dt => dx = (dt)/(pi)` `int x*cos (pi*x) dx = 1/(pi^2) int t*cos t`...

    Asked by enotes on via web

    1 educator answer.

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