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• Math
Let `s` represent the side length of the cube. We want to estimate the relative error in measuring the volume if the error in measuring the sides is 2%. The propagated error can be estimated by...

Asked by tracyngg on via web

• Math
Let `y=a_0+a_1x+a_2x^2+a_3x^3+a_4x^4+...` So: `y'=a_1+2a_2x+3a_3x^2+4a_4x^3+...` `y''=2a_2+6a_3x+12a_4x^2+...` `y(0)=-1` tells us that `a_0=-1` and `y'(0)=2` tells us that `a_1=2` Plugging...

Asked by mcolemanstar1 on via web

• Math
The man deposit \$500. Interrest rate is 5%. At the end of 1st year he will have 500*(1+5/100) So at the start of second year he has 500*(1+5/100) At the end of second year he will have...

Asked by bunnyhut on via web

• Math
If y=mx+c is straight line and y=m'x+c is another straight line they will be perpendicular when m*m' = -1 2x+5y = 12 5y = 12-2x y = (-2/5)x+(12/5) Lets say the line perpendicular...

Asked by schooledmom on via web

• Math
Find the intervals of concavity for `f(x)=2sinx` : `f'(x)=2cosx` `f''(x)=-2sinx` `-2sinx=0==>x=pi` on `(0,2pi)` On `(0,pi),-2sinx<0` (Try a test value like `x=pi/2==>-2sin(pi/2)=-2`...

Asked by annaelizabeth25 on via web

• Math
To find the intervals of concavity, we need the second derivative. In this case, we can simplify the function before taking derivatives. `f(x)=(x-2)(x+4)` ` ` `=x^2+2x-8` Now differentiate...

Asked by annaelizabeth25 on via web

• Math
You need to determine the first derivative and then you can find the second derivative and to solve the equation f''(x) = 0. f'(x) = (x^3 - x^2 + x - 3)' => f'(x) = 3x^2 - 2x + 1 f''(x) = (...

Asked by annaelizabeth25 on via web

• Math
You need to solve the equation f''(x) = 0 to be able to tell what are the intervals of concavity of the function if x in [0,2], hence, you need to find the first derivative such that: f'(x) = (x^2...

Asked by annaelizabeth25 on via web

• Math
It is given that `y = (x - 1)(x + 3)(y - 1)` The derivative `dy/dx` is determined using implicit differentiation. `dy/dx = (x + 3)*(y - 1) + (x - 1)(y - 1) + (x - 1)(x + 3)(dy/dx)` =>...

Asked by lizcnester on via web

• Math
Differentiate `y-x=sinxy` : Use implicit differentiation `d/(dx)[y-x]=d/dx[sinxy]` `(dy)/(dx)-1=cosxy(y+x(dy)/(dx))` `(dy)/(dx)-1=ycos(xy)+x(dy)/(dx)cos(xy)` `(dy)/(dx)[1-xcos(xy)]=ycos(xy)+1`...

Asked by lizcnester on via web

• Math
To find the derivative of `y=x^x` , you need to use logarithmic differentiation. Start with the function, then take logarithms of both sides then simplify. `y=x^x` take logs `ln y=ln x^x` use...

Asked by lizcnester on via web

• Math
It is given that `y + x = y^2` . The expression for `dy/dx` can be determined using implicit differentiation. `dy/dx + 1 = 2y*(dy/dx)` => `(dy/dx)*(2y - 1) = 1` => `dy/dx = 1/(2y - 1)` The...

Asked by lizcnester on via web

• Math
The derivative `dy/dx` of `y = x^2` has to be determined. For `y = x^n` , the derivative `dy/dx = n*x^(n - 1)` For `y = x^2` , `dy/dx = 2x` The derivative of `y = x^2` is `dy/dx = 2x`

Asked by lizcnester on via web

• Math
The integral `int sin x + 3*cos x dx` has to be determined. `int sin x + 3*cos x dx` => `-cos x + 3*sin x + C` The integral `int sin x + 3*cos x dx = -cos x + 3*sin x + C`

Asked by lizcstauffer on via web

• Math
The integral `int e^x + sqrt 3*x dx` has to be determined `int e^x + sqrt 3*x dx` => `e^x + sqrt 3*(x^2/2) + C` The integral `int e^x + sqrt 3*x dx = e^x + (sqrt 3/2)*x^2 + C`

Asked by lizcstauffer on via web

• Math
The integral `int x^(-1/3) + 1 dx` has to be determined. `int x^(-1/3) + 1 dx` => `(x^(-1/3 + 1))/(-1/3 + 1) + x + C` => `(x^(2/3))/(2/3) + x + C` => `(3/2)*x^(2/3) + x + C` The...

Asked by lizcstauffer on via web

• Math
The anti derivative of f(x) = 9 has to be determined. `int f(x) dx` => `int 9 dx` => `9x + C` For `f(x) = 9` , `int f(x) dx = 9x + C`

Asked by lizcstauffer on via web

• Math
To solve this problem, we need to use the speed formula `v=d/t` which can be rearranged as `d=vt`. Cyclist A: For the first 1/2 hour A has gone 5 miles. In the time up to the 1/2 hour, the...

Asked by lizcstauffer on via web

• Math
You may find x intercepts solving the equation `(1/2)(1-x)(x^2-x-2) = 0` such that: `(1/2)(1-x)(x^2-x-2) = 0 =gt 1-x = 0 =gt ` `x = 1 `` `` x^2 - x - 2 = 0` You need to use quadratic formula such...

Asked by christinaelizabeth1987 on via web

• Math
A plausible graph: Thus no beer from midnight to 8pm; 2 beers each from 8-9 and 9-10pm, 1 beer each from 10-11 and 11pm-12am. (I'm not much of a drinker) (a) `int_0^(23)f(t)dt` represents the...

Asked by christinaelizabeth1987 on via web

• Math
We are given that `f(1)=5,f(3)=7` and the tangent to the graph of `f(x)` at (3,7) is `-2x+13` . One possibility for `f(x)` is `f(x)=-3/2x^2+7x-1/2` The graph of `f(x)` and the given tangent line:...

Asked by christinaelizabeth1987 on via web

• Math
The graph of `y = (x - 1)/(3x + 1)` has to be plotted. This has a vertical asymptote at x = -1/3 and a horizontal asymptote at y = 1/3. The required graph is:

Asked by christinaelizabeth1987 on via web

• Math
To graph polynomials we know that there are no asymptotes (since polynomials are very well-behaved) so we just need to use the remaining graphing techniques. (1) Intercepts. The function is in...

Asked by christinaelizabeth1987 on via web

• Math
The differentiation of an integral is used with the FTC formula `d/{dx}int_a^x f(t)dt=f(x)`. However, with differentiating this integral, we need to switch the limits of the integral and then apply...

Asked by cspanutius on via web

• Math
To differentiate an integral use the FTC formula `d/{dx} int_a^x f(z)dz=f(x)` . However, in this case, we need to use the chain rule since the lower limit is not just x, and also split the...

Asked by cspanutius on via web

• Math
To differentiate an integral, we use the FTC formula `d/{dx} int_a^x f(t)dt=f(x)`. In this case, we also need to use the chain rule, since the upper limit of integration is not just x. `d/{dx}...

Asked by cspanutius on via web

• Math
When differentiating an integral we have the FTC formula `d/{dx} int_a^x f(s)ds=f(x)`. In this case, we need to manipulate the integral before applying the FTC. `d/{dx} int_x^6 cos(sqrt{s^4+1})ds`...

Asked by cspanutius on via web

• Math
When differentiating an integral, you have the FTC formula `d/{dx}int_a^x f(t)dt=f(x)`. In this case, we can apply the FTC directly to get `d/{dx} int_2^x cos(t^4) dt` `=cos(x^4)` The derivative...

Asked by cspanutius on via web

• Math
You should remember that `x^2 + y^2 = (x + y)^2 - 2xy` , hence, you need to substitute `(x + y)^2 - 2xy` for `x^2 + y^2` in the given condition such that: `(x + y)^2 - 2xy = 34xy =gt (x + y)^2 =...

Asked by appreciate0831 on via web

• Math
You should notice the discontinuity of the function at x=0 and you need to prove that the antiderivative of the function exists. Differentiating the product `x^2*cos(1/x)` yields: `(x^2*cos(1/x))'...

Asked by blackhotfire on via web

• Math
cos3x+cos7x=cos2x cos3x+cos7x-cos2x = 0 We know that `cos A +cos B = 2cos((A+B)/2)*cos ((A-B)/2)` cos7x+cos3x-cos2x = 0 2cos((7x+3x)/2)*cos((7x-3x)/2) - cos2x = 0 2cos5x * cos2x-cos2x = 0...

Asked by greenspo on via web

• Math
If `6i` is a zero of the function, then `(x-6i)` will divide `f(x)`. Even better, `f(x)` has only real coefficients. (No complex ones, such as `2+3i` ). This means that all the complex zeros come...

Asked by katie3848 on via web

• Math
`(3x-5)/(x+3)lt=2` To start, change the inequality sign to "`=`" .Then, make the right side zero by subtracting both sides by 2. `(3x-5)/(x+3)-2=0` Simplify left side. `(3x-5)/(x+3)-...

Asked by amber756 on via web

• Math
Let us say box contain x number of apple, bag contain y number of apple and string bag contain z number of apple. In first day shop keeper receives (9x+3y) apples. When he repack he use 11 string...

Asked by happyhelper77 on via web

• Math
Among the properties of triangles are: (I) The sum of three interior angles of the triangle is `180^o` . (II) The measure of an exterior angle is equal to the sum of two remote interior...

Asked by aneesh123 on via web

• Math
Suppose you had the system of equations: `a+b=3` `2a+2b=6` These two equations actually are "the same" (if one is true the other must be true... once you know one of these, the second doesn't...

• Math
For a population proportion, the standard error is given by : `E=z_(alpha/2)sqrt((hat(p)hat(q))/n)` where: `E` is the standard error `z_(alpha/2)` gives the area (probability) that the error...

Asked by yukielaine123 on via web

• Math
We are given a table of values: (1,16.5),(2,18.3),(3,21.8),(4,25.6),(5,29.2),(6,32.6),(7,32.6),(8,32.4),(9,30.3),(10,26.4),(11,21.3),(12,18.0) where the independent variable is the month and the...

Asked by lkballer24 on via web

• Math
To do this question we need to know the following combination. (a^2)^m = a^(2m) `(4^(1/2*x)-2^x)` `= (2^2)^(1/2*x)-2^x` `= 2^(2*1/2*x)-2^x` `= 2^x-2^x` ` = 0` `int (4^(1/2*x)-2^x) dx` = `int 0...

Asked by andraa1058 on via web

• Math
When an investment compounds semi-annually, then investment grows according to the formula `A=P(1+r/2)^{2t}` where P is the principal, r is the interest rate pa and t is the number of years of...

Asked by shivani-sharma on via web

• Math
Evaluate `1.0698 -: 0.001` (1) Using long division -- the divisor is 0.001, and the dividend is 1.0698 To use long division, it is usually simplest to make the divisor a whole number. In order to...

Asked by heidiee on via web

• Math
The water company charges an initial fee of \$40, which covers the first 4000 gallons, and \$.005 per gallon beyond that. The monthly charge would be C=.005(x-4000)+40 or C=.005x+20 where x is the...

Asked by preciousness on via web

• Math
Sketch the graph of `y=2cos(x-pi/4)` on the interval `[0,2pi]` : The base graph is `y=cosx` . There is a vertical stretch of factor 2 (The amplitude is doubled) and a horizontal shift of `pi/4`...

Asked by jordymorrow10 on via web

• Math
The three types of row operations are: 1) switching two rows2) multiplying a row by a constant3) adding a multiple of one row to another row To switch two rows, say row 1 and row 2, the matrix...

Asked by imaginethis1 on via web

• Math
is its equation

Asked by sevicankilic on via web

• Math
a(x) = 5 sin x b(x) = 4 cos(2x+pi/3) Combine wave is a(x)+b(x) a(x)+b(x) `= 5 sin x+ 4 cos(2x+pi/3)` `= sqrt(5^2+4^2)[(5/sqrt(5^2+4^2) )sin x+ 4/(sqrt(5^2+4^2))cos(2x+pi/3)]` `=...

Asked by blueboy27 on via web

• Math
The graph of the given equation will intercept x when y = 0 Simply speaking if `ax^2 - 8x +4 = 0` has no solutions then the x-axis would not be intercept. For `ax^2 - 8x +4 = 0` not to have...

Asked by martinmandee on via web

• Math
The intersection points of any two functions `f(theta)` and `g(theta)` are given by solving the equation formed by making the two functions equal to each other. That is `f(theta)=g(theta)` . Since...

Asked by lkballer24 on via web

• Math
The y-intercept is found by setting x=0 and solving for y. For the line `x-4y=-16` , we find the y-intercept by solving the equation (after setting x=0) `-4y=-16` divide both sides by -4...

Asked by iloveuu on via web