
MathThe “Account Balances.xls” data set has information on the account balances of customers at a... (1 image)(a) I do not have a current copy of Excel. The following are instructions that should get the Anova output: (1) Enter the data in columns A,B,C, and D.(2) On the toolbar select Data > Data...

Math(a) When you perform the ttest in excel you should get the following: t=0.2006236844p=.8416030944df=66.72581946`bar(x_1)=448.7179487 ` `bar(x_2)=451.7 ` SX1=71.8375172SX2=51.5592394n1=39n2=30 (b)...

Math(a) I do not have a current copy of Excel. Here are the instructions to get the results from the FTest: (1) Enter the data into columns A and B(2) From the toolbar select Data > Data...

MathThe probability that a particle with the wavefunction `Psi(x)` will be found in some region `R` is `int_R Psi(x)^2 dx.` In our problem it is `int_(oo)^0 Psi(x)^2 dx =int_(1)^0 Psi(x)^2 dx...

Math1. The Koch snowflake at stage 0 is an equilateral triangle with side length 1 unit. a) Find the... (1 image)Hello! 1. When constructing the Koch snowflake, we start with an equilateral triangle (stage `0`). On each subsequent stage the figure remains a closed polygon, all segments of this polygon have...

Math`r=2csc theta+3` To solve, express the polar equation in parametric form. To convert it to parametric equation, apply the formula `x = rcos theta` `y=r sin theta` Plugging in `r=2csctheta +3` ,...

Math`r=1sin theta` To solve, express the polar equation in parametric form. To convert it to parametric equation, apply the formula `x = rcos theta` `y=r sin theta` Plugging in `r=1sin theta` , the...

MathThe formula of arc length of a parametric equation on the interval `alt=tlt=b` is: `L = int_a^b sqrt((dx/dt)^2+(dy/dt)^2) dt` The given parametric equation is: `x=t` `y=t^5/10 + 1/(6t^3)` The...

MathThe equation for arc length in parametric coordinates is: `L=int_a^b sqrt((dx/dt)^2+(dy/dt)^2) dt` Where in this case: `dx/dt=d/dt (t^(1/2))=1/2t^(1/2)` `dy/dt=d/dt(3t1)=3` `a=0, b=1` Therefore...

MathArc length of a curve C described by the parametric equations x=f(t) and y=g(t), `a<=t<=b` where f' and g' are continuous on [a,b] and C is traversed exactly once as t increases from a to b,...

MathThe formula of arc length of a parametric equation on the interval `alt=tlt=b` is: `L = int_a^b sqrt((dx/dt)^2+(dy/dt)^2) dt` The given parametric equation is: `x = e^(t)cost` `y=e^(t)sint` The...

MathThe formula of arc length of a parametric equation on the interval `alt=tlt=b` is: `L = int_a^b sqrt((dx/dt)^2+(dy/dt)^2) dt` The given parametric equation is: `x=6t^2` `y=2t^3` The derivative of...

MathThe formula of arc length of a parametric equation on the interval `alt=tlt=b` is: `L = int_a^b sqrt((dx/dt)^2+(dy/dt)^2) dt` The given parametric equation is: `x=3t + 5` `y=7  2t` The derivative...

Math`x=cos^2 theta` `y=cos theta` First, take the derivative of x and y with respect to theta . `dx/(d theta) = 2costheta (sin theta)` `dx/(d theta)=2sintheta cos theta` `dy/(d theta) = sin theta`...

Math`x=sec theta` `y=tan theta` First, take the derivative of x and y with respect to theta. `dx/(d theta) = sec theta tan theta` `dy/(d theta) = sec^2 theta` Then, set each derivative equal to zero....

Math`x=5+3cos theta` `y= 2+sin theta` First, take the derivative of x and y with respect to theta. `dx/(d theta) = 3sin theta` `dy/(d theta) = cos theta` Take note that the slope of a tangent is...

Math`x=3cos theta` `y=3sin theta` First, take the derivative of x and y with respect to `theta` . `dx/(d theta) = 3sin theta` `dy/(d theta) = 3cos theta` Take note that the slope of a tangent is equal...

MathParametric curve (x(t),y(t)) has a horizontal tangent when its slope `dy/dx` is zero, i.e. `dy/dt=0` and `dx/dt!=0` . Curve has a vertical tangent if its slope approaches infinity i.e. `dx/dt=0`...

MathParametric curve (x(t),y(t)) has a horizontal tangent if its slope `dy/dx` is zero, i.e when `dy/dt=0` and `dx/dt!=0` Curve has a vertical tangent line, if its slope approaches infinity i.e...

MathParametric curve (x(t),y(t)) has a horizontal tangent if its slope `dy/dx` is zero i.e. when `dy/dt=0` and `dx/dt!=0` It has a vertical tangent, if its slope approaches infinity i.e. `dx/dt=0` and...

MathParametric curve has a horizontal tangent if its slope `dy/dx` is zero i.e. when `dy/dt=0` and `dx/dt!=0` Tangent line is vertical if its slope approaches infinity i.e. `dx/dt=0` and `dy/dt!=0`...

MathThe parametric equations are: `x=t^36t` (1) `y=t^2` (2) From equation 2, `t=+sqrt(y)` Substitute `t=sqrt(y)` in equation (1),...

MathGiven parametric equations are: `x=t^2t` `y=t^33t1` We have to find the point where the curves cross. Let's draw a table for different values of t, and find different values of t which give the...

MathThe given parametric equations are , `x=2picos(t), y=2tpisin(t)` The curve crosses itself for different values of t , which give the same x and y value. So, to get the point where the curve...

MathGiven parametric equations are: `x=2sin(2t)` `y=3sin(t)` Let's make a table of x and y values for different values of t. (Refer the attached image).The point where the curve crosses itself will...

MathGiven parametric equations are : `x=t3` (1) `y=t/(t3)` (2) Draw a table for different values of t and plot the points obtained from the table.(Refer the...

Math`x=sqrt(t)` (1) `y=t5` (2) Draw a table for different values of t and plot the points obtained from the table.(Refer the attached image). Connect the points to...

MathThe graph is described by the parametric equations in x, y and t: `x(t) = t^2 + t, quad y(t) = t^2  t ` A sketch of the graph is as pictured, with (as standard) the horizontal axis being the...

Math`x=t^3` (1) `y=t^2/2` (2) Draw a table for different values of t and plot the points obtained from the table.Connect the points to a smooth curve.( Refer the...

Math` x = 2t^2, quad y = t^4 + 1 ` ` <br> ` ` ` The graph described by the pair of equations in x, y and t is given above. Written in the form of those two equations, the graph is expressed in...

Math`x=1+t` (1) `y=t^2` (2) Draw a table for different values of t and plot the points obtained from the table (Refer the attached image). Connect the points to...

Math`x = 54t` `y=2+5t` To graph a parametric equation, assign values to t. Since there is no given interval for t, let's consider the values from t=3 to t=3. t=3 `x=54(3) = 17` `y= 2+5(3) = 13`...

Math`x=2t3` (1) `y=3t+1` (2) From equation 1, `x+3=2t` `=>t=(x+3)/2` Plug in the value of t in equation (2) `y=3((x+3)/2)+1` `y=(3x+9)/2+1`...

MathFrom the table of power series, we have: `(1+x)^k = 1 +kx+ (k(k1))/2! x^2 +(k(k1)(k2))/3!x^3 +` ... To apply this on the given integral `int_0^0.2 sqrt(1+x^2)dx` , we let: `sqrt(1+x^2)...

MathFrom the table of power series, we have: `(1+x)^k = 1 +kx+ (k(k1))/2! x^2 +(k(k1)(k2))/3!x^3 +` ... To apply this on the given integral `int_0.1^0.3 sqrt(1+x^3)dx` , we let: `sqrt(1+x^3)...

MathFrom a table of power series, recall that we have: `arctan(x) = sum_(n=0)^oo (1)^n x^(2n+1)/(2n+1)` To apply this on the given problem, we replace the "`x` " with "`x^2` ". We get: `arctan(x^2)...

MathFrom the Power Series table for trigonometric function, we have: `arctan(x) =sum_(n=0)^oo (1)^n x^(2n+1)/(2n+1)` `= x x^3/3 +x^5/5  x^7/7 + x^9/9...` Applying it on the...

MathFrom the table of power series, we have: `cos(x) = sum_(n=0)^oo (1)^nx^(2n)/(2n)!` `= 1x^2/(2!)+x^4/(4!)x^6/(6!)+` ... To apply this on the given integral `int_0^1 cos(x^2) dx` ,...

MathFrom the Power Series table for trigonometric function, we have: `sin(x) =sum_(n=0)^oo (1)^n x^(2n+1)/((2n+1)!)` `= x x^3/(3!) +x^5/(5!)  x^7/(7!) +...` Applying it on the integral...

MathFrom the basic list of power series, we have: `ln(x) =sum_(n=0)^oo (1)^(n) (x1)^(n+1)/(n+1)` `= (x1)(x1)^2/2+(x1)^3/3 (x1)^4/4 +...` We replace "`x` " with "`x+1` " to setup:...

MathFrom the table of power series, we have: `e^x = sum_(n=0)^oo x^n/n! ` `= 1+x+x^2/(2!)+x^3/(3!)+x^4/(4!)+x^5/(5!)+` ... To apply this on the given integral `int_0^1 e^(x^2)dx` , we replace...

MathMaclaurin series is a special case of Taylor series which is centered at a=0. We follow the formula: `f(x) =sum_(n=0)^oo (f^n(0))/(n!)x^n` or `f(x) = f(0) +...

MathMaclaurin series is a special case of Taylor series which is centered at a=0. We follow the formula: `f(x) =sum_(n=0)^oo (f^n(0))/(n!)x^n` or `f(x) = f(0) +...

MathA binomial series is an example of infinite series. It is a series that is only convergent when we have `xlt1` and with a sum of `(1+x)^k ` where k is any number. To apply binomial series in...

MathA binomial series is an example of infinite series. When we have a function of `f(x) = (1+x)^k` such that k is any number and convergent to `x lt1` , we may apply the sum of series as the value...

MathBinomial series is an example of an infinite series. When it is convergent at `xlt1` , we may follow the sum of the binomial series as `(1+x)^k` where k is any number. The formula will be:...

MathRecall binomial series follows: `(1+x)^k=sum_(n=0)^oo (k(k1)(k2)...(kn+1))/(n!)x^n` or `(1+x)^k = 1 + kx + (k(k1))/(2!) x^2 + (k(k1)(k2))/(3!)x^3 +(k(k1)(k2)(k3))/(4!)x^4+...` To...

MathRecall a binomial series follows: `(1+x)^k=sum_(n=0)^oo _(k(k1)(k2)...(kn+1))/(n!)x^n` or `(1+x)^k = 1 + kx + (k(k1))/(2!) x^2 + (k(k1)(k2))/(3!)x^3 +(k(k1)(k2)(k3))/(4!)x^4+` ... To...

MathBinomial series is an example of an infinite series. When it is convergent at `xlt1` , we may follow the sum of the binomial series as `(1+x)^k` where `k` is any number. The formula will be:...

MathRecall binomial series that is convergent when `xlt1` follows: `(1+x)^k=sum_(n=0)^oo (k(k1)(k2)...(kn+1))/(n!)x^n` or `(1+x)^k = 1 + kx + (k(k1))/(2!) x^2 + (k(k1)(k2))/(3!)x^3...
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