##log(1/100)=-2##
First, lets assume that the base of the logarithm is 10, sometimes written ##log_(10)##. Next, we’ll simplify by using the knowledge that
##log(x^a)=a*log(x)##
We can convert the ##1/100## in the expression to a power of 10:
##log(1/100)=log(100^(-1))=log((10^2)^(-1))=log(10^-2)##
Which we can rewrite as
##-2*log(10)=-2##
since ##log_10(10)=1##
How do you do this R-code problem?
Obtain an approximation to the t distribution by Monte Carlo simulation. To fix ideas, let n=10. Step S: Generate X1,…,Xn i.i.d. N(0,1) and compute the t-statistic: T = sqrt{n}* barX / hatSigma where barX is the sample mean and hatSigma the sample standard deviation, i.e., the square root of the sample variance. Repeat Step S many times (say 499 times), and collect the 499 values of T in a vector denoted by VT. Plot a histogram of VT and compare it to a plot of the t distribution with m=n-1. Also compute the Monte Carlo approximation to qt(0.975,m) by using the R command: quantile(VT, 0.975).
t Distribution ProjectQuestionObtain an approximation to the t distribution by Monte Carlo simulation. To fixideas, let n=10 .ii d Step S: GenerateT =√ n× X 1 , .. . , X n ∼ N (0 ,1) and…
How do you do this problem? A hypothetical element, D, consists of two stable isotopes. the first stable isotope, 32(<- superscript)D, has an actual mass of 31.5873 amu. the second stable isotope, 36(<- superscript)D, has an actual mass of 36.4173 amu. the atomic wieght of element D is 34.5623 amu. what are the isotopic abundances of the two stable isotopes?
how do you do this problem? In a certain population , body weights are normally distributed with a men of 152 pounds and a standard deviation of 26 pounds. How many people must be surveryed if we want to estimate the percentage who weigh more than 180 pounds? Assume that we want 96% confidence that the error is no more than 2.5 percentage points
How do you do in text citation for these website?
3x+4
Let’s first define two terms divisor and dividend
divisor = x+1& dividend = ##3x^2 +7x + 4##
Let us begin and this will be difficult explaining w/o being able to write with a pen on paper. I’ll try to go through the steps mathematically and hope that you can follow along visually.
##x+1// 3x^2+7x+4##
Use your highest order variable in the divisor to divide into the first term of the dividend. We want to ask x times what will give us something to cancel out that ##3x^2## when its being subtracted as per long division.
We can write 3x on top of the division bar as our first term and multiply 3x by (x+1) giving us ##3x^2 +3x## but now we must subtract those values underneath the ##3x^2 +7x## portion of the dividend.
This is extremely difficult to write without being able to draw what’s happening
It would look something like this:
##3x^2+7-3x^2-3x= 4x##
Ultimately you would just subtract 4x+4 by -(4x+4) which results in zero.
Thus the answer is ##3x +4##
Please note that your teacher may teach you guys this method or , which may be easier but this method always works if you follow the steps. I personally always used the standard way since I would mix up the +/- signs and would get questions wrong.
On the bright side you never have to do these operations in Calculus and above so just learn and appreciate it while in Precalc :).
I hope all this helped and made sense!
to find the tangent line of the curve, take the derivative, to determine the slope of the tangent line.
y=##sqrt(x^2+4)## y=##(x^2+4)^(1/2)##y’=##1/2####(x^2+4)^(-1/2)##(2x)y’=##x/sqrt(x^2+4)##
because you want the tangent line at x=3, plug it in to y’ to find the slop at that point, since we know that the derivative is the slope at a certain point.
y'(3)=##3/sqrt(3^2+4)##=##3/sqrt(13)##
at x=3, the point on the curve is (3,##sqrt13##)now, you can create the tangent line(y-##sqrt13##)= ##3/sqrt13##(x-3)y-##sqrt13##=##3/sqrt13##x-##9/sqrt13##y=##3/sqrt13##x-##9/sqrt13##+##sqrt13##
so your y-intercept for the tangent line at x=3 would be (##9/sqrt13##+##sqrt13##)
How do you determine the percentage of sales mix when you are given the unit selling price, unit variable cost for product A and product B? Combined unit contribution margin is $2.31 and estimated fixed cost is $346,962.
neither
To determine if a function is even/odd consider the following.
• If f(x) = f( -x) , then f(x) is even
Even functions have about the y-axis.
• If f( -x) = – f(x) , then f(x) is odd
Odd functions have symmetry about the origin.
Test for even
##f(-x)=(-x)^3+1=-x^3+1 ≠f(x)##
Since f(x) ≠ f( -x) , then f(x) is not even.
Test for odd
##-f(x)=-(x^3+1)=-x^3-1≠f(-x)##
Since f( -x) ≠ – f(x) , then f(x) is not odd.
##rArrx^3+1″ is neither even nor odd”## graph{x^3+1 [-10, 10, -5, 5]}
##y=0## ##y=-3/2##
To find any horizontal we have to evaluate:
##lim_(x rarr+-oo)f(x)##
if the limits are finite then they are horizontal asymptotes
##lim_(x rarr-oo)f(x)=lim_(x rarr-oo)3/2(e^x/(1-e^x))=##
##3/2lim_(x rarr-oo)(e^x/(1-e^x))~~3/2lim_(x rarr-oo)e^x/1=3/2*0=0##
##:. y=0## is a horizontal asymptote for ##x rarr-oo##
##lim_(x rarr+oo)f(x)=lim_(x rarr+oo)3/2(e^x/(1-e^x))=##
##3/2lim_(x rarr+oo)(e^x/(1-e^x))~~3/2lim_(x rarr+oo)(e^x/-e^x)=##
##=3/2*(-1)=-3/2##
##:. y=-3/2## is a horizontal asymptote for ##x rarr+oo##
graph{(3/2)*((e^x)/(1-e^x)) [-10, 10, -5, 5]}
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