has no antiderivative in terms of elementary functions (polynomials, exponentials, logarithms, trigonometric functions, etc), but there is a special function defined to fit that role called the error function,
, where
![\mathrm{erf}(x)=\displaystyle\frac2{\sqrt\pi}\int_0^xe^{-t^2}\,\mathrm dt](https://tex.z-dn.net/?f=%5Cmathrm%7Berf%7D%28x%29%3D%5Cdisplaystyle%5Cfrac2%7B%5Csqrt%5Cpi%7D%5Cint_0%5Exe%5E%7B-t%5E2%7D%5C%2C%5Cmathrm%20dt)
By the fundamental theorem of calculus, we can see that
![\dfrac{\mathrm d}{\mathrm dx}\mathrm{erf}(x)=\dfrac2{\sqrt\pi}e^{-x^2}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cmathrm%7Berf%7D%28x%29%3D%5Cdfrac2%7B%5Csqrt%5Cpi%7De%5E%7B-x%5E2%7D)
which means we have
![\displaystyle\int e^{-x^2}\,\mathrm dx=\dfrac{\sqrt\pi}2\mathrm{erf}(x)+C](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%20e%5E%7B-x%5E2%7D%5C%2C%5Cmathrm%20dx%3D%5Cdfrac%7B%5Csqrt%5Cpi%7D2%5Cmathrm%7Berf%7D%28x%29%2BC)
Answer:
A = $3,926.71
Step-by-step explanation:
Given: Principal (P) = $3200, Annual Rate (R) = 4.1%, Time = 5 years
To find: How much money would he have in the account after 5 years, if he made no deposits or withdrawals during that time?
Formula: ![A = P(1 + r/n)^nt](https://tex.z-dn.net/?f=A%20%3D%20P%281%20%2B%20r%2Fn%29%5Ent)
Solution: Compound interest is one of the most important concepts to understand when managing your finances. It can help you earn a higher return on your savings and investments, but it can also work against you when you're paying interest on a loan
First, convert R as a percent to r as a decimal
r = R/100
r = 4.1/100
r = 0.041 rate per year,
Then solve the equation for A
A = P(1 + r/n)![^{nt}](https://tex.z-dn.net/?f=%5E%7Bnt%7D)
A = 3,200.00(1 + 0.041/12)![^{(12)(5)}](https://tex.z-dn.net/?f=%5E%7B%2812%29%285%29%7D)
A = 3,200.00(1 + 0.003416667)![^{(60)}](https://tex.z-dn.net/?f=%5E%7B%2860%29%7D)
A = $3,926.71
Hence, Jay would have $3,926.71 after 5 years is if he made no deposits or withdrawals during that time.
-10(-12+30)
-10 multiplied by 18
-180
We know that
surface area of the square pyramid=area of the base+4*[area of lateral triangle]
area of the base=b²----> area of square
b=6 ft
area of square=6*6---> 36 ft²
area of lateral triangle=b*h/2
b=6 ft
h=9 ft
area of lateral triangle=6*9/2---> 27 ft²
surface area of the square pyramid=36+4*27----> 144 ft²
the answer is
144 ft²