Math
1,7,7,13
statistics
range=max-min=99-78=21 sample mean=(78+91+93+93+99)/5=90.8 (78-90.8)^2=163.84 (91-90.8)^2=0.04 (93-90.8)^2=4.84 (99-90.8)^2=67.24 sample variance=(163.84+0.04+4.84+4.84+67.24)/4=60.2
calculus
The equation of this plane is -3(x-7)+1(y-1)+2(z-5)=0 or -3x+y+2z+10=0
math
Let Y=1/(X+1) then y:1, 1/2, 1/3, 1/4 P(Y=y):1/6, 1/2, 1/5, 2/15 E(Y)=1*1/6+1/2*1/2+1/3*1/5+1/4*2/15
calculus
PQ^2=1+9+4=14 PR^2=25+1+9=35 QR^2=16+4+1=21
math
3*5+6^2+54-5
math
From the terms of problem => r=1 doesn't satisfy (S13=21, S21=13). From my proof => such G.P. doesn't exist.
math
I'll try to show that the equation of Reiny 21r^21-13r^13=8 has only one real solution r=1. Let F(r)=21r^21-13r^13-8, F(1)=0. F'(r)=441r^20-169r^12= =169r^12(441/169r^8-1)=169r^2(21/13r^4+1)* (21/13r^4-1)=169r^2(21/13r^4+1)* (sqrt(21/13)r^2+1)(sqrt(21/13)r^2-1) F'...
calc 1
f'(c)=(f(4)-f(1))/(4-1) f(4)=4/6=2/3 f(1)=1/3 f'(c)=1/9 f'(x)=(x+2-x)/(x+2)^2 2/(c+2)^2=1/9 (c+2)^2=18 c+2=3*sqrt(2)
1/2 cup fraction word problem
1/2=(1*7)/(2*7)=7/14
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