The number of solutions tox1+x2+x3+x4+x5≤1
in nonnegative integers:
Each xn can become =1,the remainings xn become=0,or all xn become=0.
Example:x1∈{1}{x2,x3,x4,x5}∈{0}or{x1,x2,x3,x4,x5}∈{0}
The number of solutions for nonnegative integers is 6.
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BC=3,AC=19 and AB=13.BC<(AC−AB)The requirements are pointless.
f(x)=12(x+2)/(x+1) grafic
At which integer-x is f(x) a integer?
There, f(x)=b.
No, that's not helpful. It would be helpful if you explained your solution to us.
Find the number of ordered pairs (a,b).
a+2a+1=b12
1+21+1=18123+23+1=15125+25+1=1412
11+211+1=1312
(a,b)∈{(1,18) ;(3,15) ;(5,14) ;(11,13)}
The number of solutions is 4.
Let ω be a nonreal root of x3=1.Compute (1−ω+ω2)6+(1+ω−ω2)6.
x3=1x=3√13√1 is not a transcendental number. 3√1=1ω=1(1−1+12)6+(1+1−12)6=2
0
Find the maximum value of 3x+4y+5z+x3+4x2yz+z5xy2.
Plane geometry
z2=x2+y2 Pythagorean theoremy=xz2=2x2z=x√2x2+y2+z2=1x2+x2+2x2=1
4x2=1x=12
f(x)=3x+4y+5z+x3+4x2yz+z5xy2f(x)=3x+4x+5x√2+x3+4x3x√2+(x√2)5x3f(x)=x3+6√2x2+5√2x+7x according to WolframAlphaf(x0.5)=0.53+6√2(0.5)2+5√2(0.5)+7(0.5)=9.28185ddx=3x2+3⋅252x+5√2+7=0x∈{−4.6477;−1.009}
f(x)max=(−4.6477)3+6√2(−4.6477)2+5√2(−4.6477)+7(−4.6477)f(x)max=17.4979
Find AB.
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AB=√409+(15sin(120°−arctan203))2−2∗√409∗15sin(120°−arctan203)∗cos60°=22.4
The path to the farthest corner is \sqrt (2^2+1^2)= \sqrt 5.
Franklin reaches 100% of the cube surface.
If K is the area of the triangle, what should be determined if K is the area of the triangle?