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3a^2-16a+5
x = (16+sqrt((-16)^2-4(3)(5)))/2(3)
x= (-8 +- sqrt(8^2 - 4(1)(16)))/2(1) x = -4
-3 / 1 = -3
-3x^2+4x-2 --------------- = -3 x^2 + 5
-3x^2+4x-2=(-3)(x^2+5) -3x^2+4x-2=-3x^2-15 4x-2=-15 4x=-13 x=-13/4
1-6(x-1)⇐6+6(2x-2) 1-6x-7 ⇐ 6 + 12x - 12 6x-6 ⇐ 12x - 6 6x ⇐ 12x x ⇐ 2x
x=(6-y)/3 3x=6-y 3x-6 -3x+6
x=6y^3-4 x+4=6y^3 cbrt(x+4) = 6y cbrt(x+4)/6
(x-6)/(x+9) = y (y-6)/(y+9) = x (y-6) = x(y+9) (y-6) = xy + 9x
Compound interest
P=19000
r = 0.036
t = 14yr
A = P(1+r/n)^nt A = 19000(1+(.036/1))^(114) A = 19000(1+(.036/4))^(414) A = 19000(1+(.036/12))^(1214) A = 19000(1+(.036/365))^(36514) A = 19000e^(.036*14)= 31451.26
P = 10000 t = 112
Pe^(r*t)
r= 0.02 10000e^(.02*112) = 93933.31
r = 0.03 10000e^(.03*112) = 287891.91
r= .045 10000e^(.045*112) = 1544700.15
Pe^(rt) P=10000 r = .03 t = 6 10000e^(.036) = 11972.17
I=Prt I=10000*.055*6
64^(1/2) = sqrt(64) = 8
=
q^2 + 18q +77 >= 0 (x+7)(x+11) >= 0
-7 and -11
log2(4)=2
2^2=4
x^2-x-6 > 0 (x+2)(x-3)>0
so boundaries are x= -2 and x = 3
log3x^7-log3y-log3z^6 3logx-3logy-3logz^6
ln
(
e^4
p^2+6
)^1/7
1/7ln
(
e^4
p^2+6
)
1/7(ln(e^4)-ln(p^2+6))
1/7lne^4-1/7ln(p^2+6) 4/7-1/7ln(p^2+6)
1/5log
(
(25b^5)sqrt(y^2-5)
y(x+5)^2
)
log5(25b^5*sqrt(y^2-5)) - log5(y(x+5)^2) log5(25) + log5(b^5) + log5(sqrt(y^2-5)) - log5(y) - log5(x+5)^2) 2 + log5(b^5) + log5(sqrt(y^2-5)) - log5(y) -log5((x+5)^2) 2 + 5log5(b) + log5(sqrt(y^2-5)) - log5(y) - 2log5(x+5) 2 + 5log5(b) + 1/2log5(y^2-5) - log5(y) - 2log5(x+5)
10k(k+3)=7k-12 10k^2+30k=7k-12 10k^2+23k+12=0 (k+8)(k+15)=0 -8 -15
27
n^2-3n
- 3 =
9
n-3
sqrt(3n+22)+6=n sqrt(3n+22)=n-6 3n+22=(n-6)^2 3n+22=n^2-6n-36 n^2+9n+58=0
3^(2w-9)=(3^-2)^(w+6) 3^(2w-9)=3^(-2(w+6)) 3^(2w-9)=3^(-2w-12)
2w-9 = -2w-12 2w=-2w-3 4w=-3 w=-3/4
7^y = 14
log7(7)^x = log7(14) x = log7(14)
10^(7+8x) = 139000+3600 10^(7+8x) = 142600 log10(10)^(7+8x)=log10(142600) 7+8x=(log10(142600)-7)/8 7+8x = 5.1541 8x = -2.1541 x = .2692
450e^-0.2t=90 log450e(450e)^-0.2t=log450e(90) -0.2t=log450e(90) t=(log450e(90)/-0.2)
3z+15=3-z 4z+15=3 4z+12=0 z+3=0 z=-3
7log4(3w+1)+4=25 7log4(3w+1)=21 log4(3w+1)=3 4^3=3w+1 64=3w+1 63=3w 21=w
log10(q-1)=4.7 10^4.7=q-1 50118.7233627=q-1 50119.7233627=q 50119.7234=q
log3(y)=3-log3(y-6) y=3-(y-6) y=-9-y+6 y=-3-y 2y=-3 y=1.5
log3(y)=3-log3(y-6) log3(y(y-6)=3 y(y-6)=3^3 y^2-6y=27 y^2-6y-27=0 (y-9)(y+3)
log3(9)=3-log3(9-6) 2=2
lnx+ln(x-5)=ln(7x-27) ln(x(x-5))=ln(7x-27) x(x-5)=7x-27 x^2-5x=7x-27 x^2-12+27=0 (x+3)(x+9)=0
ln3+ln(3-5)=ln(7(3)-27) 1.09+3-undefined ( no good )
ln9+ln4=ln(36) 3.58351893846=3.58351893846
26000=13000(1+.03/12)^12x 2=(1+.03/12)^12x 2=1.0025^12x log1.0025(2)=log1.0025(1.0025^12x) 277.605301589 = 12x 23.1337751324 = x
A=Pe^rt 10000=8000e^.025t 1.25=e^.02.5t loge(1.25)=loge(e^.025t) loge(1.25) = .025t loge(1.25)/.025 = t 8.92574205257=t
150(2)^-t/6
120=150(2)^(-t/6) .8 = 2^(-t/6) log2(.8)=log2(2^(-t/6)) log2(.8)=-t/6 6log2(.8)=-t -6log2(.8)=t 1.93156856932=t
30=150(2)^(-t/6) 30/150=2^(-t/6) .2=2^-t/6) log2(.2)=-t/6 6log2(.2)=-t -6log2(.2)=t 13.9315685693
26=10log(I/10^-12) 2.6=log(I/10^-12) 10^2.6=I/10^-12 10^2.6*10^-12=I 10^-9.4=I
40=10log(I/10^-12) 4.0=log(I/10^-12) 10^4.0=I/10^-12 10^4.0*10^-12=I 10^-8=I
91+160ln(7+1) 91+160ln(8) = 423
450 = 91+160ln(x)
E=1/2(pi)s^4I 2E=pis^4I 2E/pis^4
-5. 2(-5)^2-2(-5)
2(25)+10 60
-4. 2(-4)^2-2(-4) 2(16)+8 32+8 40
-3. 2(-3)^2-2(-3) 2(9)+6 18+6 24
-2. 2(-2)^2-2(-2) 2(4)+4 8+4 12
167200.19 = 50000e^r(35) 167200.19/50000 = e^r(35) ln(167200.19/50000)=r35 ln(167200.19/50000)/35=r 0.034490538 3.4%
250000 = 50000e^(.034*x) 250000/50000 = e^(.034x) ln(5)=.034x 1.609/.034=x
P=23.4e^(0.00336t)
24.2=23.4e^10r 24.2/23.4 = e^10r ln(24.2/23.4)=10r ln(24.2/23.4)/10 = r 0.003361661079898 = r 0.00336 = r
23.1=19.5e^10r 23.1/19.5=e^10r ln(23.1/19.5)=10r ln(23.1/19.5)/10=r 0.016941815195804674 = r 0.01694 = r P=19.5e^0.01694t
P=19.5e^0.01694t P=19.5e^(0.01694(20))
P=23.4e^(0.00336t) 23.4e^(0.00336(20))
greater growth rate for south pacific
P=19.5e^0.01694t 30 = 19.5e^.01694t 30/19.5=e^(.01694t) ln(30/19.5)=.01694t ln(30/19.5)/.01694 = t
30 = 23.4e^(.00336t) 30/23.4 = e^(.00336t) ln(30/23.4) = .00336t ln(30/23.4)/.00336 = t
P=23.4e^(0.00336t)
.87=e^-(.000121t) ln(.87)=-.000121t ln(.87)/-.000121 = t
.275 = e^-.000121t ln(.275)/-.000121 = t
0.5 = e^-k(87.7) ln0.5 = -87.7k ln0.5/-87.7 = k 0.00790 = k
3.5e^-.00790t
3.5e^-.00790t = 1.7 e^-.00790t = 1.7/3.5 -.00790t = ln(1.7/3.5) t = ln(1.7/3.5)/-.00790 t = 91.4
10e^-k(6) = 0.5 e^-k(6) = 0.05 -6k = ln(.05) k = ln(.05)/-6 k = .1155
10e^-.1155t
6 = 10e^-.1155t .6 = e^-.1155t ln(.6) = -.1155t ln(.6)/-.1155 = t 4.4 = t
2/3 = 300e^-k174 (2/3)/300 = e^174k ln((1/3)/300) = -174k ln((1/3)/300)/-174 = k 0.03909 = k
300e^(-.03909t)
i was wrong idk why
150 = 300e^-.00631t
150/300 = e^-.00631t 1/2 = e^-.00631t ln(1/2) = -.00631t ln(1/2)/-.00631 = t
15.9e^0.01462(x) = 30
e^0.01462(x) = 30/15.9
0.01462(x) = ln(30/15.9) x = ln(30/15.9)/.01462
32^(x+5) = 4^(3x-1)
19=17-log2(2x+4) 2 = -log2(2x+4) 2^-2 = 2x + 4 2^-2 -4 = 2x (2^-2 -4)/2 = x -15/8
8000*.069*3
8000e^(.065*3)
36^1/2 = 6
7^2)^x+8) = 7^4x 7^(2x+16) = 7^4x 2x+16 = 4x 16 = 2x 8 = x
2 = -log2(2x+4) 2^-2 = 2x+4 1/4 = 2x + 4 1/4 - 4 = 2x -3.75 = 2x -3.75/2 = x -1.875 = x -1.875 = -15/8
15.9e^0.01462(x) = 30
e^0.01462(x) = 30/15.9
0.01462(x) = ln(30/15.9) x = ln(30/15.9)/.01462
( 37.5 35.9 39 38.1 + x ) / 5 = 35.2 37.5 + 35.9 + 39 + 38.1 + x = 5(35.2) 176 = 150.5 + x 176 = 150.5 + 25.5
11136 - 232x = 0 -232x = -11136 232x = 11136 x = 11136/232
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