Index
stringlengths 1
5
| Challenge
stringlengths 41
1.55k
| Answer in Latex
stringclasses 122
values | Answer in Sympy
stringlengths 1
774
| Variation
stringclasses 31
values | Source
stringclasses 61
values |
|---|---|---|---|---|---|
16501
|
If $\log_{2 \left(69\right) } x - 2 \left(63\right) \log _{2 \left(69\right) } y=2 \left(63\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*63*(2*log(x)*63 - log(2*69))**(-1)*log(2*69))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16502
|
If $\log_{2 \left(32\right) } x - 2 \left(64\right) \log _{2 \left(32\right) } y=2 \left(92\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*64*(2*log(x)*92 - log(2*32))**(-1)*log(2*32))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16503
|
If $\log_{2 \left(23\right) } x - 2 \left(97\right) \log _{2 \left(23\right) } y=2 \left(44\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*97*(2*log(x)*44 - log(2*23))**(-1)*log(2*23))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16504
|
If $\log_{2 \left(31\right) } x - 2 \left(79\right) \log _{2 \left(31\right) } y=2 \left(10\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*79*(2*log(x)*10 - log(2*31))**(-1)*log(2*31))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16505
|
If $\log_{2 \left(75\right) } x - 2 \left(13\right) \log _{2 \left(75\right) } y=2 \left(19\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*13*(2*log(x)*19 - log(2*75))**(-1)*log(2*75))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16506
|
If $\log_{2 \left(35\right) } x - 2 \left(78\right) \log _{2 \left(35\right) } y=2 \left(44\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*78*(2*log(x)*44 - log(2*35))**(-1)*log(2*35))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16507
|
If $\log_{2 \left(32\right) } x - 2 \left(60\right) \log _{2 \left(32\right) } y=2 \left(78\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*60*(2*log(x)*78 - log(2*32))**(-1)*log(2*32))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16508
|
If $\log_{2 \left(25\right) } x - 2 \left(67\right) \log _{2 \left(25\right) } y=2 \left(18\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*67*(2*log(x)*18 - log(2*25))**(-1)*log(2*25))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16509
|
If $\log_{2 \left(38\right) } x - 2 \left(17\right) \log _{2 \left(38\right) } y=2 \left(44\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*17*(2*log(x)*44 - log(2*38))**(-1)*log(2*38))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16510
|
If $\log_{2 \left(18\right) } x - 2 \left(92\right) \log _{2 \left(18\right) } y=2 \left(63\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*92*(2*log(x)*63 - log(2*18))**(-1)*log(2*18))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16511
|
If $\log_{2 \left(91\right) } x - 2 \left(23\right) \log _{2 \left(91\right) } y=2 \left(13\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*23*(2*log(x)*13 - log(2*91))**(-1)*log(2*91))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16512
|
If $\log_{2 \left(20\right) } x - 2 \left(69\right) \log _{2 \left(20\right) } y=2 \left(92\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*69*(2*log(x)*92 - log(2*20))**(-1)*log(2*20))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16513
|
If $\log_{2 \left(94\right) } x - 2 \left(41\right) \log _{2 \left(94\right) } y=2 \left(42\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*41*(2*log(x)*42 - log(2*94))**(-1)*log(2*94))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16514
|
If $\log_{2 \left(82\right) } x - 2 \left(43\right) \log _{2 \left(82\right) } y=2 \left(44\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*43*(2*log(x)*44 - log(2*82))**(-1)*log(2*82))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16515
|
If $\log_{2 \left(52\right) } x - 2 \left(19\right) \log _{2 \left(52\right) } y=2 \left(75\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*19*(2*log(x)*75 - log(2*52))**(-1)*log(2*52))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16516
|
If $\log_{2 \left(66\right) } x - 2 \left(99\right) \log _{2 \left(66\right) } y=2 \left(47\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*99*(2*log(x)*47 - log(2*66))**(-1)*log(2*66))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16517
|
If $\log_{2 \left(71\right) } x - 2 \left(52\right) \log _{2 \left(71\right) } y=2 \left(85\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*52*(2*log(x)*85 - log(2*71))**(-1)*log(2*71))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16518
|
If $\log_{2 \left(11\right) } x - 2 \left(24\right) \log _{2 \left(11\right) } y=2 \left(47\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*24*(2*log(x)*47 - log(2*11))**(-1)*log(2*11))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16519
|
If $\log_{2 \left(66\right) } x - 2 \left(31\right) \log _{2 \left(66\right) } y=2 \left(83\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*31*(2*log(x)*83 - log(2*66))**(-1)*log(2*66))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16520
|
If $\log_{2 \left(82\right) } x - 2 \left(26\right) \log _{2 \left(82\right) } y=2 \left(79\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*26*(2*log(x)*79 - log(2*82))**(-1)*log(2*82))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16521
|
If $\log_{2 \left(80\right) } x - 2 \left(79\right) \log _{2 \left(80\right) } y=2 \left(48\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*79*(2*log(x)*48 - log(2*80))**(-1)*log(2*80))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16522
|
If $\log_{2 \left(34\right) } x - 2 \left(49\right) \log _{2 \left(34\right) } y=2 \left(97\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*49*(2*log(x)*97 - log(2*34))**(-1)*log(2*34))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16523
|
If $\log_{2 \left(37\right) } x - 2 \left(80\right) \log _{2 \left(37\right) } y=2 \left(12\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*80*(2*log(x)*12 - log(2*37))**(-1)*log(2*37))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16524
|
If $\log_{2 \left(23\right) } x - 2 \left(70\right) \log _{2 \left(23\right) } y=2 \left(16\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*70*(2*log(x)*16 - log(2*23))**(-1)*log(2*23))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16525
|
If $\log_{2 \left(33\right) } x - 2 \left(38\right) \log _{2 \left(33\right) } y=2 \left(25\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*38*(2*log(x)*25 - log(2*33))**(-1)*log(2*33))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16526
|
If $\log_{2 \left(32\right) } x - 2 \left(96\right) \log _{2 \left(32\right) } y=2 \left(36\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*96*(2*log(x)*36 - log(2*32))**(-1)*log(2*32))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16527
|
If $\log_{2 \left(54\right) } x - 2 \left(71\right) \log _{2 \left(54\right) } y=2 \left(28\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*71*(2*log(x)*28 - log(2*54))**(-1)*log(2*54))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16528
|
If $\log_{2 \left(55\right) } x - 2 \left(13\right) \log _{2 \left(55\right) } y=2 \left(10\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*13*(2*log(x)*10 - log(2*55))**(-1)*log(2*55))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16529
|
If $\log_{2 \left(68\right) } x - 2 \left(93\right) \log _{2 \left(68\right) } y=2 \left(80\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*93*(2*log(x)*80 - log(2*68))**(-1)*log(2*68))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16530
|
If $\log_{2 \left(81\right) } x - 2 \left(67\right) \log _{2 \left(81\right) } y=2 \left(34\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*67*(2*log(x)*34 - log(2*81))**(-1)*log(2*81))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16531
|
If $\log_{2 \left(37\right) } x - 2 \left(90\right) \log _{2 \left(37\right) } y=2 \left(37\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*90*(2*log(x)*37 - log(2*37))**(-1)*log(2*37))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16532
|
If $\log_{2 \left(77\right) } x - 2 \left(53\right) \log _{2 \left(77\right) } y=2 \left(46\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*53*(2*log(x)*46 - log(2*77))**(-1)*log(2*77))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16533
|
If $\log_{2 \left(21\right) } x - 2 \left(12\right) \log _{2 \left(21\right) } y=2 \left(38\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*12*(2*log(x)*38 - log(2*21))**(-1)*log(2*21))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16534
|
If $\log_{2 \left(17\right) } x - 2 \left(86\right) \log _{2 \left(17\right) } y=2 \left(40\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*86*(2*log(x)*40 - log(2*17))**(-1)*log(2*17))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16535
|
If $\log_{2 \left(73\right) } x - 2 \left(35\right) \log _{2 \left(73\right) } y=2 \left(17\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*35*(2*log(x)*17 - log(2*73))**(-1)*log(2*73))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16536
|
If $\log_{2 \left(14\right) } x - 2 \left(50\right) \log _{2 \left(14\right) } y=2 \left(14\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*50*(2*log(x)*14 - log(2*14))**(-1)*log(2*14))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16537
|
If $\log_{2 \left(62\right) } x - 2 \left(95\right) \log _{2 \left(62\right) } y=2 \left(69\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*95*(2*log(x)*69 - log(2*62))**(-1)*log(2*62))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16538
|
If $\log_{2 \left(83\right) } x - 2 \left(16\right) \log _{2 \left(83\right) } y=2 \left(38\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*16*(2*log(x)*38 - log(2*83))**(-1)*log(2*83))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16539
|
If $\log_{2 \left(70\right) } x - 2 \left(27\right) \log _{2 \left(70\right) } y=2 \left(81\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*27*(2*log(x)*81 - log(2*70))**(-1)*log(2*70))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16540
|
If $\log_{2 \left(41\right) } x - 2 \left(90\right) \log _{2 \left(41\right) } y=2 \left(33\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*90*(2*log(x)*33 - log(2*41))**(-1)*log(2*41))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16541
|
If $\log_{2 \left(59\right) } x - 2 \left(40\right) \log _{2 \left(59\right) } y=2 \left(15\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*40*(2*log(x)*15 - log(2*59))**(-1)*log(2*59))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16542
|
If $\log_{2 \left(24\right) } x - 2 \left(87\right) \log _{2 \left(24\right) } y=2 \left(82\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*87*(2*log(x)*82 - log(2*24))**(-1)*log(2*24))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16543
|
If $\log_{2 \left(86\right) } x - 2 \left(32\right) \log _{2 \left(86\right) } y=2 \left(66\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*32*(2*log(x)*66 - log(2*86))**(-1)*log(2*86))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16544
|
If $\log_{2 \left(95\right) } x - 2 \left(28\right) \log _{2 \left(95\right) } y=2 \left(78\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*28*(2*log(x)*78 - log(2*95))**(-1)*log(2*95))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16545
|
If $\log_{2 \left(51\right) } x - 2 \left(52\right) \log _{2 \left(51\right) } y=2 \left(78\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*52*(2*log(x)*78 - log(2*51))**(-1)*log(2*51))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16546
|
If $\log_{2 \left(70\right) } x - 2 \left(63\right) \log _{2 \left(70\right) } y=2 \left(33\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*63*(2*log(x)*33 - log(2*70))**(-1)*log(2*70))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16547
|
If $\log_{2 \left(25\right) } x - 2 \left(50\right) \log _{2 \left(25\right) } y=2 \left(93\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*50*(2*log(x)*93 - log(2*25))**(-1)*log(2*25))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16548
|
If $\log_{2 \left(76\right) } x - 2 \left(44\right) \log _{2 \left(76\right) } y=2 \left(72\right) $, determine $y$, as a function of $x$
|
e**(-2*log(x)*44*(2*log(x)*72 - log(2*76))**(-1)*log(2*76))
|
Numeric-All-2-S
|
OlympiadBench
oe_to_maths_en_comp
2498
|
|
16549
|
If $f(x)=2 \left(71\right) x+ (1 \left(74\right) )$ and $g(f(x)) = 4 \left(97\right) x^{2}+ (1 \left(47\right) )$, determine an expression for $g(x)$.
|
47 + 97*(x - 74)**2*71**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16550
|
If $f(x)=2 \left(12\right) x+ (1 \left(72\right) )$ and $g(f(x)) = 4 \left(58\right) x^{2}+ (1 \left(69\right) )$, determine an expression for $g(x)$.
|
58*(x - 72)**2*12**(-2) + 69
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16551
|
If $f(x)=2 \left(41\right) x+ (1 \left(47\right) )$ and $g(f(x)) = 4 \left(89\right) x^{2}+ (1 \left(22\right) )$, determine an expression for $g(x)$.
|
22 + 89*(x - 47)**2*41**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16552
|
If $f(x)=2 \left(56\right) x+ (1 \left(65\right) )$ and $g(f(x)) = 4 \left(20\right) x^{2}+ (1 \left(55\right) )$, determine an expression for $g(x)$.
|
20*(x - 65)**2*56**(-2) + 55
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16553
|
If $f(x)=2 \left(60\right) x+ (1 \left(47\right) )$ and $g(f(x)) = 4 \left(93\right) x^{2}+ (1 \left(59\right) )$, determine an expression for $g(x)$.
|
59 + 93*(x - 47)**2*60**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16554
|
If $f(x)=2 \left(61\right) x+ (1 \left(18\right) )$ and $g(f(x)) = 4 \left(20\right) x^{2}+ (1 \left(82\right) )$, determine an expression for $g(x)$.
|
20*(x - 18)**2*61**(-2) + 82
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16555
|
If $f(x)=2 \left(59\right) x+ (1 \left(25\right) )$ and $g(f(x)) = 4 \left(23\right) x^{2}+ (1 \left(60\right) )$, determine an expression for $g(x)$.
|
23*(x - 25)**2*59**(-2) + 60
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16556
|
If $f(x)=2 \left(49\right) x+ (1 \left(90\right) )$ and $g(f(x)) = 4 \left(19\right) x^{2}+ (1 \left(95\right) )$, determine an expression for $g(x)$.
|
19*(x - 90)**2*49**(-2) + 95
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16557
|
If $f(x)=2 \left(13\right) x+ (1 \left(87\right) )$ and $g(f(x)) = 4 \left(58\right) x^{2}+ (1 \left(38\right) )$, determine an expression for $g(x)$.
|
38 + 58*(x - 87)**2*13**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16558
|
If $f(x)=2 \left(44\right) x+ (1 \left(26\right) )$ and $g(f(x)) = 4 \left(80\right) x^{2}+ (1 \left(61\right) )$, determine an expression for $g(x)$.
|
61 + 80*(x - 26)**2*44**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16559
|
If $f(x)=2 \left(95\right) x+ (1 \left(97\right) )$ and $g(f(x)) = 4 \left(56\right) x^{2}+ (1 \left(22\right) )$, determine an expression for $g(x)$.
|
22 + 56*(x - 97)**2*95**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16560
|
If $f(x)=2 \left(64\right) x+ (1 \left(58\right) )$ and $g(f(x)) = 4 \left(56\right) x^{2}+ (1 \left(59\right) )$, determine an expression for $g(x)$.
|
56*(x - 58)**2*64**(-2) + 59
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16561
|
If $f(x)=2 \left(84\right) x+ (1 \left(12\right) )$ and $g(f(x)) = 4 \left(32\right) x^{2}+ (1 \left(54\right) )$, determine an expression for $g(x)$.
|
32*(x - 12)**2*84**(-2) + 54
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16562
|
If $f(x)=2 \left(61\right) x+ (1 \left(11\right) )$ and $g(f(x)) = 4 \left(48\right) x^{2}+ (1 \left(63\right) )$, determine an expression for $g(x)$.
|
48*(x - 11)**2*61**(-2) + 63
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16563
|
If $f(x)=2 \left(27\right) x+ (1 \left(91\right) )$ and $g(f(x)) = 4 \left(69\right) x^{2}+ (1 \left(16\right) )$, determine an expression for $g(x)$.
|
16 + 69*(x - 91)**2*27**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16564
|
If $f(x)=2 \left(39\right) x+ (1 \left(83\right) )$ and $g(f(x)) = 4 \left(20\right) x^{2}+ (1 \left(66\right) )$, determine an expression for $g(x)$.
|
20*(x - 83)**2*39**(-2) + 66
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16565
|
If $f(x)=2 \left(14\right) x+ (1 \left(88\right) )$ and $g(f(x)) = 4 \left(78\right) x^{2}+ (1 \left(10\right) )$, determine an expression for $g(x)$.
|
10 + 78*(x - 88)**2*14**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16566
|
If $f(x)=2 \left(18\right) x+ (1 \left(40\right) )$ and $g(f(x)) = 4 \left(56\right) x^{2}+ (1 \left(14\right) )$, determine an expression for $g(x)$.
|
14 + 56*(x - 40)**2*18**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16567
|
If $f(x)=2 \left(39\right) x+ (1 \left(63\right) )$ and $g(f(x)) = 4 \left(66\right) x^{2}+ (1 \left(90\right) )$, determine an expression for $g(x)$.
|
66*(x - 63)**2*39**(-2) + 90
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16568
|
If $f(x)=2 \left(98\right) x+ (1 \left(33\right) )$ and $g(f(x)) = 4 \left(75\right) x^{2}+ (1 \left(69\right) )$, determine an expression for $g(x)$.
|
69 + 75*(x - 33)**2*98**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16569
|
If $f(x)=2 \left(96\right) x+ (1 \left(91\right) )$ and $g(f(x)) = 4 \left(38\right) x^{2}+ (1 \left(78\right) )$, determine an expression for $g(x)$.
|
38*(x - 91)**2*96**(-2) + 78
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16570
|
If $f(x)=2 \left(24\right) x+ (1 \left(75\right) )$ and $g(f(x)) = 4 \left(54\right) x^{2}+ (1 \left(10\right) )$, determine an expression for $g(x)$.
|
10 + 54*(x - 75)**2*24**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16571
|
If $f(x)=2 \left(67\right) x+ (1 \left(88\right) )$ and $g(f(x)) = 4 \left(49\right) x^{2}+ (1 \left(55\right) )$, determine an expression for $g(x)$.
|
49*(x - 88)**2*67**(-2) + 55
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16572
|
If $f(x)=2 \left(31\right) x+ (1 \left(53\right) )$ and $g(f(x)) = 4 \left(64\right) x^{2}+ (1 \left(75\right) )$, determine an expression for $g(x)$.
|
64*(x - 53)**2*31**(-2) + 75
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16573
|
If $f(x)=2 \left(76\right) x+ (1 \left(49\right) )$ and $g(f(x)) = 4 \left(67\right) x^{2}+ (1 \left(95\right) )$, determine an expression for $g(x)$.
|
67*(x - 49)**2*76**(-2) + 95
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16574
|
If $f(x)=2 \left(29\right) x+ (1 \left(73\right) )$ and $g(f(x)) = 4 \left(92\right) x^{2}+ (1 \left(62\right) )$, determine an expression for $g(x)$.
|
62 + 92*(x - 73)**2*29**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16575
|
If $f(x)=2 \left(42\right) x+ (1 \left(21\right) )$ and $g(f(x)) = 4 \left(77\right) x^{2}+ (1 \left(99\right) )$, determine an expression for $g(x)$.
|
77*(x - 21)**2*42**(-2) + 99
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16576
|
If $f(x)=2 \left(22\right) x+ (1 \left(64\right) )$ and $g(f(x)) = 4 \left(45\right) x^{2}+ (1 \left(41\right) )$, determine an expression for $g(x)$.
|
41 + 45*(x - 64)**2*22**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16577
|
If $f(x)=2 \left(16\right) x+ (1 \left(91\right) )$ and $g(f(x)) = 4 \left(37\right) x^{2}+ (1 \left(28\right) )$, determine an expression for $g(x)$.
|
28 + 37*(x - 91)**2*16**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16578
|
If $f(x)=2 \left(75\right) x+ (1 \left(52\right) )$ and $g(f(x)) = 4 \left(44\right) x^{2}+ (1 \left(56\right) )$, determine an expression for $g(x)$.
|
44*(x - 52)**2*75**(-2) + 56
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16579
|
If $f(x)=2 \left(56\right) x+ (1 \left(61\right) )$ and $g(f(x)) = 4 \left(14\right) x^{2}+ (1 \left(79\right) )$, determine an expression for $g(x)$.
|
14*(x - 61)**2*56**(-2) + 79
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16580
|
If $f(x)=2 \left(80\right) x+ (1 \left(36\right) )$ and $g(f(x)) = 4 \left(63\right) x^{2}+ (1 \left(85\right) )$, determine an expression for $g(x)$.
|
63*(x - 36)**2*80**(-2) + 85
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16581
|
If $f(x)=2 \left(34\right) x+ (1 \left(28\right) )$ and $g(f(x)) = 4 \left(25\right) x^{2}+ (1 \left(10\right) )$, determine an expression for $g(x)$.
|
10 + 25*(x - 28)**2*34**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16582
|
If $f(x)=2 \left(83\right) x+ (1 \left(23\right) )$ and $g(f(x)) = 4 \left(99\right) x^{2}+ (1 \left(16\right) )$, determine an expression for $g(x)$.
|
16 + 99*(x - 23)**2*83**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16583
|
If $f(x)=2 \left(94\right) x+ (1 \left(99\right) )$ and $g(f(x)) = 4 \left(31\right) x^{2}+ (1 \left(62\right) )$, determine an expression for $g(x)$.
|
31*(x - 99)**2*94**(-2) + 62
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16584
|
If $f(x)=2 \left(86\right) x+ (1 \left(21\right) )$ and $g(f(x)) = 4 \left(97\right) x^{2}+ (1 \left(71\right) )$, determine an expression for $g(x)$.
|
71 + 97*(x - 21)**2*86**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16585
|
If $f(x)=2 \left(99\right) x+ (1 \left(21\right) )$ and $g(f(x)) = 4 \left(54\right) x^{2}+ (1 \left(41\right) )$, determine an expression for $g(x)$.
|
41 + 54*(x - 21)**2*99**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16586
|
If $f(x)=2 \left(15\right) x+ (1 \left(97\right) )$ and $g(f(x)) = 4 \left(10\right) x^{2}+ (1 \left(58\right) )$, determine an expression for $g(x)$.
|
10*(x - 97)**2*15**(-2) + 58
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16587
|
If $f(x)=2 \left(84\right) x+ (1 \left(23\right) )$ and $g(f(x)) = 4 \left(25\right) x^{2}+ (1 \left(50\right) )$, determine an expression for $g(x)$.
|
25*(x - 23)**2*84**(-2) + 50
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16588
|
If $f(x)=2 \left(45\right) x+ (1 \left(79\right) )$ and $g(f(x)) = 4 \left(22\right) x^{2}+ (1 \left(25\right) )$, determine an expression for $g(x)$.
|
22*(x - 79)**2*45**(-2) + 25
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16589
|
If $f(x)=2 \left(33\right) x+ (1 \left(26\right) )$ and $g(f(x)) = 4 \left(16\right) x^{2}+ (1 \left(50\right) )$, determine an expression for $g(x)$.
|
16*(x - 26)**2*33**(-2) + 50
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16590
|
If $f(x)=2 \left(76\right) x+ (1 \left(38\right) )$ and $g(f(x)) = 4 \left(50\right) x^{2}+ (1 \left(43\right) )$, determine an expression for $g(x)$.
|
43 + 50*(x - 38)**2*76**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16591
|
If $f(x)=2 \left(36\right) x+ (1 \left(35\right) )$ and $g(f(x)) = 4 \left(81\right) x^{2}+ (1 \left(10\right) )$, determine an expression for $g(x)$.
|
10 + 81*(x - 35)**2*36**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16592
|
If $f(x)=2 \left(97\right) x+ (1 \left(42\right) )$ and $g(f(x)) = 4 \left(84\right) x^{2}+ (1 \left(43\right) )$, determine an expression for $g(x)$.
|
43 + 84*(x - 42)**2*97**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16593
|
If $f(x)=2 \left(12\right) x+ (1 \left(26\right) )$ and $g(f(x)) = 4 \left(65\right) x^{2}+ (1 \left(57\right) )$, determine an expression for $g(x)$.
|
57 + 65*(x - 26)**2*12**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16594
|
If $f(x)=2 \left(81\right) x+ (1 \left(89\right) )$ and $g(f(x)) = 4 \left(89\right) x^{2}+ (1 \left(76\right) )$, determine an expression for $g(x)$.
|
76 + 89*(x - 89)**2*81**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16595
|
If $f(x)=2 \left(62\right) x+ (1 \left(42\right) )$ and $g(f(x)) = 4 \left(14\right) x^{2}+ (1 \left(53\right) )$, determine an expression for $g(x)$.
|
14*(x - 42)**2*62**(-2) + 53
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16596
|
If $f(x)=2 \left(85\right) x+ (1 \left(54\right) )$ and $g(f(x)) = 4 \left(95\right) x^{2}+ (1 \left(42\right) )$, determine an expression for $g(x)$.
|
42 + 95*(x - 54)**2*85**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16597
|
If $f(x)=2 \left(76\right) x+ (1 \left(72\right) )$ and $g(f(x)) = 4 \left(37\right) x^{2}+ (1 \left(79\right) )$, determine an expression for $g(x)$.
|
37*(x - 72)**2*76**(-2) + 79
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16598
|
If $f(x)=2 \left(73\right) x+ (1 \left(74\right) )$ and $g(f(x)) = 4 \left(57\right) x^{2}+ (1 \left(20\right) )$, determine an expression for $g(x)$.
|
20 + 57*(x - 74)**2*73**(-2)
|
Numeric-All-2-S
|
OlympicArena
Math_1381
|
|
16599
|
Solve the following integral.
$\int_0^{\frac{\pi}{2 \left(50\right) }} \frac{ \left(69\right) x \sin(2 \left(50\right) x)}{(1 \left(30\right) ) + \cos^2(2 \left(50\right) x)} dx$
|
pi*50**(-2)*30**(-1/2)*atan(30**(-1/2))*69/4
|
Numeric-All-2-S
|
OBMU 2019 - Q21
|
|
16600
|
Solve the following integral.
$\int_0^{\frac{\pi}{2 \left(75\right) }} \frac{ \left(53\right) x \sin(2 \left(75\right) x)}{(1 \left(66\right) ) + \cos^2(2 \left(75\right) x)} dx$
|
pi*75**(-2)*66**(-1/2)*atan(66**(-1/2))*53/4
|
Numeric-All-2-S
|
OBMU 2019 - Q21
|
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