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Vipster
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Left hand side - sec(2x)csc(2x)= 1/ cos(2x) 1/sin(2x) = 1/(Cos2x)* 1/(2 Sinx Cosx) Right Hand side = 1/2Sinx Equating LHS & RHS 1/{Cos2x}* 1/(2 Sinx Cosx) = 1/2Sinx or 1/{Cos2x}* 1/cos x = 1 or {Cos2x}* Cosx = 1 this actually only holds true for x = 0 and
kg--->g/1000, to get kg on the top of the fraction divide "g" by 1000 m^3 ----> (100cm)^3 = 1000000cc = 1000000ml ml = m^3/1000000 so 4g/ml = 4* 1/1000*1000000 kg/(m^3) = 4 * 1000000/1000 = 4000kg/m^3
interest - P* R * t /100 P = $7915 R = 9% t = 9 months = 9/12 yrs = 0.75 I = 7915*9*0.75/100
look at it as a triangle Angle is 4 degree tan of 4 = Side opposite(10m)/ Side adjacent distance required = Side adjacent = 10 / tan 4
divide by 5 27 56 30 divide by 3 9 56 10 divide by 2 9 28 5 answer is 5 x 3 x 2 x 9 x 28 x 5
V(t) = dS/dt = 18t^2 - 14t -9 Acceleration = dV/dt = 36t-14 Plug the value of "t" in the above and that's the answer
Force required to accelerate the car vertically = m * (v^2) = 1200 * (0.8^2) = 1200 * 0.64 This force will be equal to the tension on the rope.
Potential energy at the topmost point = mg(2r) Kinetic energy at dip bottommost point= 1/2 m (v^2) so conservation of energy means mg 2r = 1/2 m(v^2) or 4rg= v^2 or v = 2sqrt(rg)
probability of an incorrect address = 5/100 to have atleast 1 incorrect address out of the 12 customers (choice of 1 out of 12 customers) 12C1 x (5/100) = (12!/ 1! 11!) (5/100) = 12 x (5/100) = 60/100 So for none to be incorrect it will be (1 - Prob of
1st spot can be filled in 4 ways (Matt, Bob, Amy or John) 2nd spot can be filled in 3 ways (since 1st spot is now filled by one of the 4) 3rd spot will be filled in 2 ways 4rd spot will be filled in 1 way since the rest all spots are taken Total # of ways
Kinetic energy = 1/2 m (v^2) you know the KE and the speed (have to convert km/h into m/s) find the "m" using the formula
How about calculating compound interest CI = P * {(1+ R/100)^N} P = Principal R = Rate of interest N = No. of years CI is the compound interest generated So you first go for the bracket (1+ R/100) ---- B then do the "^N" --- O and then finally multiply by
you gotto look at he numbers at hand if it ends in a 5 or 0 then it can be divided by 5, if it ends in a multiple of 2 , then number is divisible by 2 if the digits added up are divisible by 3 then number is divisible by 3 that's how you choose, you first
x + 3x = 60 ; x boys ; x = 15 x + 2x = 135; x boys; x = 45 so combined total 60 boys & (45+90)girls ratio is 135 : 60
yes, because the bracket takes precedence it would be undefined
135 56 150 divide by 5 27 56 30 divide by 3 9 56 10 divide by 2 9 28 5 so the LCM is 5 x 3 x 2 x 9 x 28 x 5 = 37800
the sandwich can be chosen in 13 ways and chips in 5 ways so total combinations possible = 13x 5 = 65 different types of lunches
you gotto differentiate the function so if T= 700* (t^-2) + 4t + 10 dT/dt = 700* (-2) (t^ -3) +4 now just plug in t = 1 in the above same with the others too
X * 0.07 + (7000-X) * 0.11 = 690 0.07X + 770 - 0.11X = 690 0.04X = 80 X = 2000 @ 7% 5000 @ 11%
8 litres of 40% acid 3.2 litres acid and 4.8 litres of water lets say you add x litres 3.2 / (8+ x) = 10% 3.2 = 0.8 + 0.1x x = 24 litres of water needs to be added
c1 v1 + c2 v2 = c3 (v1+v2) 5 x 6 + 100(Pure acid) x v2 = 40(6+v2) 30 + 100v2 = 240 + 40v2 60v2 = 210 v2 = 21/6 = 7/2 = 3.5ml is the answer
C1 V1 = C2 V2 0.4 x 65 = 0.8 x V2 V2 = 65/2 = 32.5 gallons amount that must evaporate = 65-32.5 = 32.5
C1 x V1 + C2 x V2 = C3 x (V1+V2) 0.25 x 40 + 0.60 x V2 = 0.30 x (40+V2) 10 + 0.60V2 = 12 + 0.30V2 0.30V2 = 2 V2 = 20/3 litres
Not sure what you exactly want but here is what you will need to get your answers: V1 - Velocity of the jet V2 - Velocity of Wind So 2500km/(V1+V2) = 2.5hrs ----- (1) 2000km/(V1-V2) = 2.5hrs ----- (2) Solving for the above 2 equations: 2500V1 -2500V2 =
lets say you want LCM of 2 and 6 . we know it is 6 Similarly you have here 11(z-3) and 33(z-3); 33(z-3) can be written as 11*3 (z-3) So the LCM should be 33(z-3)
9x-5y = 2; y = 9/5x -(2/5) (using y=mx+c) Slope of the given line = 9/5 hence the required line will have the same slope(9/5) since it is parallel. Now putting the given point(5,-8)in y=mx+c; since it passes through (5,-8) -8 = m * 5 + c where m= slope =
