Friday
August 1, 2014

Posts by Henry


Total # Posts: 8,921

math
1. 0x+6y-5x = 5x+6y. 2. 9x^2+10+4x^2+7 = 13x^2+17.

algebra
P1(1,-3),P2(2,4). D^2 = (2-1)^2 + (4+3)^2 = 50 D = 7.07

Maths
tan 60o = (Y1+Y2)/X1 = 3000/X1 X1*tan 60 = 3000 X1 = 3000/tan60 = 1732 m. tan 30o = (Y1+Y2)/(X1+X2)=3000/(1732+X2) (1732+X2)*tan30 = 3000 1732+X2 = 3000/tan30 = 5196 X2 = 5196-1732 = 3464 m tan30 = Y2/X2 = Y2/3464 Y2 = 3464*tan30 = 2,000 m. Y1 = 3000-2000 = 1,000 m. = Distance...

introduction to finance-16
1. P = Po*(1+r)^n Po = $4,000. r = (4%/100%) = 0.04 n = 1Comp./yr * 5yrs = 5 Compounding periods. Plug the above values into the given Eq and get: P = $4,866.61. 2. P = Po(1+(y-1))*(1+r)^n Y = Length of loan = 5 years. P = 4000(1+4)*(1.04)^5 = $24,333.06

math
Eq1: x*y = -84 Eq2: x+y = 5 x+y = 5 y = 5-x In Eq1, replace y with 5-x: x*(5-x) = -84 5x-x^2 = -84 -x^2+5x+84 = 0 Use Quadratic Formula and get: X = -7, and 12.

Math
The angles are assumed to be complimentary(sum=90o). DCE + ECF = 90o 4x+15 + 6x-5 = 90 10x + 10 = 90 10x = 80 X = 8 DCE = 4*8 + 15 = 47o

Mechanics, Waves and Optics
Wt. of crate=m*g=18kg * 9.8N/kg=176.4 N. Fv = 176.4*cos0 = 176.4 N. = Force perpendicular to the surface. Fk = u*Fv = 0.5 * 176.4 = 88.2 N. = Force of kinetic friction. Fap*cos20-Fk = m*a Fap*0.94-88.2 = 18*0 = 0 0.94Fap = 88.2 Fap = 93.9 N. = Force applied b. Tension = Fap = ...

physical science
V = Vo + a*t = 10 m/s. 6 + a*2 = 10 2a = 4 a = 2 m/s^2.

geometry
a. RS + ST = RT 8y+4 + 4y+8 = 15y-9. Solve for y. b. Replace y with the value calculated in prob. a.

Algebra
P = Po(1+r)^n P = $5000 Po = $3500 r = (4.5%/12)/100% = 0.00375 = Monthly % rate expressed as a decimal. n = 12Comp/yr * T yrs = 12T = The # of compounding periods. P = 3500*(1.00375)^12T = 5000 (1.00375)^12T = 5000/3500 = 1.42857 Take Log of both sides: 12T*Log (1.00375) = Lo...

Mathematic
1. 2/(2/3) + 3/4/(4/5). 2/(2/3) + (3/4)/(4/5) = 2*(3/2) + (3/4)*(5/4) = 6/2 + 15/16 = 48/16 + 15/16 = 63/16 2. (2/5)(2/3)/(5/6)/(3/10) = (2/5)(2/3)(6/5)(10/3) = 240/225 = 48/45 = 16/15. The answer cannot be less than one.

All subjects
You are welcome! We are glad we can help.

MatHS
The angle of inclination is always between 0o and 180o and is measured CCW from the positive x-axis. A. x+y+1 = 0 x+y = -1 Tan A = m = -A/B = -1/1 = -1 Ar = -45o = Reference angle. A = -45 + 180 = 135o. B. 3-2y = 9x 9x+2y = 3 Tan A = m = -A/B = -9/2 = -4.5 Ar = -77.47o A = -77...

maths
See previous post: Tue,8-6-13,12:09 PM

maths
See previous post: 12:09 PM.

maths
Y = 2x Tan A = m1 = 2 A = 63.43o (-1,7/3),(0,2). m2 = Tan B = (2-7/3)/(0+1) = (-1/3)/1 = -1/3. B = -18.43o = -18.43o C = A-B = 63.43 - (-18.43) = 81.9o = Angle between A and B.

Math
What is the question?

maths
CORRECTION: m1 = m2 = -A/B = 6/2 = 3 Y = mx + b = -1 3*3 + b = -1 b = -10 Eq: Y = 3x - 10

maths
(3,-1). -6x + 2y = 1 Parallel lines have equal slopes: m1 = m2 = -A/B = 6/-2 = -3 Y = mx + b = -1 -3*3 + b = -1 b = 8 Eq: Y = -3x + 8

mathematics
P(-6,-2). 3x + 2y = 6 m1 = -A/B = -3/2 m2 = -(-2/3) = 2/3 = Negative reciprocal Y = mx + b = -2 2x/3 + b = -2 (2*-6)/3 + b = -2 -4 + b = -2 b = 2. Eq: Y = 2x/3 + 2

physics
See previous post.

physics
Assuming no wind: Vo*t + 0.5g*t^2 = 1.4 m. 0 + 0.5*1.63*t^2 = 1.4 0.815t^2 = 1.4 t^2 = 1.72 t = 1.31 s.

algebra
Yes, post your problem.

Physics
h1 = Vo*t + 0.5g*t^2 h1 = -9*18 + 4.9*18^2 = 1426 m Above ground when bag was released. h2 = 9*18 = 162 m.. Above point of release. h = 1426 + 162 = 1588 m. Above ground.

physics
A = 3.45 m/s[90o] B = 2.39 m/s[270o] C = V m/s 3.45[90o]+2.39[270]+V = 0 @ the peak of its' trajectory. 3.45*cos90+2.39*cos270+i3.45*sin90+i2.39*sin270 + V = 0 0+0 + 3.45i-2.39i + V = 0 0 + 1.06i + V = 0 V=-1.06i = 1.06 m/s[270o]=1.06m/s[-90o].

math
3X5Y/2Y8 = 15x/16. 15x/16 = 1 = The smallest whole number. 15x = 16 X = 16/15 = 1 1/15. According to my analysis, x cannot equal 0,2,4, nor 6.

science
The current through all elements of a circuit is the same IF there are no elements in parallel.

Physics
tan A = 50m/79m = 0.63291 A = 32.3o East of North = 57.7o CCW. b. Vs = 1.9m/sin57.7 = 2.25 m.[57.7o] = Velocity of swimmer. Vc = 2.25m/s[57.7o] - 1.9[90o] X = 2.25*cos57.7 - 1.9*cos90=1.20 m/s. Y=2.25*sin57.7 - 1.9*sin90 = 0 m/s. b. Vc = 1.20 + i0 = 1.20 m/s =Velocity of the c...

physics
See 6:26 PM post.

physics
See 5:58 PM post.

physics
20*Log(V1/Vo) = 38 db Log(V1/Vo) = 1.9 V1/Vo = 79.4

physics
130db/19 = 6.84 db.

physics
130db/19 = 6.84 db.

physics
a. 10*Log(I1/Io) = 17db Log(I1/Io) = 1.7 I1/Io = 50.1 b. 10*Log(I1/Io) = -32 db Log(I1/Io) = -3.2 I1/Io = 0.00063

physics
Vs = 332 m/s @ 0oC. = Velocity of sound. Vs = 332m/s + (22-0)oC*0.6m/s/oC Vs = 332 + 13,2 = 345.2 m/s. @ 22oC. a. d = Vs*t = 345 * 0.8 = 276 m b. d1 = d V*T = Vs*(T+0.8) 3*10^8T = 345(T+0.8) 3*10^8T = 345T+276 3*10^8T = 276 T = 92*10^10^-8 s. d = V*T = 3*10^8 * 92*10^-8 = 276 m.

math
2L + 2W = 42 2*11 + 2W = 42 2W = 20 W = 10 L = 11

Physics
K = k1 + k2 = 35 + 55 = 90N/cm.

Math (Triangles)
A = B = (180-40.33)/2 = 69.83o = Base angles. sinA/a = sinC/c sin69.83/320 = sin40.33/c c*sin69.83 = 320*sin40.33 c = 320*sin40.33/sin69.83 = 220.6 mm Or cosA = 0.5*AB/AC AC*cosA = 0.5*AB AB = 2AC*cosA = 2*320*cos669.83=220.7 mm

Discrete Mathematics
Year 1--2013--3^0*500 = 500 Rabbits Year 2--2014--3^1*500 = 1500 Year 3--2015--3^2*500 = 4500 Year n--20xx--3^(n-1)*500 = 100,000 3^(n-1)*500 = 100000 3^(n-1) = 200 (n-1)*Log 3 = Log 200 n-1 = Log 200/Log 3 = 4.82 n = 5.82 or 6 Yrs.

Discrete Mathematics
Fx) = 2x + 3*1/x F(x) = 2x + 3/x

hs math
P = 249.73/mo * 72mo = $17,980.56 P = (Po*r*t)/(1-(1+r)^-t) = 17,980.56 r = (3.599%/12)/100% = 0.0029992 = Monthly % rate expressed as a decimal. (Po*0.0029992*72)/(1-(1.0029992)^-72)= 17,980.56 Po*0.21594/(1-(1-(1.0029992)^-72)=17980.56. 0.21594Po/0.19396 = 17980.56 1.11332Po...

physics
Eq1: 4*t = d Eq2: 5*t = 6 + d In Eq2, replace d with 4t: 5t = 6 + 4t 5t-4t = 6 t = 6 s. In Eq1, replace t with 6: d = 4 * 6 = 24 m.

physics
L1 = 0.810 m. Temp. Change = +18o C. T.C. = 1.9*10^-5/C a. T^2 = 4pi^2(L/g) T^2 = 39.4(0.81/9.8) = 3.25653 T = 1.8046 s. b. L2 = L1 + L1*(T.C.)*18 L2=0.81 + 0.81(1.9*10^-5)*18=0.81027702 m. T^2 = 39.4(0.81027702/9.8)=3.25764 T = 1.8049 s. Change in period = 1.8049-1.8046 = 0.0...

physics
m1*g = 0.30kg * 9.8N/kg = 2.94 N. L1 = 0.26 m. m2*g = 1.90kg * 9.8N/kg = 18.62 N. L2 = 0.75 m. a. K = (N2-N1)/(L2-L1) K = (18.62-2.94)/(0.75-0.26) = 32 N/M b. (2.94N/32N) * 1M = 0.092 M. L + 0.092 = 0.26 L = 0.26 - 0.092 = 0.168 M.

General Physics
Wt. of block=m*g = 4kg * 9.8N/kg=39.2 N. Et = Ek + Ep = 0.5m*V^2 Ek + Ep = 0.5*4*(5.1)^2 = 52 J. 0 + Ep = 52 @ hmax. Ep = 52 @ hmax Ep = mg*h = 52 39.2h = 52 h = 1.33 m. Dist. up ramp = h/sinA = 1.33/sin13= 5.91 m.

General Physics
F1 = (0.2m/1m) * 28N = 5.6 N. To stretch spring 0.2 m. Work = F1 * d = 5.6 * 0.2 - 1.12 J. F2 = (0.2m+0.06m)/1m) * 28 N.=7.28 N. Work = F2 * d = 7.28 * 0.26 = 1.89 J. 1.89-1.12 = 0.77 J. to stretch it an additional 0.06 m.

General Physics
m*g = 7453 N. m*g = 7453 N. Fp = 7453*sin25.9 = 3256 N. = Force parallel to incline. Fap = Fp = 3256 N. = Force applied. Work = F * d = 3256 * 4.04 = 13,152 J. fp =

geometry
<1 = <2 = 4x-9 = 63o. 4x-9 = 63 4x = 63+9 = 72 X = 18o. The value of 9 is 9.

physics
Vo = 60km/hr = 60000m/3600s = 16.67 m/s. V^2 = Vo^2 + 2a*d a = (V^2-Vo^2)/2d a = (0-(16.67)^2)/60 = -4.63 m/s^2. Wt. of car = m*g = 15000 N. mass = 15000/9.8 = 1531 kg F = m*a = 1531 * -4.63 = -7.1 N.

physics
a=(V-Vo)/t = (-48.4--43.8)/1.08=-85.37 m/s^2. F = m*a = 0.148 * -85.37 = -12.6 N.

Math
3^2 + 3 = 12. Units digit = 2.

calculus
V^2 = Vo^2 + 2g*h h = (V^2-Vo^2)/2g h = ((190)^2-(30)^2)/64 = 550 Fi.

compound intrest
T = 365 + 57 = 422 Days. r = (3.5%/365)/100% = 9.58904*10^-5 = Daily % rate expressed as a decimal. I = Po*r*T I= 32000*0.00009589*422 = $1294.90

Physics
Vc = 81000m/3600s = 22.5 m/s. = Velocity of car. F = ((V+Vr)/(V+Vc)))*Fh = 958Hz. ((345+22.5)/(343-22.5))*Fh = 958 367.5Fh/322.5 = 958 1.140Fh = 958 Fh = 841 Hz. = Freq. of horn.

Physics
A. h = Vo*t + 0.5g*t^2 = 0.481 m. 0 + 4.9t^2 = 0.481 t^2 = 0.09816 t = 0.313 s. Each ball. B. V = Vo + g*t V = 0 + 9.8*0.313 = 3.07 m/s. Each ball.

algebra
2^3*sqrt(18)/6 = 8*sqrt(9*2)/6 = 8*3*sqrt(2)/6 = 24*sqrt(2)/6 = 4*sqrt(2). sqrt means square root.

science
See previous post.

science
A = 5m[240o] B = 2.5+6i C = -2.5i X = 5*cos240 + 2.5 = 0 Y = 5*sin240 + 6 - 2.5 = -0.83 D = 0-0.83i = 0.83m[-90o].

general physics
V^2 = Vo^2 + 2g.h Vo^2 = V^2-2g.h Vo^2 = 0-(-19.8)*190sin13 = 837.7 Vo = 28.9 m/s.

dynamics
See 10:35am post.

Dynamics
Ek = 0.5m*V^2 *h - = 750 * 6^2 = 27,000 J. Wt. = Fg = 1500kg * 9.8N/kg = 14,700 N. Ep = Fg * h = 27000-Fk*d 14700*5*sin20 = 27000-Fk*5 25138.5 = 27000-5Fk 5Fk = 27000-25138.5 = 1861.5 Fk = 372 N.

dynamics
V^2 = Vo^2 + 2g*h h = (V^2-Vo^2)/2g h = (0-625)/-19.6 = 31.89 m. NOTE: V = 0 @ max. Ht.

general physics
Di + Db = Dsw 917 + Db = 1025 kg/m^3 Db = 108 kg/m^3 = Density of the bear. Mass of bear = 6.76m^3*108kg/m^3=730 kg Wt. of bear = 730kg * 9.8N/kg = 7154 N.

science
CORRECTION: Ek = 84.672 J.

science
V^2 = Vo^2 + 2g*d Vo^2 = V^2-2g*d Vo^2 = 0-(-19.6*1.2 = 23.52 Vo = 4.85 m/s. Ek = 0.5m*Vo^2 = 3.6*(4.85)^2 = 11.76 J. vo^2

MATH
h = 125-5t^2 = 0 -5t^2 + 125 = 0 t^2 - 25 = 0 (t+5)(t-5) = 0 t = -5 t = 5 s. V = g*t = 9.8 * 5 = 49 m/s.

physics
Vs = 25 m/s = Velocity of the source. F = 260 Hz(NOT 26Hz). Fo = 240 Hz. Vr = Velocity of the receiver(person) F = (V+Vr)/(V-Vs)*Fo = 260 Hz. (V+0)/(V-25)*240 = 260 240V/(V-25) = 260 240V = 260V - 6500 -20V = -6500 V = 325 m/s.

Math
P = (Po*r*t)/(1-(1+r)^-t) Po = $81,000. r = (9%/12)/100% = 0.0075 = Monthly % rate expressed as a decimal. t = 25yrs. * 12mo/yr. = 300 Months. Plug the above values into the given Eq and get: P = $203,924.72 Monthly Payments = P/t Monthly Int. = (P-Po)/t. Monthly Prin. = (P/t)...

physics/science
See previous post.

physhcs
Xc = 1/W*C = 1/314.2*3*10^-6 = 1061 Ohms Z = R-jXc = 500 -j1061 = 1173[-64.8o]. 1. I = V/Z=12/1173[-64.8o]=0.01023[64.8] 2. Vc= I * Xc = 0.01023[64.8]*1061[-90o]= 10.85 Amps.[-25.2o] 3. A = -25.2o 4. P = I^2*R = (0.01023)^2 * 500= 0.0523 W. 5. Pf = cosA = cos(-64.8) = 0.426

phys ics
b. V = (0.243/0.335) * 28m/s = 20.3 m/s.

physics
Circumference=pi*2r=3.14*0.67=2.1=2.1 m. Va = 24.1m/s * 6.28rad/2.1m=72.1 rad/s.

physics
d = 0.5g*t^2 = 5.95 m. 4.9t^2 = 5.95 t^2 = 1.21 s. t = 1.10 s. 2.55rev/s * 1.1s = 2.8 revs.

physics
a. 28.9rad/s * 1rev/6.28rad = 4.60 rev/s. t = (13.6/4.60) * 1s = 3.0 s. b. V = Vo + at = 0 When @ rest. 28.9 + a*3 = 0 3a = -28.9 a = -9.63 rad/s^2.

physics
a. d = 2870rev * 6.28rad/rev = 18,024 rad. t = 18,024rad/131rad/s = 138 s. V = Vo + a*t = 131 rad/s Vo + 0.170*138 = 131 Vo = 131-23.4 = 108 rad/s. b. t = 138 s.

physics
V = Vo + at = 4.4 rad/s. 0 + 4.2t = 4.4 t = 4.4/4.2 = 1.05 s.

physics
d1 + d2 = 2pi rads = A complete circle. V1t + V2t = 2pi 2.46*10^-3 + 7.91*10^-3 = 6.28 10.37*10^-3t = 6.28 t = 606 s.

Math
See previous post.

Math
See previous post.

Math
Eq1: x^2 + y^2 = 34 Eq2: x + y = 2 x + y = 2 Y = 2 - x In Eq1, replace Y with 2 - x. x^2 + (2-x)^2 = 34 x^2 + 4 - 4x + x^2 = 34 2x^2 -4x + 4 = 34 2x^2 -4x - 30 = 0 Divide both sides by 2: x^2 - 2 - 15 = 0 (x+3)(x-5) = 0 x+3 = 0 X = -3. Y = 2- x = 2-(-3) = 5 x-5 = 0 X = 5. Y = ...

physics
Wt. = (6.0/1.0)^2 * 45.8 = 1649 N.

Elementary mechanics
My answer is the Rise Time or time to reach max. height. R = Vo*cosA * (Tr+Tf) Tr = Tf. Therefore, R = Vo*cosA * 2Tr. Tr = Rise time. Tf = Fall time. Vo*cosA = Hor. component of initial velocity.

Physics
Circumference=pi*D = 3.14 * 41=128.8 cm= 1.288 m. Vo = (86rev/min)*1min/60s*1.288m/rev = 1.85 m/s. V = (342/86) * 1.85 = 7.34 m/s a=(V-Vo)/t = (7.34-1.85)/3.4=1.61 m/s^2 d =Vo*t + 0.5*a*t^2 d=1.85*3.4 + 0.5*1.61*(3.4)^2= 15.6 m.

physics
Wt. = Fg = m*g = 60kg * 9.8N/kg=588 N.= Wt. of skier. Fp=588*sin35 = 337 N.=Force parallel to incline. Fv = 588*cos35 = 482 N. = Force perpendicular to incline. Fk = u*Fv = 0.08 * 482 = 38.5 N. = Force of kinetic friction. d =h/sinA = 2.5/sin35 = 4.36 m. Ek + Ep = Ekmax - Fk*d...

Physics
Wt. = m*g = 10kg * 9.8N/kg = 98 N. = Wt. of the luggage. F = 98N.[60o] = Force of luggage. Fp = 98*sin60 = 84.9 N. = Force parallel to incline. Fv=98*cos60 = 49 N.=Force perpendicular to incline = Normal. a. Work=mg * h = 98 * 6.5sin60= 552 J. b. Work = -98 * 6.5sin60 = -552 J...

physics
Density of water = 1000kg/m^3. V = 3m * 0.20m * 0.05m = 0.03 m^3=Vol. of board. 1 - (350/1000) = 0.65 = 13/20.

Physics
Impulse = m*V1-m*V2 Impulse = 2.4*2.5 - 2.4*1.5 = 2.4kgm/s

Elementary mechanics
F1 = 100[170o] F2 = 100[50o] X = 100*cos170+100*cos50o = -34.2 N. Y = 100*sin170+100*sin50 = 94 N. tan Ar = Y/X = 94/-34.2 = -2.74838 Ar = -70o = Reference angle. A = -70+180 = 110o Fr = X/cosA = -34.2/cos110 = 100N.[110o]

Trigonometry
Draw a picture of the situation: 1.Draw ver. line AC with A on the bottom. 2. Add point D on line AC. 3. Draw a hor. line from A to the left. Label it AB. Now we have a rt angle. 4. Draw hyp. BC. 5. Draw hyp. BD. <ABC = <ABD + <DBC = 61.5o 56.33 + <DBC = 61.5 <D...

Physics
T^2 = 4*pi^2(L/g) 1a. Longer. A smaller g increases the ratio of L/g which increases the period. 1b. Unchanged. The mass is not included in the Eq. 1c. Shorter. The ratio of L/g decreases which decreases the period. 1d. Unchanged. The ratio of L/g remains the same. Therefore, ...

science
The 100W bulb.

Physics
Wc = m*g = 1650kg * 9.8N/kg = 16,170 N.= Wt. of car. k = 16,170N./3.5m. = 4620 N/m.

Physics
Wc = m*g = 1840kg * 9.8N/kg = 18032 N. = Wt. of car. Fc = 18,032N[12.5o] = Force of the car. Fp = 18,032*sin12.5 = 3903 N. = Force parallel to incline. F-Fp = m*a = m*0 = 0 F-3903 = 0 F = 3903 N. Parallel to the incline Work = F*d = 3903 * 14 = 54,642 J.

physics
g = 9.8/6 = 1.633333 m/s^2 on moon. d = o.5g*t^2 = 50 m. 0.5*1.63333*t^2 = 50 0.81666t^2 = 50 t^2 = 61.22 t = 7.82 s.

physics
b. Fn = m*a a = Fn/m = (940-521)/95.9 = 4.37m/s^2. V = Vo + a*t = 0 Vo = -a*t = -(-4.37*1.63) = 7.1 m/s.

physics
Wp = m*g = 95.9kg * 9.8N/kg = 940 N. = Wt. of player. a. Fk = 0.554 * 940 = 520.7 N.

physics
CORRECTION: b. hmax = 3 + 0.141 = 3.141 m.

physics
a. V^2 = Vo^2 + 2g*h h(up) = (V^2-Vo^2)/2g. h(up) = (0-2.76)/-19.6 = 0.141 m. V^2 = Vo^2 + 2g*h V^2 = 0 + 19.6(0.141+3) = 61.6 V = 7.85 m/s. b. 0.141 m.

math
See previous post: 7:09pm.

Physics
d = 0.5g*t^2 = 122.5 m. 4.9t^2 = 122.5 t^2 = 25 t = 5 s. = Fall time. d = r*t = 122.5 m. 343t = 122.5 t = 0.357 s. T = 5 + 0.357 = 5.357 s.

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