Thursday

February 26, 2015

February 26, 2015

Total # Posts: 10,138

**physics**

a=(V^2-Vo^2)/2d=(0-15^2)/14=-16.07 m/s^2 d = (V^2-Vo^2)/2a d = (0-(32^2))/-32.14 = 31.86 m.
*March 3, 2014*

**Physics**

F = m*g = 0.05kg * 9.8N/kg = 0.49 N. d = 18-12 = 6 cm = 0.06 m. k = 0.49N/0.06m = 8.17N/m.
*March 3, 2014*

**Consumer Math**

Po = $235,000 APR = ? T = 30 yrs?
*March 3, 2014*

**Alegbra**

Eq1: Po1+ Po2 = 5000 Po1*0.05*1 + Po2*0.08*1 = 331 0.05Po1 + 0.08Po2 = 331 Eq2: 5Po1 + 8Po2 = 33100 Multiply Eq1 by -5 and add Eq1 and Eq2: -5Pol - 5Po2 = -25,000 +5Po1 + 8Po2 = 33,100 Sum: 3Po2 = 8100 Po2 = $2700 Pol = 5000-2700 = $2300.
*March 2, 2014*

**Math**

See previous post.
*March 2, 2014*

**MATH**

Po = Amt. invested @ 6%. Po/3 = Amt. invested @ 8% Po + Po/3 = $33,000 3Po + Po = 99000 4Po = 99000 Po = $24,750 @ 6%.(2nd security). Po/3 = 24,750/3 = $8,250 @ 8%.(1st security). Int. = 24,750*0.06*1yr + 8,250*0.08*1yr= $2145.
*March 2, 2014*

**mat116**

Y = 3x-7 Y = 3x+5 Each has a slope of 3. Y-intercepts are -7 and 5.
*March 2, 2014*

**science**

X = -122 km Y = -15 km Vw = d/t = 15/0.52 = 28.8 km/h B. Tan Ar = Y/X = -15/-122 = 0.12295 Ar = 7.0o = Reference angle. A = 7 + 180 = 187o = 7o S of W. C. X = 225 km/h. Y = 42 km/h. Tan A = 42/225 = 0.18667 A = 10.57o S of W. Pilot should head 10.57o N of W.
*March 2, 2014*

**Physics**

a. Range = Vo^2*sin(2A)/g = 60 m. Vo^2*sin(60)/9.8 = 60 0.0884Vo^2 = 60 Vo^2 = 679 Vo = 26.06 m/s.[30o] b. Yo = 26.06*sin30 = 13.03 m/s = Ver. component. hmax = (Y^2-Yo^2)/2g hmax = (0-13.03^2)/-19.6 = 8.66 m.
*March 2, 2014*

**Pre-Calculus**

Vo = 32Ft/s[35o] Xo = 32*cos35 = 26.21 Ft/s. Yo = 32*sin35 = 18.35 Ft/s. a. Y = Yo + g*Tr = 0 @ max. ht. Tr=(Y-Yo)/g = (o-18.35)/-32.4=0.566 s = Rise time or time to reach max. ht. hmax = ho + Yo*t + 0.5g*Tr^2 hmax = 4.5 + 18.35*0.566 - 16.2*0.566^2 = 9.70 Ft above gnd. b. ...
*February 28, 2014*

**Physics**

h = 0.5g*t^2 = 4.9*2^2 = 19.6 m.
*February 28, 2014*

**Math**

V = 325mph[340o] + 30mph[300o] X = 325*cos340 + 30*cos300 = 320.4 mph = Hor. component. Y = 325*sin340 + 30*sin300 = -137.1 mph = Ver. component. TanA = Y/X = -137.1/320.4 = -42802 A = -23.17o,CW = 336.8 CCW. V = 320.4/cos336.8 = 348.6mph[336.8o]
*February 28, 2014*

**physics**

Work = F*d = 2 * 0 = 0
*February 28, 2014*

**physics**

d = r*t = 3 m. r * 0.3 = 3 r = 10 m/s. = Rate of speed.
*February 28, 2014*

**Algebra**

1. Quadratic. 2. h = Yo*0.75 - 16.2*0.75^2 = 77 Ft. Yo*0.75 - 9.11 = 77 0.75Yo = 86.11 Yo = 114.82 Ft/s. Y = Yo + g*Tr = 0 @ max. ht. Tr=(Y-Yo)/g = (0-114.82)/-32.4 = 3.54s. = Rise time. hmax = Yo*Tr + 0.5g*Tr^2 hmax=114.82*3.54 - 16.2*3.54^2=203.8 Ft. Eq: h = -16.2t^2 + 114.82t
*February 28, 2014*

**math**

r mi/h When leaving. (r-20)mi/h When returning. (r + (r-20))22 = 1400 mi. r + 22r-440 = 1400 23r = 1400+440 = 1840 r = 80 mi/h r-20 = 80-20 = 60 mi/h. = Speed on return trip.
*February 27, 2014*

**Math**

P(2,-7), M(x,y), Q(-4.-1) X = (x1+x2)/2 = (2+(-4))/2 = -1. Y = (y1+y2)/2 = (-7+(-1))/2 = -4. M(-1,-4)
*February 27, 2014*

**Physics**

a. Speed = 120m/20s = 6 m/s. b. Speed = (70m-30m)/(10s-5s) = 8 m/s. c. No, Jack did not travel at a constant speed: 30m/5s = 6 m/s after 5 s. 70m/10s = 7 m/s after 10 s.
*February 27, 2014*

**math**

a. $28/mo * 24mo. = $672. b. $672 - $500 = $172 c. $500/$28/mo = 18 Mo.
*February 27, 2014*

**physics**

See previous post: Wed, 2-26-14, 9:07 PM.
*February 27, 2014*

**Physics**

post it.
*February 27, 2014*

**Physics**

h = 0.5g*t^2 = 150 m. 4.9t^2 = 150 t^2 = 30.61 t = 5.53 s. = Fall time. d = Xo * t = 150m/s * 5.53 s = 830 m.
*February 27, 2014*

**Alegbra**

Width = W Ft. Length = (2W + 3)Ft P = 2W + 2(2W+3) = 72 2W + 4W+6 = 72 6W = 72-6 = 66 W = 11 Ft. Length = 2*11 + 3 = 25 Ft
*February 27, 2014*

**physics**

Tr = 2.68/2 = 1.34 s. = Rise time. V = Vo + g*Tr = 0 @ max. ht. Vo = -(g*Tr) = -(-9.8*1.34) = 13.13 m/s. D = h - ho = 1m - 1m = 0
*February 26, 2014*

**physical science**

a = (V-Vo)/t = (20-0)/15 = 1.33 m/s^2.
*February 26, 2014*

**physics**

a = (V-Vo)/t = (11.9-0)10 = 1.19 m/s^2.
*February 26, 2014*

**Physics**

Correction: Work = 180*cos33 * 1577 = 238,065 J.
*February 26, 2014*

**Physics**

Vo = 11km/h = 11,000m/3600s = 3.056 m/s. d=r*t=3.056m/s * 8.6min * 60s/min=1577 m Work = F*d = 180*cos33 * 1577 = 238 J. Power = F*V = 180*cos33 * 3.056 = 461.3 J./s = 461.3 Watts.
*February 26, 2014*

**Physics**

Dx = Xo * T = 59 m. Xo * 4.8 = 59 Xo = 12.29 m/s = Hor. component of initial velocity. Vo = Xo/cosA = 12.29/cos43 = 16.81 m/s k = F/d = m*g/d = 72*9.8/3.7m=191N/m
*February 26, 2014*

**Physics**

a.=Wt. of skier=m*g=79kg9.8N/kg=774.2 N. Fp = 774.2*sin30 = 387.1 N. = Force parallel to the slope. Work = F*d = 387.1 * 80 = 30,968 J. b. Power=F*V = 387.1 * 3.4=1316 J./s. = 1316 Watts. 1316W * 1hp/746W. = 1.76 hp.
*February 26, 2014*

**Physics 130**

PEmax = mg*hmax - FE PEmax = 20*9.8*25 - FE = (4900-FE) J. KE + PE = 4900 - FE 0.5m*V^2 + mg*h = 4900-FE 10*16^2 + 196*10 = 4900-FE 2560 + 1960 = 4900-FE 4520 = 4900-FE FE = 4900-4520 = 380 J. = Energy loss due to friction.
*February 25, 2014*

**math**

r = d/t = (1500-1200)/1min = 300 m/min = Rate of speed. T = 1500m * 1min/300m = 5 Min.
*February 25, 2014*

**physics**

V^2 = X^2 + Y^2 = 22^2 + 25^2 = 1109 V = 33.3 m/s.
*February 25, 2014*

**physics**

PE = mg*h = 0.272*9.81 * 0.71 = 1.89 J.
*February 25, 2014*

**math**

AD/AB = DE/BC AD/6 = 20/8. Solve for AD.
*February 25, 2014*

**physics**

A. Work = F*cosA * d = 43 J. 60*cosA * 2.0 = 43 120*cosA = 43 cosA = 0.35833 A = 69o B. a = (V^2-Vo^2)/2d a = (2.7^2-0)/4 = 1.82 m/s^2. F*cos69 = m*a 60*cos69 = m*1.82 m = 60*cos69/1.82 = 11.80 kg.
*February 25, 2014*

**physics**

Incomplete.
*February 25, 2014*

**physics**

Work = F*d = 1.24 * 0 = 0
*February 25, 2014*

**physics**

hmax = (V^2-Vo^2)/2g hmax = (0-18^2)/-19.6 = 16.53 m. V^2 = Vo^2 + 2g*h V^2 = 18^2 - 19.6*(16.53/2) = 162 V = 12.73 m/s. Momentum = m*V = 0.13 * 12.73 = 1.65 kg-m/s.
*February 24, 2014*

**physics**

See 12:35 PM post.
*February 24, 2014*

**physics**

r = Vr/I = = (9-7.8)/1.5*10^-3=800 Ohms
*February 24, 2014*

**physics**

L = Lo + a(T-To)Lo = 20 cm Lo + 19*10^-6(200-20)Lo = 20 Lo + 0.00342Lo = 20 1.00342Lo = 20 Lo = 19.93 cm. = Initial length.
*February 24, 2014*

**physics**

Eff. = Eo/Ei = (7000-3000)/7000 = 0.57 = 57%
*February 24, 2014*

**Physics**

L = V*(1/F) = V/F F = V/L = 1.97*10^8/3.81*10^-7 Hz.
*February 24, 2014*

**science**

post it.
*February 24, 2014*

**science**

F = 3000*cos30
*February 24, 2014*

**physics**

Vo = 18m/s[39o] Xo = 18*cos39 = 13.99 m/s. Yo = 18*sin39 = 11.33 m/s. Y = Yo + g*Tr = 0 @ max ht. 11.33 - 9.8*Tr = 0 9.8Tr = 11.33 Tr = 1.16 s. = Rise time. hmax = ho + (Y^2-Yo^2)/2g hmax = 22 + (0-11.33^2)/-19.6 = 28.55 m. Above gnd. h = 0.5g*t^2 = 28.55 m. 4.9*t^2 = 28.55 t^...
*February 23, 2014*

**physics**

V^2 = X^2 + Y^2 = 2^2 + 10^2 = 104 V = 10.20 m/s.
*February 23, 2014*

**PHYSICS**

Wt. of stone = m*g Fp = mg*sin30=Force parallel to incline. Fn = mg*cos30 = Normal force = Force perpendicular to incline. Fs = u*Fn = Force of static friction. Fp-Fs = m*a = m*o = 0 Fp = Fs mg*sin30 = u*mg*cos30 Divide both sides by mg: sin30 = u*cos30 u = sin30/cos30 = 0.577...
*February 23, 2014*

**PHYSICS**

Wt. of block=m*g = 126kg * 9.8N/kg=1235N = Fn = Normal force. Fk = u*Fn = 0.7 * 1235 = 864.5 N.= Force of kinetic friction. Fap-Fk = m*a = m*0 = 0 Fap = Fk = 864.5 N = Force applied.
*February 23, 2014*

**Physics**

a. Wt.of box=m*g=7.8kg * 9.8N/kg=76.44 N =Fn=Normal force or force perpendicular to the floor. Fs = u*Fn = u*76.44 N.=Force of static friction. Fap-Fs = m*a 48 - u*76.44 = m*0 = 0 u*76.44 = 48 u=0.628 = Coefficient of static friction b. A. No, it is a ratio. u = Fs/Fn c. Fap-...
*February 23, 2014*

**physics**

h = Yo*t + 0.5g*t^2 = 34.3 39.2t - 4.9t^2 = 34.3 -4.9t^2 + 39.2t - 34.3 = 0 t = 1 s. (Used Quad. Formula).
*February 23, 2014*

**Physics**

V = Vo + a*t = 27.8 0 + a*3.4 = 27.8 a = 8.18 m/s^2. V = Vo + a*t = 0 + 8.18*5.1 = 41.70 m/s.
*February 22, 2014*

**Physics**

Range = Vo^2*sin(2A)/g 200^2*sin(160)/9.8 = 1396 m.
*February 22, 2014*

**Physics**

See Related Questions: Wed,2-19-14,9:27 PM.
*February 22, 2014*

**physics**

Range = Vo^2*sin(2A)/g = 301.5 m. Vo^2*sin(50)/g = 301.5 .07817Vo = 301.5 Vo^2 = 3857 Vo = 62.10 m/s.
*February 22, 2014*

**physics**

To calculate the required force, we'll need to know the force of friction or the coefficient of frictional force.
*February 22, 2014*

**physics**

A. F = Fp = 71.5*sin24.1 = 29.20 N. B. Fn = 71.5*cos24.1 = 65.27 N. = Normal force = Force perpendicular to the plane Fs = u*Fn = 0.26 * 65.27 = 16.97 N = Force of static friction. F-Fp-Fs = m*a = m*0 = 0 F-29.20-16.97 = 0 F = 46.17 N. C. Fk = u*Fn = 0.13 * 65.27 = 8.49 N. = ...
*February 22, 2014*

**physics**

Fp=mg*sin16.6 = 509.6*sin16.6=145.6 N. = Force parallel to the ramp. Fn = 509.6*cos16.6 = 488.4 N. = Normal force = Force perpendicular to the ramp. d = Vo*t + 0.5a*t^2 = 3.98 m. 0 + 0.5a*4.1^2 = 3.98 8.405a = 3.98 a = 0.474 m/s^2. Fp-Fk = m*a 145.6 - Fk = 52*0.474 -Fk = 24.62...
*February 22, 2014*

**Physics**

Vo=20mi/h * 5280Ft/mi*1h/3600s=29.33Ft/s a = (V^2-Vo^2)/2d a = (0-29.33^2)/40 = -21.51 Ft/s^2. V = Vo + a*t = 0 29.33 - 21.51*t = 0 21.51t = 29.33 t = 1.36 s. To stop.
*February 22, 2014*

**Physics**

1.Fs = mg*sin A = 583.1*sin1o=10.18 N. 2. Fn = mg*cos1o = 583.1*cos1o=583.0 N.
*February 21, 2014*

**Physics**

1. a=(V-Vo)/t = (25.7-0)/0.54=47.6 m/s^2 2. F = m*a = 900.7 * 47.6 = 42,867 N.
*February 21, 2014*

**physics**

See previous post: Thu,2-20-14,5:05 PM.
*February 21, 2014*

**Physics**

Incomplete.
*February 21, 2014*

**Physics**

a. Fe = 710N.[11o] = Exerted force. Xe = 710*cos11 = 697.0 N. = Hor. component of exerted force. a = Xe/m = 697/89.1 = 7.82 m/s^2. b. V = Vo + a*t = 0 + 7.82*0.7=5.48 m/s. NOTE: I used 11o for the given angle, because 110o is not possible.
*February 21, 2014*

**physics**

c. a = (95-75-12)/21 = 0.381 m/s^2. d. a = (95-75-20)/21 = 0/21 = 0.
*February 20, 2014*

**Math**

6/15 = 30/Y Solve for Y.
*February 20, 2014*

**physics**

Wt. of block = 71.5 N. Fp = 71.5*sin24.1 = 29.20 N. = Force parallel to the plane. Fn = 71.5*cos24.1 = 65.27 N. = Normal force = Force perpendicular to the plane. Fs = u*Fn = 0.26 * 65.27 = 16.97 N. = Force of static friction. F-Fp-Fs = m*a = m*0 = 0 F-29.20-16.97 = 0 F = 46....
*February 20, 2014*

**Finance**

P = Po(1+r)^n = $1,000,000 Po = $420,000 r=Monthly % rate expressed as a decimal. n = 12comp/yr * 23yrs = 276 Compounding periods. P = 420,000(1+r)^276 = 1,000,000 (1+r)^276 = 1,000,000/420,000 = 2.38095 276*Log(1+r) = Log 2.38095 Log(1+r) = Log 2.38095/276 = 0.00136504 1+r = ...
*February 20, 2014*

**physics**

Speed = 80km/h = 80000m/3600s = 22.22m/s a = (V-Vo)/t = (22.22-0)/16 = 1.4 m/s^2.
*February 20, 2014*

**math**

Hyp. = 200 yds. X = 200*cos43.2 = 145.8 yds. Y = 200*sin43.2 = 136.9 yds. Total = 200 + 145.8 + 136.9 = 482.7 yds.
*February 20, 2014*

**Physics**

A. 0.250kW * 10h/day * 365days/yr. = 912.5 kWh./yr Cost = 912.5kWh/yr * $0.15/kWh=$137/yr. B. (0.100/0.250) * 912.5kWh/yr=365kWh/yr Cost = 365kWh/yr * $0.15/kWh = $55/yr Savings = 137 - 55 = $82/yr $100/$82 = 1.22 Years.
*February 19, 2014*

**Physics**

Wb = m*g = 21kg * 9.8N/kg = 205.8 N. = Wt. of the block. Fp = 205.8*sin33 = 112.1 N. = Force parallel to the incline. Fe-Fp = m*a = m*0 = 0 Fe - 112.1 = 0 Fe = 112.1 N. = Force exerted.
*February 19, 2014*

**Physics**

Y^2 = Yo^2 + 2g*h = o Yo^2 - 19.6*(150-50) = 0 Yo^2 = 1960 Yo = 44.27 m/s. = Ver. component of the initial velocity. Vo = Yo/sin A = 44.27/sin30 = 88.54 m/s. = Initial velocity. Xo = Vo*cos A = 88.54*cos30 = 76.68 m/s. = Hor. component of initial velocity. Y = Yo + g*Tr = 0 @ ...
*February 19, 2014*

**Physics**

The procedure is the same as your 8:56 PM. post.
*February 19, 2014*

**Physics**

Vo = 150m/s[85o] 1. Xo = 150*cos85 = 13.07 m/s. 2. Yo = 150*sin85 = 149.4 m/s. 3. X = Xo 4. Y = 0 5. a = g = 9.8 m/s^2. 6. h = ho + (Y^2-Yo^2)/2g h = 20 + (0-149.4^2)/-19.6 = 1159 m. Above the plain. 7. Y = Yo + g*t = 0 @ peak. 149.4 -9.8t = 0 9.8t = 149.4 Tr = 15.2 s. = Rise ...
*February 19, 2014*

**Physics**

Tf = 5.7/2 = 2.85 s. = Fall time. h = Yo*t + 0.5g*Tf^2 h = 0 + 4.9*2.85^2 = 39.8 m.
*February 19, 2014*

**algebra**

Correction: Y = (2/3)x - 1.
*February 19, 2014*

**algebra**

2x - 3y = 3 -3y = -2x + 3 Y = (-2/3)x - 1. Slope-intercept form. I don't know which form you want.
*February 19, 2014*

**physic**

Incomplete.
*February 19, 2014*

**physic**

d = 40km[315o]+2.8km[30o]+5.2km[112o] X = 28.28 + 2.425 - 1.948 = 28.76 km. Y = -28.28 + 1.4 + 4.821 = -22.06 km. d = sqrt(28.76^2+(-22.06)^2) = 36.2 km. NOTE: To find X, multiply by the cosine; to find Y, multiply by the sine.
*February 19, 2014*

**physic**

Speed=1450mi/h = 1450mi/3600s=0.403mi/s.
*February 19, 2014*

**math**

First Day: X-pencils sold. 2X-notebooks sold. Second Day: 2X-pencils sold. 3X-notebooks sold. First Day: X + 2X = 18 Pencils X = 6 Pencils. 2x + 3x = 30 Notebooks X = 6 Notebooks First Day: X = 6 Pencils sold. 2x = 2*6 = 12 Notebooks sold. Second Day: 2x = 2*6 = 12 Pencils ...
*February 19, 2014*

**Math**

4. P = Po*r*t/(1-(1+r)^-t)) Po = $700 r = (15%/12)/100% = 0.0125 = Monthly % rate expressed as a decimal. t = 12 Months. Plug the above values into the given Eq and get: P = 758.17 Monthly payment = P/12 5. Po = 0.80 * 128,000 = t = 30yrs * 12mo/yr = 360 mo. Answer: P = $283,...
*February 19, 2014*

**Math**

4. P = Po*r*t/(1-(1+r)^-t)) Po = $700 r = (15%/12)/100% = 0.0125 = Monthly % rate expressed as a decimal. t = 12 Months. Plug the above values into the given Eq and get: P = 758.17 Monthly payment = P/12 5. Po = 0.80 * 128,000 = t = 30yrs * 12mo/yr = 360 mo. Answer: P = $283,...
*February 19, 2014*

**Physics**

F = F1 + F2 = -9.5 + 19.5[10o] F = -9.5 + 19.5*cos10 + (19.5*sin10) F = -9.5 + 19.20 + 3.39i F = 9.7 + 3.39i a = X/m = 9.7/21 = 0.462 m/s^2.
*February 19, 2014*

**Physics**

a. Tan A = Y/X = -100/38 = -2.63158 A = -69.2o = 69.2o S of E=20.8o E of S. The bird must head 20.8o W of S. b. d = V*t = 600 km 100t = 600 t = 6 h.
*February 19, 2014*

**Physics**

A. F = F1 + F2 = 81N[80o] + 90N[22o] F=(81*cos80+90*cos22)+(81*sin80+90*sin 22)i = 97.51 + 113.5i F = sqrt(97.51^+113.5^2) = 149.6 N. B. Tan A = Y/X = 113.5/97.51 = 1.16398 A = 49.3o = Direction.
*February 19, 2014*

**physics**

V^2 = Vo^2 + 2a*d a = (V*2-Vo^2)/2d a = (0.59^2-0)/0.86 = 0.405 m/s^2. Fn = m*a = 72 * 0.405 = 29.1 N.
*February 19, 2014*

**physics**

Y^2 = Yo^2 + 2g*h = 0 Yo^2 - 19.6*0.291 = 0 Yo^2 = 5.70 Yo = 2.39 m/s = Ver. component of initial velocity. Vo = Yo/sin A = 2.39/sin3.42 = 40.0 m/s. [3.42o]
*February 18, 2014*

**Physics**

Dx = Xo * Tf = 0.315 m. 0.582 * Tf = 0.315 Tf = 0.541 s. = Fall time or time in air Y = Yo + g*t = 0 + 9.8*0.541 = 5.30 m/s. = Ver. component of final velocity.
*February 18, 2014*

**Physics**

d = Vo*t + 0.5g*t^2 = 5.15 m. 0 + 4.9t^2 = 5.15 t^2 = 1.05 Tf = 1.025 s. = Fall time. Dx = Xo * Tf = 11.9 m. Xo * 1.025 = 11.9 Xo = 11.6 m/s = Required speed.
*February 18, 2014*

**physics**

Vo = 35.2 Ft/s * 1m/3.3Ft = 10.7 m/s.
*February 18, 2014*

**physics**

Y^2 = Yo^2 + 2g*h = 0 Yo^2 - 64*11.7 = 0 Yo^2 = 748.8 Yo = 27.4 Ft/s = Ver. component of the initial velocity. Vo = Yo/sinA = 27.4/sin51 = 35.2 Ft/s = Initial velocity = Speed at which the animal must leave gnd.
*February 18, 2014*

**Physics**

1a. 2.5m[30o] X = 2.5*cos30 = 2.17 m. Y = 2.5*sin30 = 1.25 m. P1(2.17,1.25). 3.8m[120o] X = 3.8*cos120 = -1.9 m. Y = 3.8*sin120 = 3.29 m. P2(-1.9,3.29). 1b. (2.17,1.25), (-1.9,3.29) d^2=(-1.9-2.17)^2 + (3.29-1.25)^2= 20.73 d = 4.55 m. 2. A + B = -14 29i + B = -14 B = -14 -29i...
*February 17, 2014*

**physics**

Fr = ((Vs+Vr)/(Vs-Vc))*Fc = 392 Hz. ((770+0)/(770-Vc))*349 = 392 ((770)/(770-Vc))*349 = 392 268,730/(770-Vc) = 392 301,840 - 392Vc = 268,730 -392Vc = -33,110 Vc = 84.5 mi/h = Velocity of the car. Vs = Speed of sound in air. Vr = Velocity of the receiver(hearer) of the sound.
*February 17, 2014*

**Physics**

L = V/F = 2*0.70 = 1.40 m. V/470 = 1.40 V = 1.40 * 470 = 658 m/s.
*February 17, 2014*

**Math**

The solution should satisfy both Eqs.
*February 17, 2014*

**Math**

Y = 15*sin(90-62) = 7.04 mi. X = 7 + 15*cos(90-62) = 20.2 mi. d = sqrt(20.2^2+7.04^2) = 21.4 mi.
*February 17, 2014*

**Math**

Tan13.25 = h/(X+156.25) h = (X+156.25)*Tan13.25 h = 0.23547x + 36.79 Tan18.17 = h/X h = 0.32820x h = 0.23547x + 36.79 = 0.32820x 0.23547x - 0.32820x = -36.79 -0.09273x = -36.79 X = 396.7 Ft. Tan18.17 = h/396.7 h = 396.7*Tan18.17 = 130.2 Ft = Ht. 0f tower.
*February 17, 2014*

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