tan x + sec x = 1 (sin x)/(cos x) + 1/cos x = 1 (sin x + 1)/cos x = 1 sin x + 1 = cos x cos x - sin x = 1 x = 0º, 270º, 360º
tan x + sec x = 1 (sin x)/(cos x) + 1/cos x = 1 (sin x + 1)/cos x = 1 sin x + 1 = cos x cos x - sin x = 1 x = 0º, 270º, 360º
y = cos (cot x) y' = -sin (cot x) * -csc2 x = csc2 x * sin (cot x) When you have a trigonometric function, you must take a derivative of the function first & then multiply it by the derivative of the angle.
Sin θ = -12/13 Cos θ = 5/13 Tan θ = -12/5 Sin 2θ = 2*sin θ * cos θ = 2(-12/13)(5/13) = -120/169 Cos 2θ = 2*cos2 θ - 1 = 2(5/13)2 - 1 = -119/169 Tan 2θ = (sin 2θ)/(cos 2θ) = 120/119
All triangles have three angles that must add up to 180 degrees. It is impossible to have 2 right angles in a triangle because then the measure of the third angle would be 0 (which means there isn't an angle). Two of the angles cannot be obtuse angles because the combined angle measure would over...
1.Cos 64 = Cos 2(32) Cos 2x = 2cos2 x - 1 Cos 2x = cos2x - sin2x Cos 2x = 1 - 2sin2x We will use the last trig identity. Cos 2(32) = 1 - 2sin2 32 2) Sin 185 = Sin .5(370 Sin .5x = √((1 - cos x)/2) Sin...
1) 1 Kilometer = 1000 meters 1 meter = 100 centimeters 1 kilometer = 100,000 centimeters 1 centimeter = 1/100000 kilometer = 1 * 10-5 kilometer 1 cubic centimeter = (1 * 10-5 kilometer)3 = 1 * 10-15 cubic kilometer ...
Al(NO3)3 + 3KOH -------> 3KNO3 + Al(OH)3 50 ml * .2 moles/ liter = .01 Moles of Al(NO3)3 200 ml * .1 moles/liter = .02 Moles of KOH Since the ratio between the two reactants according to the chemical equation is 1:3, we would...
E = E0(1.019)t where E represents earth's present population, E0 is the original population of Earth & t represents time E(40) = 6(1.019)40 = 6 * 2.12308 = 12.739 billion
√x + 8 = 2xy2 y2 = 1/(2√x) + 4/x y = √(1/(2√x) + 4/x) Differentiate via power rule & product rule 1/(2√x) = 2y2 + 4xy*dy/dx 1/(2√x) - 2y2 = 4xy*dy/dx dy/dx = 1/(8x3/2y) - y/2x dy/dx...
R = 0.5x2 + 4x + 143 Take derivative with respect to time dR/dt = x*dx/dt + 4*dx/dt dx/dt = rate at which the paper circulation is changing = 3 x = present circulation = 13 + 3*3 = 22 dR/dt = 22*3 +...
q = 7000e-.006p q($350) = 7000e-2.1= 857.19 dq/dt = -42e-.006p * dp/dt dp/dt = -dq/dt * e.006p/42 = (40/42)(e.006*350) = $7.78/week
y = x2 y' = 2x y'(1) = 2*1 = 2
To solve this, we need to use the temperature-volume equation when it comes to expanding/contracting gases. V1/T1 = V2/T2 V1 represents the initial volume of the gas & V2 represents the new volume of the gas. T1 represents the initial temperature &...
a/2 = ae-7.444t Divide by a on both sides: e-7.444t= 1/2 Take a natural log of both sides -7.444t = ln (1/2) t = (ln .5)/(-7.444) = 0.093 days
Let t = the speed to LV Let f = the speed from LV t = f + 52.8 The distances both way are the same so: 3t = 12.6f f = t - 52.8 3t = 12.6t - 665.28 -3t ...
Speed of plane with the wind = 1104 miles/16 hours = 69 mph Speed of plane against the wind = 1104 miles/23 hours = 48 mph Speed of plan in still air = (69+48)/2 = 58.5 mph Speed of wind = (69 - 48)/2 = 10.5 mph
f(t) = (1/t)et/6 f'(t) = (1/6t)et/6- (1/t2)et/6 0 = (1/6t)et/6- (1/t2)et/6 0= et/6(1/6t - 1/t2) 0 = t - 6 t = 6 When t<6, the slope of the function is negative meaning that the function is decreasing...
sin x + cos x = 0 - cos x -cos x sin x = -cos x /cos x /cos x tan x = -1 x = arctan -1 = 3π/4, 7π/4
C = CDs B = Bonds S = Stocks C + B + S = 185000 .035C + .05B + .119S = 11035 B = C +15000 Substitute the last equation into the first two: 2C + S = 170000 .085C + .119S = 10285 Multiply the...
H'(x) = f'(ln (x)) + g'(x)/g(x) H'(1) = f'(ln 1) + g'(1)/g(1) H'(1) = f'(0) + g'(1)/g(1) H'(1) = 2 + -8/5 = 2/5