u = 2d or u - 2d = 0 u + d = 5 so the matrix would be 1 -2 0 1 1 5 add -1 times the 1st row to the 2nd row. Then you get 1 -2 0 0 3 5 multiply the 2nd row by 1/3: 1 -2 0 0 1 5/3 The 2nd row tells us that d = 5/3, so u = 10/3
A+B = 60 (1) A/3 = B/2 A = 3B/2 (2) combine (1) and (2) 3B/2+B = 60 3B/2+2B/2 = 60 5B/2 = 60 B = 24 A = 36
x = original # of pieces w = gave to wife = 10x/100 m = gave to meg = 3 (x-w-m)/4 = j = gave to joe 18 = x - w - m - j combine and solve for x
sin = opposite / hypotenuse so, hypotenuse = 8 opposite leg = 7 adjacent leg = sqrt(8^2 - 7^2) = sqrt(15) 1/cot = tan tan = opposite / adjacent = 7/sqrt(15) in the 4th quadrant the tangent is negative, so add a minus sign: 1/cot(theta) = -7/sqrt(15)
grade 12 trig
cos(A) -1 = 0 or cos(A) = 1 arccos(1) = A = 0
distance = velocity x time or time = distance / velocity total time=d1/v1+d2/v2=2.5 hrs (1) where d1 = car distance = 30 (2) v1 = car speed d2 = train distance = 120 - d1 (3) v2 = train velocity = v1+20 (4) combine (1), (2), (3), and (4) and solve for v1
It doesn't seem like there is enough information to determine the answer
a)centripetal acceleration is v^2/r. In this case, v is 30 mi/hr and r = 200 ft. The inertial force would be: F = ma = mv^2/r (1) This would be the friction force required to keep the car on its path. b) The static friction is: F = uN (2) where u is the static friction coeffic...
Assuming an ideal spring (linear) and using Hooke's law, the force generated by the spring is: F = -kx (1) where x is the distance the spring is stretched from the rest position. So, substituting the info into (1) you get: -10 = -k(2) or k = 5 lb/in work is the 1st integra...
if you bisect one of the angles, you have a right triangle with a hypotenuse of 1 cm and a short leg of 0.5 cm. Using the Pythagorean theorem, the height would be: height = square root (1^2 - 0.5^2)
Oops. Thanks for the correction.
let the 3 dimensions be a, b, and c where a and b are the bottom edges and c is the height. v is the volume s is the surface area a = 7b v = abc = 7b^2c or rearranging, c = v/7b^2 s = ab + 2ac + 2bc = 7b^2 + 14bc + 2bc = 7b^2 + 16bc = 7b^2 + 16bv/7b^2 = 7b^2 + (v16/7)/b set th...
From 1920 to 1980 is 60 years. The record was shortened by 1.2 seconds. The slope of the line is the rise over the run, or: -1.2/60 for t=0, R(t) = 46.6 so the y intercept is 46.6. The format of a line is y = mx + b where m is the slope and b is the y intercept. So, a) so the ...
rearranging the given line, y = (9/5)x - 4/5 (1) which has the form y = mx + b (2) where m is the slope and b is the y intercept. The new line would have the same slope to be parallel, so it would have the form: y = (9/5)x + b (3) to solve for b, input the given coordinates, o...
It doesn't look right to me sec Q - 1/sec Q = 1/cos - cos = 1/cos - cos^2/cos = (1-cos^2)/cos = sin^2/cos
using the Pythagorean theorem, opposite side = sqrt(13^2-12^2) sin x = opposite side / 13 tan x = opposite side / 12
Newton's law of gravitation: F = G m1 m2 /r^2 let m2 = mass of ice cube and s = G m1/r^2 so, F = s m2 rearranging, s = m2/F let V = orbital speed centripetal acceleration = V^2/r For an object to remain in orbit s must equal the centripetal acceleration so, s = V^2/r
12.60 - 23.00 = A A / -1.30 = standard deviation
if you are traveling along the leg of the star, the deflection angle is the angle you have to turn to get to the next leg. d = deflection angle at a point = 180 - 12 = 168 since there are points, the total point deflection angle at the points is 1680. x = dent angle = 180+y y ...
It could be interpreted as the azimuth, which in surveying applications is typically measured in a clockwise direction from north.
180+arctan(12/-5) = 112.6
a = angular acceleration I = rotational inertia w = angular velocity v = linear velocity Torque = RxFT = Ia so, a = RxFT/I = (R/I)(4t-0.10t^2) w = integral(a) with respect to t v= wR
It looks right to me. The easiest way to check is to plug the number back into the formula: e^.6931 = 2 2*2-3 = 4-3 = 1
Permutations of 9 objects taken 5 at a time = 9!/(9-5)! where 4! = 4x3x2x1 and 9! = 9x8x7x6x5x4x3x2x1
yes, it could be. You just need to change the sign, so you would have 8-y over y-4 PLUS 7y-9 over y-4
dist from station to trains = D ta = time in hours from when A passes station to when trains A & B meet. D = 80ta D = 88(ta-15/60) solve for ta Time at catch-up = 1:20 AM + ta
NO. 500 = A - A x 0.28 = A (1-.28) = .72A so, A = 500/0.72 = 694
csc=1/sin cot=cos/sin so, csc^2-1/cotcsc = ((1/sin^2)-1)sin/(cos/sin) = sin((sin/sin^2)-sin)/(cos) = (sin^2/sin^2-sin^2)/cos = (1-sin^2)/cos = cos^2/cos = cos A ((sin^2/sin^2)-sin/(sin^2 cos)
1) it is not correct. The second term would be log3(-2) and you can't take the log of a negative number. 2) it is not correct. The base angle would be 45 degrees, so the cotangent would be 1.
9cos^2(t)+3cos(t)=0 subtract 3cos(t) from both sides 9cos^2(t)=-3cos(t) divide both sides by 3cos(t) 3cos(t)=-1 cos(t)=-1/3 t=arccos(-1/3)
# of ways of selecting winning quintuple = permutations of 5 objects = 5! = 5 x 4 x 3 x 2 x 1 probability of winning = n!/(r!(n-r)!) = 44!/(5!39!)
x = original # of tickets y = original price you have 2 equations: xy = 180 (x-2)(y+9)=180+36 substitute equation 1 into 2 and solve.
16-15.2 = 0.8 0.8/0.03 = n = 26 standard deviations so, erf(n/sqrt(2)) = approximately 1 so, 50% of the data would be between 15.2 and 16.
The formulas given look like they are for sinusoids and not circles.
the graph of y=sin(theta) is moved vertically along the y axis a distance of q to obtain y=sin(theta)+q.
= (y/3)(y^2+5y+6) = (y/3)(y+2)(y+3)
= (18+4)r^2 +7s = 22r^2+7s
for example, for x = 2, y = 0 x = 3, y = -1/3 x = 4, y = -2/3 x = 5, y = -1
A = amt invested at 8.5% B = amt invested at 10% A + B = 50000 or A = 50000 - B income = 0.085A + 0.10B = 4700 substitute A in terms of B and solve
c = # of chest freezers u = # of upright freezers c+u>=100 or u >= 100-c assume a total of 100 units cost = 250c + 400u = 250c +400(100-c) = 250c + 40000 - 400c = 40000 - 150c = 800 - 3c so obviously the more type c units, the lower the total cost. profit = 40c + 60u >...
cos(x)=15/17 so x = arccos(15/17) tan(76) = 13/x so x = 13/tan(76)
dmA/dt = cmB^2/mA where c is a constant mB=m-mA so dmA/dt = c (m-mA)^2/mA = (c/mA)(mA^2-2mmA+m^2) = cmA-2cm+cm^2/mA integrate with respect to t
sin(a+b)/cos(a)cos(b) = = (sin(a)cos(b)+cos(a)sin(b))/cos(a)cos(b) = sin(a)cos(b)/(cos(a)cos(b) + cos(a)sin(b)/(cos(a)cos(b) = sin(a)/cos(a) + sin(b)/cos(b) = tan(a) + tan(b)
It would take 10 minutes.
Moles of solute = 16 g / 60 g/M = = 0.267 M volume of H2O = 39g/1.3 g/ml = 30 ml = 0.03 l molarity = 0.267 M / 0.03 l = 8.89 M/l
the probability that the 1st marble is red is 10/13. So, the probability that both marbles are red is (10/13)^2 or (100/169)
(a) 3y = x - 10 substitute in the 2nd equation 3(x-2) = x - 10 3x - 6 = x - 10 simplifing... 2x = -4 or x = -2 and y = -4 this is a unique solution (b) this system has infinitely many solutions and cannot be solved without more information. 3x + 3y = 15 divide equation by 3 (3...
y = (x-2)^2 y = x^2-4x -4 dy = 2xdx - 4dx so, dy/dx = 2x-4 dx/dt = 2 so, dy/dt = dy/dx dx/dt = 2(2x-4) = 4x-8 for x=1 then dy/dt = 4(1)-8 = -4 units per second
dx/dt = 2 inches/min V = x^3 so, dV/dt = 2^3 = 8 cubic inches/min
Area = A x B Total length = 3000 = A + 2B B = (3000-A)/2 so, Area = A x (3000-A)/2 = = 3000A/2 - (1/2)A^2 take 1st derivative 0 = 1500 - A and solve for A A = 1500 and B = 750
Physics...not sure what formula to use
mb = mass of bullet vb = velocity of bullet ma = mass of bag vab = velocity of bag and bullet from conservation of momentum: mb*vb = (ma + mb)*vab then from conservation of energy: (ma + mb)*vab^2/2 = (ma + mb)*g*h
A: it depends how the cube is painted. If the 3 blue sides of the original cube share a common corner then 7 of the smaller cubes have at least 2 sides that are blue. If 2 opposite faces of the original cube are blue then 6 of the 27 have at least 2 faces that are blue. B: 19 ...
books = (2ft x 12in/1ft)/(0.75in/book)
sa = 4 x pi x r^2 so r = sqrt( sa/(4 x pi))
2x^2-5x = x(2x-5) = 0 x = 0, 5/2
There is no answer. x would have to be less than zero which is beyond the bounds where the equation is valid.
If there are more than three authors you can use: Doe, Mary Jane, et al.
That is what I got also.
centripetal acceleration = a = v^2/L Period = T = 2 x pi x L / v m = mass of stone tension = f = m x a L1 = L x 1.01 if f and m are constant, then a is constant. Then v1 = sqrt(a x L1) T1 = 2 x pi x L1/v1 percentage change = 100x(T1-T)/T
function of x equals x minus the absolute value of x, where x is greater than zero.
flooding, water pollution, and eutrophication can be a problem in either ocean or freshwater. Aquifer depletion, overdrawing surface water, and saltwater intrusion are freshwater problems.
the function is not continuous when the denominator is zero, or... 0 = x^2+1 solving for x then x = i It is a removable discontinuity since it can be repaired by replacing a single point.
0 = 4x^4-18x^2 = 4x^2(x^2-9/2) = 4x^2(x+sqrt(9/2))(x-sqrt(9/2))
connect your ipod to an FM transmitter
v0 = 20m/s D = dist from int. = 110 - v0 x 0.50 t0 = time to stop final velocity must equal zero... 0 = v0 - a x t0 t0 = v0/a D = v0 x t0 - a x t0^2/2 substitute for t0... D = v0^2/a - a x (v0/a)^2/2 solve for a...
Profit = revenue - TC Revenue = [Price] x [tons of coal] Take the first derivative of profit with respect to Q and set this equal to zero, then solve for Q.
with a loan
two more equations are: m1+m2=M v2-v1=20m/s
the formula for water is H2O. Therefore, two atoms of hydrogen are released for each atom of oxygen. You could test the gases by putting them in a balloon and seeing which one floats.
circumference = pi*D = 10m, so D = 10m/pi = 3.183m radius = D/2 = 1.59m
4^(2x-5)=2^2*(2x-5) 8^(x-3)=2^3*(x-3) so 2(2x-5)=3(x-3) simplifying, 4x-10=3x-9 x=1
1/2N2+3/2H2 => NH3 or 1/3N2+H2 => 2/3NH3 so 12*2/3 = 8 moles HN3
More information is needed besides the mean to answer the question.
to convert degrees to rad, multiply by pi and divide by 180.
I'm not sure I understand what angle the 56.4 degrees represents, but assuming it is the difference in horizontal azimuth to the pillar from the 1st setup to the 2nd setup then solution is: If the distance to the pillar is "P" then: tan(56.4)=10/P or P=10/tan(56....
The three angles of a triangle equal 180 degrees. The third angle is 80 degrees. Therefore, it is not a right triangle.
if c is one of the legs of the triangle then it equals four. If it is the hypotenuse then it equals: c=sqrt(5^2+3^2)
College Calculus (Binomial Series)
Taylor series is as follows: f(x)=f(a)+f'(a)(x-a)/1!+f''(a)(x-a)^2/2!+f'''(a)(x-a)^3/3!+...
compound interest formula is: FV=PV(1+(r/n))^(nT) As n approaches infinity, this formula becomes: FV=PV*e^(rt) for the 1st $1000 invested: FV=1000*e^(.07*20) for the 2nd $1000 invested: FV=1000*e^(.07*19) and so on for 20 years. The sum total of future values minus $20,000 dep...
z-score = (raw score - mean)/standard deviation
Frederick the Great
Assuming compound interest with a period of 1 year, the annual rate would be 4.3%
"Record wages expense incurred and to be paid next month" Payable implies an expense you owe.
Cash 10,000 debit Brown, Equity 10,000 credit
Decrease in liabilities of $71,000
I believe an easement is correct.
A line from the center of the curve to the midpoint of the chord is 8ft. If h=half of the chord length then 10^2=h^2+8^2, or h=sqrt(10^2-8^2) = 6 the chord length is 2*h or 12ft.
Since the equation is for a line, you really only need two points. If you plug x=0 into the equation, the value of y is also zero. This gives you the first point (0,0). For x=1, y=k, so the second point is (0,k). The graph of the equation is a line passing through these two po...
2x-4y+5=a so rearranging, -4y=a-2x-5 or y=-a/4+2x/4+5/4 The slope of this line is 2/4. A line normal to this would have a slope of minus the inverse, or -4/2, or -2. So the equation of normal line would be: y=-2x
screen height = h screen width = w h = w*3/4 (1) 27 = sqrt(h^2+w^2) = sqrt((3w/4)^2+w^2) solve this equation for w calculate h from (1) movie width = screen width movie height = m m=w/2 darkened strip = (h-m)/2
(x-h)^2/a^2+(y-k)^2/b^2=1 is the equation for an ellipse, where (h,k) is the center, a is the semimajor axis, and b is the semiminor axis.
If you take a sample of air in your neighborhood and compare the concentration of various contaminants with the maximum allowed values, the maximum allowed values would be the air quality standards. If you measure the output of various compounds from a piece of equipment, such...
Math Algebra 2
I got a maximum profit of $4200 with 40 pants and 80 shirts.
Math Algebra 2
human hrs = 160, or 2x+6y=160 machine hrs = 200, or 2x+9y=200 minimum of 15 pants, or y>=15 must make more shirts than pants, or x>=y the maximum profit is where the equation 25x+55y=profit has a local maximum. One way to determine this is using the 1st derivative and se...
a circle has 360 degrees or 2 pi radians, so: radians = 2.7*pi/180
Log10x = -7 is the same as 10^-7 = x or x = 0.0000001
The problem asked for the ratio of length to width, with the length being the smaller of the two numbers. Therefore, the ratio would have to be less than one. If you are allowed to round off, then the nearest whole number ratio would be one. If you want to reduce the fraction ...