1 white + 1 yellow + 1 red = 3 total
Answers by Robert J.
perpendicular or parallel lines (answer)
1) a, since they are the same line. 2) c, since they have the same slope of -2/5, but do not share the same line.
Easy Grade 9 math help! (answer)
There are 288/.9 = 320 cans of pop. So there are (3/4)320 = 240 bags of chips. The income from the chips = 240(0.90/1.5) = $144.
Easy grade 9 math! Help! (answer)
d = 1800 m t = 2*60+24 = 144 sec v = d/t = 1800/144 = 12.5 m/sec <==Answer
What's the potential energy? (answer)
F = kx => 10 = 20x => x = 1/2 Ep = (1/2)kx^2 = (1/2)(20)(1/2)^2 = 2.5 J <==Answer ----- Attn: Here I just used absolute values for all variables.
What's the maximum speed? (answer)
Use energy conservation. When the object reaches its maximum speed, all the potential energy is converted to kinetic energy. So, (1/2)mv^2 = 16 Plug in m = 2 kg, and solve for v, v = 4.0 m/s <==Answer
This is a parabola, which opens down. Therefore, at its vertex you get the maximum number of drills. P = -b/(2a) = -174/(2(-3)) = $29 <==Answer
2xy^2+3*ln(y)=x^2-3y^3 Differentiate both sdies with respect to x, 2(y^2 + 2xyy') + 3y'/y = 2x-9y^2y' Plug in (3, 1), 2(1+6y')+3y' = 6-9y' Solve for y', 24y' = 4 y' = 1/6 <==Answer ------ Attn: To get it done simpler, plug in (3,1) before you solve y' as a function...
cos^2xcot^2+cos^2x = cos^2x(cot^2x+1) = cos^2x csc^2x = cot^2x <==Answer
2sec^x-2sec^2x sin^2x (answer)
2sec^x-2sec^2x sin^2x = 2sec^x(1-sin^2x) = 2sec^x cos^2x = 2 <==Answer
Q2 POW #3 -Trig Identities (answer)
1) cos(3θ) = cos(2θ+θ) = cos2θ cosθ - sin2θ sinθ = (cos^2 θ - sin^2θ)cosθ - 2sin^2θ cosθ = cos^3θ - 3cosθ sin^2θ cos4θ = cos^2(2θ) - sin^2(2θ) = (cos^2θ-sin^2θ)^2 - 4sin^2θ cos^2θ = cos^4θ - 6cos^2θ sin^2θ + sin^4θ <==You had a typo here.) You can...
How long will it be before there is 1 full box of leotards cut and waiting for their side seams to be stitched? (answer)
1. Regular approach: Let t be the length of the time to be found. (1/9)t = (1/27)t + 1 Solve for t, t = 13.5 hours 2. Mental math approach: Since the difference in working rate is (1/9-1/27) = 2/27, it takes 27/2 = 13.5 hours before 1 full box of leotards cut and waiting...
Here is another way: tan4t+tan2t = tan2t(tan2t+1) = (sec2t-1)(sec2t), since tan2t+1 = sec2t = sec4t-sec2t
what is the limit of this problem? (answer)
This is the derivative of x^5 at x = 0.5. Lim h-->0 (((.5 + h)5) - ((.5)5))/h = 5x^4 at x = 1/2 = 5/16 <==Answer
9^1/4 / 9^3/4 solve (answer)
9^1/4 / 9^3/4 = 1/9^(3/4-1/4) = 1/9^(2/4) = 1/9^(1/2) = 1/3 <==Answer
If you want to prove from the left to the right, here is one way: (cos^2x+1+sinx)/(cos^2x+3) = (1-sin^2x + 1+sinx)/(1-sin^2x+3) = (1+sinx)(1-sinx+1)/[(2+sinx)(2-sinx)] = (1+sinx)/(2+sinx), after canceling 2-sinx.
find the domain (answer)
Since the domain of ln(x) is x > 0, solving 8-2^(x^2) > 0 for x, 8 = 2^3 > 2^(x^2) x^2 < 3 Answer: -sqrt(3) < x < sqrt(3)
Using vertex form, y = a(x-1)^2-4 Plug in (2, -3), -3 = a-4 => a = 1 Answer: y = (x-1)^2 - 4
how to integrate arc tangent x (answer)
Use integration by parts, ∫arctan x dx = x arctan x - ∫x darctan x = x arctan x - ∫x/(1+x^2) dx = x arctan x - (1/2)ln(1+x^2) + c
Differentiate both sides with respect to x implicitly, 2x+y^2+2xyy'+3y^2y' = -2csc^2y y' Solve for y', y' = -(2x+y^2)/(2xy+3y^2+2csc^2y) <==Answer