assuming a proper allocation of papers and distance, then 1/x = 1/70 + 1/80 x = 112/3 minutes
1000x + 2000(x+.005) = 190 x = 6%
draw a diagram, as usual. If the tower has height h and the wire is meets the ground at distance d, h/d = sin 52 h/(d+32) = sin 21 eliminate d and you have h/sin52 = h/sin21 - 32 now just solve for h
1/2 pi (24/2)^2 = 72pi in^2 Maybe in this case it actually should be 72 pie !
If you mean (as in area of trapezoid) h = 2A/(b1+b2) hb1 + hb2 = 2A hb1 = 2A-hb2 b1 = (2A-hb2)/h
from my experience, it f and sounds just like water. After all, vinegar is just a mild solution of acetic acid in water.
3-digit cubes are 125 216 343 512 729 you can probably take it from there
b/g = 4/3 (b-160)/g = 4/5 g = 300
they are part of the area, not the perimeter.
Math Analysis 2
when x=2, using the chain rule, we get dy/dt = 3x^2 dx/dt = 3(4)(5) = 60
math - typo?
sorry, 3 doesn't divide 40 evenly
need asap trigg
recall that tan(2x) = 2tanx/(1-tan^2 x)
type that in at wolframalpha.com
well, we know that y = c1 e^-2x + c2 e^-3x y' = -2c1 e^2x - 3c2 e^-3x so, c1 + c2 = 4.87 -2c1 - 3c2 = β Now just work out the maximum point as usual.
12 * 4^3
sorry. i don't buy it. If both cars had driven the same distance (599.5 miles) in the same time, they had the same average speed.
oh, please. What is the first and most fundamental trig identity you ever learned? cos^2 + sin^2 = 1 right? Time for the duhh! and head slap.
tanA = cotC sinC = 3/5, so cotC = 4/3 You are correct No idea what the 0/9 is supposed to mean.
same old same old e^6x + 2 <= 3 e^6x <= 1 6x <= 0 x <= 0 see http://www.wolframalpha.com/input/?i=plot+y%3De^%286x%29%2B2+and+y%3D3+for+-1+%3C%3D+x+%3C%3D+1
just chug away as usual 2e^3 - 6 - 16e^-x = 0 16e^-x = 2e^3 - 6 e^-x = (e^3-3)/8 e^x = 8/(e^3-3) x = ln(8/(e^3 - 3))
I get 62°, but that's pretty close.
sin2x = 2 sinx cosx = 2(1/4)(√15/4) = 2√15/16 cos2x = cos^2x - sin^2 x = 15/16 - 1/16 = 7/8 tan2x = 2tanx/(1-tan^2 x) = 2/√15 / (1 - 1/15) = 2/√15 * 15/14 = √15/7
csc positive, tan negative means QII since sinx = 1/cscx, sinx = 1/4 cosx = √15/4 tanx = 1/√15 Now just apply your double-angle formulas
Please help Math
cos^2 x = (1+cos2x)/2, so cos^4 x = (1 + 2cos2x + cos^2 2x)/4 = (1 + 2cos2x + (1+cos4x)/2))/4 = (3 + 4cos2x + cos4x)/8 what do you get for the others?
Go with Damon.
My Bad. I used <3,2,4>
we need slope of 3/2, so the line is y-6 = 3/2 x prism: volume = (2y+1)(y)(y+3)
y = 70 sin41° t - 16t^2 x = 70 cos41° t solve for t when y = 10 use that t to get x.
parametric equations would be x = (32 cos 35°) t y = 4.5 + (32 sin 35°)t - 16t^2 solve for t when y=0 4.5+32t-16t^2 is valid only if the ball is hit straight up.
17% is 17/12 = 1.417% per month .01417 * 2000 = $28.33
Not trivial; some trial and error will probably be needed (5u+v)(u-2v) gives -9uv (5u+2v)(u-v) gives -3uv TA DAA!
(3,-1) is 4 below y=3, so its reflection will be to 4 above y=3, or (3,7) Similarly for x=-1, to (-5,7)
4/7 = 57%
since there's only one variable, use the number line. Go to http://www.wolframalpha.com/input/?i=2y%2B8+%3D+0 and scroll down to the bottom to see the point plotted.
I assume you want to solve for x. So, x+6 = 4 or -4 x = -2 or -10
Math - incomplete
Nothing to solve for. There's no equation. Now, if you meant 3x+20 = 0, then 3x = -20 x = -20/3
no idea. If D is between G and F, then GED+DEF=GEF, so 70+5x-10 = 2x+10 3x = -50 x = -17/3 Not likely. If F is between D and G, then DEF+GEF = GED 5x-10 + 2x+10 = 70 7x = 70 x = 10 DEF = 40 GEF = 30 Next time, describe the figure more clearly, eh?
Math Gr. 7
I assume you mean a regular polygon where the interior angle is 290. No. All the angles must be less than 180. However, it is certainly possible to draw a polygon where the interior angles, measured counterclockwise, include one with a measure of 290 degrees. The polygon will ...
c+h+p = 99 c = 4h h = 2p 4(2p) + 2p + p = 99 11p = 99 p = 9 so, 18 horses, 72 cows, 9 pigs
if we let x = entering new reservations y = verifying old ones z = confirming then x + y + z = 13.5 x = 2y z = 1.5 y 2y + y + 1.5y = 13.5 4.5y = 13.5 y = 3 so, x = 2y = 6 hours on new reservations.
just start fitting in the facts. 1st 2 divisible by 5 means they end in 0 or 5 last 2 divisible by 9 and all different means not 09,45,54 or 90 units = twice tens means they are 36 so, the number is xx36. That means the first two digits also add to 9, which means the number is...
arccos is the inverse cosine. If x = cos(y) then y = arccos(x) Mosey on over to http://rechneronline.de/function-graphs/ and enter arccos(x) for the function. Then set the x and y ranges from -1 to 1 and draw the graph. You can then get a feel for the y values needed. They wil...
math - typo?
2/7 = 5/x 2x = 35 x = 17.5 eh?
plot the number as a point in the x-y (real-imaginary) plane. -1-i corresponds to (-1,-1) That point is a distance of √2 from (0,0), and at an angle of 225° measured counterclockwise from the positive x-axis. In other words, (√2,5π/4) The very basic nature...
Trigonometry - LONESTAR
if the diameter is 191, then the radius is 191/2 = 95.5 That is the amplitude of the sin/cos curve Add 11 to that since the wheel doesn't scrape the ground. H = 95.5 sin(kt) + 106.5 Since H is at its minimum at t=0, it will look like H = -95.5 cos(kt) + 106.5 since cos(x) ...
11 4/9 + 5 3/9 = 16 7/9
x^4 > x^2 x^2 > 1 x > 1 or x < -1
implicit differentiation 1/(xy) (xy)' = 1 + y' 1/(xy) (y + xy') = 1 + y' y + xy' = xy + xyy' y'(x-xy) = xy-y y' = y(x-1) / x(1-y) or, ln(xy) = x+y lnx + lny = x+y 1/x + 1/y y' = 1 + y' y'(1/y - 1) = 1 - 1/x y' = (1 - 1/x) / (1/y ...
assuming the crosswind is at right angles to the flight, √(130^2+20^2) = ...
none, since there was no change in height.
as usual, draw a diagram. We want the diagonal of a right triangle with legs 3.6 and 5.2 so, the distance is √(3.6^2+(5.2-2.6)^2) = 4.4
1 and -2 I suspect a garbled question coefficients are the numbers multiplying the variables. In the expression "3x" the coefficient of x is 3. now, if you want a solution, there is none. The lines have the same slope, but no point on the first line is also on the se...
well, we can find an approximation to h(4) by assuming that the tangent line at (5,3) stays close to the curve. So, assuming that you meant the slope is 7/(2t), h'(5) = 7/10 The tangent line is thus 7-3 = 7/10 (x-5) now, plug in x=4 to approximate h(4) If you meant h'(...
the fraction remaining after t years is (1/2)^(t/5730) So, you want (1/2)^(t/5730) = .7 t/5730 = log(.7)/log(.5) ...
since we're dealing with line segments, I'd say C
tan u = 5/2 tan v = 4/3 now just use your tan addition formula
just substitute in for x f(t-2) = 5+6(t-2)-(t-2)^2 = -t^2 + 10t - 11 do the others the same way.
if each side is multiplied by 5, the area is multiplied by 5*5 = 25 So, D
oops y-x = t+1 (y-x)^2 = t^2+2t+1 = 1/2(t^2+t) + 1/2 t^2 + 1 = y/2 + 1/2(t^2-1) + 3/2 = y/2 + x/2 + 3/2 (x-y)^2 = 1/2 (x+y+3)
x^2 = t^4-2t^2+1 y^2 = t^4+2t^3+t^2 xy = t^4+t^3-t^2-1 x^2-2xy+y^2 = -3t^2 = -3(x+1) x^2-2xy+y^2+3x+3 = 0
the graph is an ellipse (x-30)/40 = -cos t (y+50)/30 = sin t (x-30)^2/1600 + (y+50)^2/900 = 1 the ellipse has semi-axes 30 and 40 Not sure how many lattice points lie on the curve. At least 8.
the period for x is pi/2 the period for y is 2pi/3 So, I'd say I=[-pi/3,pi/3]
(x-2)^2/4 + (y-k)^2/16 = 1 (x-1)^2 + (y+3)^2 = 1 We have an ellipse with center at (2,k) and radii 2 and 4 and a circle with center (1,-3) with radius 1 They are tangent internally at (0,-3) if k = -3 If they are tangent externally, then there will be two values at k = -3&plus...
no way to tell from the given information. That's like saying if f(1)=1647123, what's f(12)? who knows?
volume grows by 2^3 = 8
English--Please, help me!
Twas bryllyg, and ye slythy toves Did gyre and gymble in ye wabe: The "did" indicates that the following words are verbs. "in" is a preposition, requiring a noun as an object. Carroll's nonsense poem, poking fun at literary pretensions, has been studied...
If the marbles are packed in a square grid, the box will hold 8x8=64 marbles in each layer. So, since it will take 4 layers to hold all 200 marbles, the box must be 48mm high. If you want to get into most efficient packing, that is a complex subject, but you can research it to...
a(1-r^8)/(1-r) / a(1-r^4)/(1-r) = 97/81 so, (1-r^8)/(1-r^4) = 97/81 81 - 81r^8 = 97 - 97r^4 81r^8 - 97r^4 + 16 = 0 (r^4-1)(81r^4-16) = 0 r^4 = 1 or 16/81 r = ±1 or ±2/3 Naturally, r=±1 are out, but ±2/3 both work
If there are x vans and y buses, then we want to minimize c=305x+985y subject to 8x+40y >= 320 3x+y >= 36 use 10 vans, 6 buses
(x+2)^2=16 x+2 = 4 or -4 x = 2 or -6
pick the set with perimeter=12 since 12*3=36
um, try 4/20
No, Ada travels from A on a heading of 60˚ because B lies on a bearing of 60˚ from A. Then she apparently gets lost . . .
I'd say where the graphs intersect.
if you rearrange into the same format, you have 2x+4y = -1 6x+12y = -3 If you multiply the 1st by 3, you see that it is the same as the 2nd. So, they are really the same line, and there are infinitely many solutions. That is, every point on the 1st line is also on the 2nd line...
162 = 18r^2 r = 3 18 = 9a, so a = 2 S7 = 2(1-3^7)/(1-3) = 2186 check: 2+6+18+54+162+486+1458 = 2186
is there a problem with finding 1/4 or 1/8 of the values shown? 16/4 = 4 16/8 = 2 and so on
Science - ?
Hmmm. I get d3 = 6*4 + 1/2 (-6/4)*4^2 since v goes from 6 to 0 in 4 seconds. bob's the physicist, but ...
h = 15.8 + (25.2 sin 32.7°)t - 4.9t^2 = 15.8 + 13.61t - 4.9t^2 I get max height = 25.25 at t=1.388, which is as you say, 9.46m above the roof. h=0 when t=3.66 v = 13.61 - 9.8t = -22.26 when h=0
x + x/(3/2) + x+2 = 98 x = 36 so, the sides are 36,24,38
under addition, each element x has an inverse such that x + x^-1 = 0 (the additive identity) under multiplication each element has an inverse such that x * x^-1 = 1, except zero. both operations are associative and commutative, which fill out the necessary conditions.
depends on the length, unless the width is the diameter of a circular pool, in which case you have 3/4 * pi * 100^2 * 48 cm^3 divide that by 1000 to get liters
If you mean 16^2 √24 / 6√56 then that is 128/√21 I suspect that is not what you meant, so try again using √ instead of the character from your other application.
7√2 * 3√9 = 7√2 * 3*3 = 63√2
just substitute in for x f(t-2) = 5+6(t-2)-(t-2)^2 = -t^2 + 10t - 11 do the others the same way.
p -> q q -> r p -> r valid
cost: 40*3.20 = 128.00 after spoilage there are only 32 dinners to sell Now, if the 32 dinners are supposed to cover the entire cost + 80% markup, that would mean they must sell at a price p such that 32p = 1.80*128 p = 7.20 So, the $1 discount is a 13.9% discount off the mark...
181.278 and 418.722 not sure how you want to round them
c'mon, snow -- take a look. There's a 1.75 fee just to start with. After that, each ticket costs 25, so for t tickets, that would be 24t. $25t+1.75 fits the conditions plug in 6 for t and pick the final answer.
If not, the only value that does not fit with integer x is -21
v = 4/3 pi r^3 a = 4pi r^2 dv/dt = 4pi r^2 dr/dt da/dt = 8pi r dr/dt when v=500pi/3, r=5 5 = 100pi dr/dt dr/dt = 1/(20pi) da/dt = 8pi r dr/dt = 8pi*5/(20pi) = 2
looks like D to me
aha. As before, you divided by 100 twice, not just once.
18% is about 1/5 1/5 of 880 is 176. How do you come up with such a small value?