c+a = 52 c = 3a 3a+a = 52 a = 13 so, c=39
someone who is disgruntled likely feels 1- optimistic 2- generous 3- depressed 4- irritated my answer is D
draw a diagram. Label these points: T = top of pole B = base of pole on road S = tip of shadow on road Draw a horizontal line from S to where it intersects the extension of TB below the road. Call that point C. Now, we want the height h = BT Let x = SC y = CB Now, we have y/60...
sorry - I mean (1/6)(2x-y)^3 + C
since x is the variable of integration, y acts just like any other constant, so it's just (1/8)(2x-y)^4 + C
log(n) is undefined for n <= 0, so we need 1a 2x-5 > 0 x > 5/2 1b x^2+3x-4 > 0 x < -4 or x>1 #2 4^x + 12 = 4^2x (4^x)^2 - 4^x - 12 = 0 (4^x - 4)(4^x + 3) = 0 4^x = 4 or -3 x = 1
Q: What do you call two crows on a tree limb? A: Attempted murder!
plus ça change, plus cest la même chose.
if you know that the slope is zero, then it is clear that the graph is a horizontal line through (0,-1).
3 ln 2 ln 4 + 5 ln x = ln 3 + 2 ln 5 ln (2^3 / 4 * x^5) = ln(3 * 5^2) ln 2x^5 = ln 75
Foundations Math 12
P(1+.039/52)^(48) = 225.50 P = 217.59 225.50-217.59 = 7.91 interest
7.03 x 10^9
14^2/15^2 = .871 r^2/10^2 = .871 r = 9.3 so, the crust edge will be 0.7 inch
if you meant 3 1/2 years, then you will need 25000/(1+.12/2)^(2*3.5) = $16,626.43
since P/T remains constant 111/(23+271) = P/(475+271) P = 281.65 kPa
duct tape or bubble gum and baling wire
since tanθ = cot(90-θ), tan(4x-4) = tan(90-(3x+10)) 4x-4 = 80-3x 7x = 84 x = 12
we know that y = a(x+1)-1 4 = a(1)-1 so a = 5 y = 5(x+1)-1 y = 5x^2 + 10x + 4
since the lines are not the same or parallel, then they have a single solution. I'm sure you can come up with it. So, the equations are independent and consistent. dependent means they are the same line inconsistent means they are parallel lines.
2x+2y = 102 x^2+y^2 = 39^2 A 5-12-13 right triangle looks promising. Scale that up to a 15-36-39 size, and we see that 15+36=51, so our rectangle is 15 by 36
Quick math help
for elimination, you want all the equations to look the same, so it's easy to add/subtract. The usual way is to give them the form ax+by = c So, for #1, we have 4y=13+2x 6x+4y=9 On the first one, subtract 2x from each side and you have -2x+4y = 13 the 2nd is ok, so you now...
Quick math help
since I just showed you how to do three others just like these, do you have any ideas on these? elimination or substitution will work fine.
#1 we want to find p such that (80)(0.90)p = 80(3.50)(1.60) #2 assuming the retail price p above, we want to find q such that q = 1/p * 100
well, just plug in your data. A = 36730 * .82^(7.5)
assuming you meant log4√(a^2/b) then that would be log4a - 1/2 log4b
science - Damon?
Yeah, you may be right. It could be that the hydraulics involve prove that the weight of air in the beaker remains constant regardless of how much is displaced, but I'd have to research it. I guess you can do that on your own, or hope Damon or someone will stop by with gre...
since you displace some of the air in the beaker, its side of the lever should rise.
Quick math help
to do them by elimination, make the following steps: #2 4x-y = 9 3x+y = 12 add them and eliminate y. Then solve for x. #3 x+3y = 13 x+y = 5 subtract them and eliminate x, then solve for y #4 9a+3b = 18 a+3b = 10 subtract and solve for a
The problem is that Katy cannot accurately transcribe the exercise or proofread her submission. On the off chance that she wants to know the radius of a circle with the same perimeter as the square, then since c = 2πr, 32 = 2πr r = 16/π On the off-off chance tha...
If you mean |4x-1| = 1 then you need to recall that |n| = n if n>=0 |n| = -n if n<0 So, we have two cases, which must be solved separately 4x-1 >= 0 4x-1=1 4x=2 x = 1/2 Since x=1/2 satisfies the condition that 4x-1 >= 0, it is a solution 4x-1 < 0 -(4x-1) = 1 -4x...
20*.72 = 14.4 (144+(.76-.56))/20 = .73 so (C)
the slope of the line from (-1,-12) to (5,12) = 4, so think of the Mean Value Theorem.
Quick English help
#1. dark and light are opposites, so (B) #2. ok #3. in a dinner you eat the food, but in a meal you don't eat the recipe. An agenda is a plan for a meeting, so (A)
8.37g/3.1cm^2 = 2.7 g/cm^3 Looks like aluminum to me.
area of field = 3km^2 area of lake = (.9)(.3) = .27 km^2 so, assuming the pilot just flies around randomly till she crashes, P(lake) = .27/3 = .09
you know the vertex of y=a(x-h)^2+k is at (h,k). The minimum value of (x-h) is zero, when x=h. For any other value of x, (x-h)^2 gets larger. So, you want to get your function in that form and then you can just read off the coordinates of the vertex. f(x) = 2x^2+8x+9 = 2(x^2+4...
w(w+8) = 172 w = 2(√47 - 2) Now you can get the other values. Q1 since the larger is 9 times the area, it has 3 times the perimeter. So, the two squares have perimeters 50 and 150. Q2 x^2 + y^2 =425 4x+4y = 100 The squares have sides 5 and 20 Q3 If there are x students p...
80*(6380/7980)^2 = 51 kg is mass, which does not change. The weight would become the weight of a 51kg man.
using common notation, we have 2(x+h)^2 + 5(x+h) - 6 - (2x^2 + 5x - 6) 2h^2 + h(4x+5)
(5+√3)/(4+√3) * (4-√3)/(4-√3) (5+√3)(4-√3)/(16-3) (17-√3)/13
well, they told us that f(x) = 10/(x^2+1) Looks to me like f(0) = 10/(0+1) = 10
(a) well, we have a point and a slope (5), so y-8 = 5(x+1) (b) dy = 10/(x^2+1) dx, so if dx=1, dy = 10/2 (1) = 5 So, the estimate is 8+5 = 13 (c) F(0)-F(-1) = 7.854 F(0) = 7.854 + F(-1) = 7.854+8 = 15.854 I hope that (c) had a typo and didn't want f(0), since f(0) = 10. (f...
If 4^x = 4+√19, then take logs, recalling that log(x^n) = n*log(x) x*log(4) = log(4+√19) and so on log(x^2) = (log x)^2 2 logx = (logx)^2 logx(2-logx) = 0 logx = 2 or 0 x = b^2 or 1 to whatever base b you are using for the logs.
I assume you meant (1/2)^(3-2x). If so, make everything powers of 2 and you have 2^(2x) * 2^(2x-3) = 2^3 * 2^(2x) so, adding powers, 2x + 2x-3 = 3 + 2x x=3
assuming base 5 throughout, 2log(x+2) = 2 + log(x-2) log[(x+2)^2 / (x-2)] = 2 (x+2)^2 = 25(x-2) x = 3 or 18
do a little multiplying, and we have 25*5^x + 5*5^x = 5 30*5^x = 5 5^x = 1/6 x = -log(6)/log(5)
well, that would be cos^2(pi/15) + sin^2(pi/15) = 1 In fact, (f+g)(x) = 1 for any x.
we need 25-1.25t-4.9t^2 = 0 t=2.135 so, we have a final v of v = -1.25 - 9.8(2.135) = ?
T10+T11+T12 = (a+9d)+(a+10d)+(a+11d), so 3a+30d = 129 Similarly, for the last three terms, 3a+57d = 237 a=3 d=4 and the sequence is 3,7,11,...,83
Calculus 3 - Damon is correct
and you would be correct. I knew there was something not right.
the cylinder has parametric equations x = t y = t^2 Intersect that with the ellipsoid and you get x = t y = t^2 z = 1/5 √(25-t^2-5t^4)
it takes 8/300 hours to get to cruising height. That's 1.6 minutes in the remaining 3.4 minutes it travels 3.4/60*450 = 25.5 km during the climb, it traveled 8cot26° = 16.4 km along the ground. After flying the additional 25.5 km, it is 41.9 km away along the ground. S...
convenience stores like 7-11 big box stores like Sam's club
since the square has side x, the surrounding area has side 6+x+6 = x+12 So, the green area is (x+12)^2 - x^2 = 24x+144
Rational Exponents - Please Help!!!!
#1 (0.00252d^(9/4))/e = (0.00252*90^(9/4))/1.4 90^(1/4) = ∜90 = 3.0801 90^(9/4) = 3.0801^9 = 24948.5693 So, we now have 0.00252 * 24948.5693 / 1.4 = 44.9074 If you visit wolframalpha.com you can play around with arbitrarily complex expressions, just to see how things com...
at time t, we must have s^2 + (vt)^2 = (ut)^2 (u^2 - v^2)t^2 = s^2 t = s/√(u^2-v^2)
h/140 = sin 36° gives the height in yards
s0 = 28.7 @ 95.0° = -2.501,28.591 v0 = 4.85 @ 40.0° = 3.715,3.119 a = 1.94 @ 200° = -1.823,-0.664 Now, we just plug in our usual equations: v = v0 + at s = s0 + v0*t + 1/2 at^2 and then convert back to polar form as needed.
Caculus f'(x) - typo
typo near the end y = 2x + 8/3
y = ax^3 y' = 3ax^2 at x=-2, y' = 12a The line y=2x+b has slope 2, so 12a=2 a = 1/6 at x = -2, y = -8a = -4/3 so the line must go through (-2,-4/3) So, the tangent line has slope 2 and goes through (-2,-4/3) y = 2x+b -4/3 = -4 + b b = 8/3 So, now we have y = 2x - 8/3 i...
p = 4w just take the number of words and multiply by the score for each word.
Simplify - correction
oops, the answer is 9, not ∛9 9 is in fact ∛729
since 729 = 9^3, you are correct. Your method was also correct. 81 = 9^2, so 81^(1/3) = (9^2)^(1/3) = 9^(2/3) and 9^(1/3) * 9^(2/3) = 9^(3/3) = 9 fractional exponents are just like any others. Add them when multiplying, and multiply them when raising powers to powers.
divide 21000g by the number of grams/mole That will give you the number of moles.
7 moles of O2 in every 2 moles of Na2Cr2O7. I assume you have some other data of interest.
PV/T remains constant, so (75.0)(500)/(-185+271) = (55)(221.0)/T T = 28°K Note that we don't really have to convert to L and Pa, because the same conversion factors would be applied to both sides of the equation. The only wrinkle is the °C-°K conversion, becaus...
Anne Frank (another question :/)
Sounds like a question from Connections Academy and Mrs Markly's class.
unless he meant that S18 = 549 In that case, 18/2(2a+17*3) = 549 a = 5 T56 = 5+55*3 = 170 S32 = 32/2(2*5+31*3) = 1648
∛98 = ∛(49*2) sorry, I see no way to simplify it. Now, if you had ∛108, that would be ∛(27*4) = ∛27∛4 = 3∛4
good catch. You are correct h'(0) = 10-0+2-7 = 5 what was I thinking? the answer is 1 if it was supposed to be -2sin(x) instead of +2sin(x)
Calculus - 2nd verse
Ahem: h'(0) = 5*2-0+0-7 = 3
well, what's h'(x)? Use the chain rule: h'(x) = 5g'(x) - 6x + 2sinx - 7 h'(2) = 5g'(2) - 6(2) + 2sin(2) - 7 = 5*2 - 6*2 + 2sin(2) - 7 = 2sin(2) - 9
Z(.674) = 0.25 So, (52-μ)/5 = .674 μ = 52-5*0.674 = 48.63
Converting the data to seconds, we have * fastest: 7439 * mean: 7474 * nedian: 7467 * mode: 7467 * range: 57 * two other fast times: 7493 and 7495 So, we have 7439 x x x x x x (fastest) 7439 x x x x x 7596 (range) 7439 x x 7467 x x 7596 (median) 7439 x x 7467 7493 7495 7596 (o...
If she made x 3-pointers, then she made 3x two-pointers. x+3x = 8 x = 2 So, 2 3-pt and 6 2-pt
If you mean the x-intercepts are at 5 and 15, then y = a(x-5)(x-15) 75 = a(-5)(-15) a = 1 so, y = (x-5)(x-15)
since you give no choices, I'll just say that v = pi r^2 h v = pi (5x+2)^2 (2x+8) expand that as necessary to conform to the format of the choices
h/d = tan 27° so find d when h=875 if flight distance is f, d/f = cos 27° the time needed is thus f/651 hours tanθ = 875/400
(a) 500*2^3 = 500*8 = 4000 (b) 500*2^0 = 500*1 = 500 (c) when 3x=1 or every 1/3 hour (d) 500*2^3x= 32000 2^3x = 32000/500 = 64 2^3x = 2^6 3x = 6 x = 2
well, if you can't pick out the correct choice from my solution, you're in some trouble. Take a good look and see what you can factor out.
(6x)(9x)-π(4x)^2 = 54x^2-16πx^2 = (54-16π)x^2 or about 3.73x^2
C(0) = 0 Naturally, at t=0, there has been no drug added As t->∞, e^-bt and e^-at ->0, so we again have C(∞) = 0 All the drug has been absorbed or eliminated. If C(t) = (500)(8.5)/(3700)(8.5-0.09) (e^-0.09t - e^-8.5t) then max C is at t=0.54
MAT-134 Math XL
intercepts are easiest when x=0, 4y=12, so y=3 when y=0, 3x=12, so, x=4 So, plot the points (0,3) and (4,0) and draw a line through them.
all these are basically the same, so I'll do one for you. If you get stuck on the others, come on back and show ehere you get stuck. z+(1/7)sk = (1/6)yk^2 (1/7)sk = (1/6)yk^2-z (k/7)s = (1/6)yk^2-z s = (7/k)(1/6)yk^2-z s = (7/6)yk - 7z/k
since √81 = 9, I'd say the winner is #2 10 is the largest of 8,10,4,9 largest radius means largest circumference.
figure the slope m between the two points pick one of the points and call its coordinates (h,k) Then, since the slope never changes, the slope between (x,y) and (h,k) is the same for any (x,y) on the line. So, (y-k)/(x-h) = m, the slope between the two given points. This is us...
v(t) = 4-2t dv/dt = -2 There is no local min/max, and v is constantly decreasing, so max v in the interval is at t=0, or v=4
f'(x) = 3x^2+1 g'(2) = 1/f'(g(2)) = 1/f'(1) = 1/4
1.30*10^3 @ W = (-1300,0) 9.90*10^2 @ N30E = (445,857) add the forces to get (-855,857) = 1211 @ N45W Since F=ma, a = 1211/.159 = 7613 m/s^2 in that direction
just solve for t when h=0. It factors nicely, or your good old quadratic formula should do the trick. Did you get 1.5 seconds?
how about -24/30 ?
P = E^2/R = 120^2/15 = 960W
Since the horizontal speed is constant, the time it takes to reach the fence is 8/v The height is h = 4.9 - 4.9t^2 We want h(t) = 2.4 when t=8/v, so 4.9 - 4.9(8/v)^2 = 2.4 v = 11.2 m/s
geometry - incomplete
since I know neither the angles nor their relation to x, you better provide a bit more description of the figure, eh?
so, we know that now there are 12 cards left: 5 even and 6 odd and #1 P(red) = 6/12
area and perimeter
if the length is x and the width is y, then 2x+3y = 1200 a = xy = x(1200-2x)/3 = 400x - 2x^2/3 max area when x = 400*3/4 = 300 So, the field is 300 by 200 Note that as in all such problems, the fencing is divided equally among the lengths and widths.
Algebra (Integer Problem)
x+y+z = 33 y = x+3 z = 4x Now substitute y and z to get x+(x+3)+(4x) = 33 6x = 30 x = 5 so the numbers are 5,8,20