x^2+11^2 = 24^2 now just solve for x
depends. Is the same formula used for tv's and computers? If so, retail = 2*wholesale-75 wholesale = (retail+75)/2 so, plug in a retail price of $550
a^-3 = 1/a^3 c^-1 = 1/c, so 1/(c^-1) = c^1 and we have bc/a^3
4 times the diameter, 16 times the area
cos2a = 1 - 2sin^2(a) = 1 - 2*9/25 ... in this case, it doesn't really matter which quadrant a is in, as sin^2 is always positive. extra credit: which quadrant is 2a in?
math help !
Looks like D to me For #2, always check to see how much y changes when x changes by a fixed amount. That will give the slope of the line (the coefficient of the x term). Here, when x changes by +2, y changes by -1. So, the slope will be -1/2 and the function rule will look lik...
Better check B. It's the differences that are constant, not the ratios. A gives an exponential function. Consider y = 2^x when x grows by 1, y doubles. But, if y = mx+b (a linear function) when x grows by 1, y grows by m, and the difference is constant over equal intervals.
you want to find c. So, since y(1) = 4, plug it in -1/(1^3+c) = 4 -1/4 = 1+c c = -5/4 Now the particular solution is y = -1/(x^3 - 5/4)
You wan to find c, so plug in the point (-4,-1) which is on this particular solution curve: (-3*16)/(2+4+c) = -1 The way the function is worded makes me suspect a typo. Fix that, and find c for a particular solution.
or, 2,000,000 = 10,000,000/5, so log 10^7 - log5 = 7-.699 = 6.301
log2000000 = log 2 + log 10^6 = 6.301
intraocular fluid is the answer I think
you can check your results at wolframalpha.com Just type "derivative" or "2nd derivative" and your function. Check to be sure it interprets your input as you intended. Parentheses are your friend. For your function, you correctly extracted the 9/e constant,...
log(1000000x^19) = log(10^6)+log(x^19) = 6 + 19logx assuming logs base 10 :-)
Assuming ã means √, √338-√200+√162 = √169√2 - √100√2 + √81√2 = 13√2-10√2+9√2 = 12√2 Do the other in the same way: extract perfect roots, and combine the other factors under a single √
#1 -4√2+6√72-√32 = -4√2 + 6√36√2 - √16√2 = -4√2 + 36√2 - 4√2 = 28√2 #2 ok #3 12√13-74√2 remember that √8 = 2√2 #4 ok
correct except for the inconsistent capitalization
4! The fact that you are asking this question indicates that you are studying permutations. Surely it was explained in the text.
view it at wolframalpha.com This site will show you how to graph any function you care to enter. Play around some. http://www.wolframalpha.com/input/?i=1%2F3|x|-2+ Be sure to check to see how it interprets your input. It is pretty strict about using parentheses to alter the or...
If y = -2x^2 + 3, then just use the values of x and calculate the values of y: x y -3 -2(9)+3 = -15 -2 -2(4)+3 = -5 -1 -2(1)+3 = 1 0 -2(0)+3 = 3 1 1 2 -5 3 -15 Plot those points and sketch a smooth curve through them. Your graph should look like the one given by wolframalpha: ...
since the circumference of the ball is 2pi*11.5 = 72.26 cm, divide that into 2800cm to see how many times it rolls.
add 5 to get the next terms.
algebra - typo?
I suspect a typo, since log3(√10+1)+log3(√10+1) = log3(10-1) = log3(9) = 2 the log7 of powers of 2 is not amenable to simplification. Is there a typo? At the very least, the parentheses are not balanced.
12 = 2^2 * 3 15 = 3*5 18 = 2*3^2 The smallest number which is a multiple of all of those must contain the highest power of each of the listed primes. So, that will be 2^2 * 3^2 * 5 = 180 But, we also want our number to be a perfect square, so we need to have 5^2 in the product...
Judging from the graph at http://www.wolframalpha.com/input/?i=[3x^13]e^%28%E2%88%927x%29+for+x%3D0..3 I'd say it is concave down in that interval. In fact, since f"(x) = 3x^11 e^-7x (49x^2-182x+156) if the roots are where you say they are, then since the quadratic fa...
concave down where f" < 0 better review your text, where it is surely explained and illustrated. f" < 0 means that the slope is decreasing. So, f is either rising either rising more slowly or falling more quickly. Consider a parabola which opens downward.
gain of what? perimeter will gain 10% area will grow by a factor of 1.1^2 = 1.21, or 21%
average and instantaneous rate of change
average is measured over some finite time interval. Instantaneous is not. It is the limit of the average rate, as the measured interval decreases to zero.
Ethan donates 1/25 of which money? His earnings, the total earned, the total donated, or what?
you can convert the hours to minutes 14 X 60 = 840 then add the 3 minutes 840 +3 =- 843 then divide 843/3 = 281 then divide by 60 = 4 hours and 41 minutes
Simplify the expression 14 to the minus 4 power
Simplify the expression (-8x) times 3x squared
Math homework help
AG CE FH
the 3.02375 is correct, but you lost a factor of 10^-8 So, what you really have is .03 micrograms
Math - Bazinga!
you gotta be kidding. I suggest you pick out one or two of the types of questions that bother you, post your solutions, and we can check and/or critique them.
Calc Help Please Again!
the volume is just a stack of thin discs, of thickness dx, and radius y So, the volume is the integral of pi * y^2 dx = pi*(e^2x + 8e^x + 16) all pretty straightforward. C'mon back if you get stuck, and show where.
first, draw the asymptotes. Then pick a few values of x near the vertical asymptotes, so you get a feel for how y behaves in that region. Then pick a few more values a little farther away, and draw the curve, keeping in mind that it will approach the horizontal asymptote on th...
tanθ=1/7 means sinθ=1/√50 cos 2θ = 1-2sin^2θ = 1-1/25 = 24/25 tanØ=1/3 means sinØ=1/√10 and cosØ=3/√10 sin2Ø = 2sinØcosØ = 3/5 so, cos2Ø = 4/5 sin4Ø = 2sin2Øcos2Ø = 24/25
not geometric. The ratio between terms changes. What you have is a modified Fibonacci sequence, where for n>=2, T(n+1) = 2*(T(n-1)+T(n))
Assuming L is the right angle, the other two angles are complementary cos(N) = sin(90-N) = sin(M) the co- in cosine, cotangent, cosecant means "complementary" as in complementary angle.
how many moles in 13g of CS2? The equation tells you that it takes 5 times that many moles of C. same for SO2. Figure the moles of C, then take 2/5 that many of SO2. Then go back to grams. Again, figure the moles, and recall that one mole of a gas occupies 22.4L at STP.
well, of course they have two answers. They wanted to know the amount invested at each of two interest rates! So, what don't you understand? They gave you the equation. If P1 is invested at 12% (which is evident from the equation), then the rest of the money (30000-P1) was...
draw a diagram of a vertical cross-section of the cone, and mark off the altitude. You have a right triangle. The radius of the base is found from r/7.5 = cot(70)
business and finite calc
28000 is 0.666 std below the mean 35000 is 2.666 std above the mean. Now go to your Z table. Or, you can play around with this stuff at http://davidmlane.com/hyperstat/z_table.html
I assume you mean y=2^x and y=-2^x plot them just as you would any other functions. Mark off some points on the x-axis, and calculate the y values, then plot the points. x 2^x -2 1/4 -1 1/2 0 1 1 2 2 4 ... -2^x is just -(2^x), so it is below the x-axis, instead of above it. To...
the distance s(t) = 12t - t^2 + c for some c. Since s(1) = -10, c=-21, and so s(t) = -21 + 12t - t^2 a = dv/dt = -6t so just plug in t=4 plug in t= 0 and 10 to find where the particle is at each time, then get the displacement by evaluating s(10)-s(0)
algebra - typo?
do you mean two numbers a and ar such that a+ar=28 and a*ar = 512? If so, then there's no real solution. Maybe there's something wrong with the way the problem is presented, eh?
#1 There must be a typo here. Not factorable #2 (x^2-25)(x^2+4) now it should be easy #3 a little tinkering shows that you have (x+3)(x^2-6x+13) again, complex roots.
Math - Int Trig
#31 since f'(x) = -3x^2+2 the extrema are at x = ±√(2/3) f' > 0 for -√(2/3) x < √(2/3) so f is decreasing on that interval, and increasing elsewhere. #32 Since f(x) is odd, and the x^3 coefficient is -1, it rises to the left and drops to ...
Math - Algebra2
#1 surely you don't have to ask about this one -- the terms get ever larger #2 is simply a geometric series, with |r| < 1, so it converges.
actually, you start with one bacterium. You need a function that doubles every time you add 1 to the time. You probably already are aware that this models exponential growth, so what such function doubles as needed? 2^x does the job. So, starting at time x=0, at time x hours l...
clearly f(x) increases as x increases, since the slope is always positive.
Math problem or trick
sounds like it to me, since no one (probably) was wearing both.
so, what's the trouble? Just fill in the table x x^2 : x-x^2 0 0 : 0-0 = 0 1 1 : 1-1 = 0 2 4 : 2-4 = -2 and so on for whatever values you want.
Write a table for the following quadratic function. y = x - x squared
Write a quadratic function rule for the following table x -10 -5 0 5 10 y 80 5 -20 5 80
well, what is 3500 + 200 ln(1000) ??
P(even,~8) = P(2,4,6,10,12) = 1/36 + 3/36 + 5/36 + 3/36 + 1/36 = 13/36 P(8) = 5/36 P(odd) = 1-(13/36 + 5/36) = 1/2 So, Fred gets 8*13/36 + 1*5/36 - 2*1/2 = 73/36, or about $2
what is the slope? (f(x1)-f(x2)) / (x1-x2) both are positive, so the slope is always positive.
what you mean is .25x = 20 x = 80
10 days is 1.33 std below the mean 21 days is 2.33 std above the mean just consult your Z table.
most important factor: do not watch the clock!
x y 30 84 90 74 So, every extra 60 trees reduces the yield by 10kg, so y = -(10/60)x + c Since y(30)=84, (-1/6)(30)+c = 84 c=89 y = -x/6 + 89 The total yield is trees * avgyield, so x(-x/6+89) = -x^2/6 + 89x This is just a parabola, where the vertex is at x = 3*89 You can figu...
the police car is moving 20 km/hr faster, and must make up 1.6km. That will take 1.6km / 20km/hr = 1.6/20 hr No idea when that will be...
First step: sort the values from low to high. mean: add them up and divide by how many values there are median: the middle value -- same number less as greater. If there are an even number of values, take the average of the two center values. mode: The value(s) which occurs mo...
just substitute in 1,2,3,4,... for n 3*1+5 = 8 3*2+5 = 11 3*3+5 = 14 3*4+5 = 17 Or, just start with 8 and keep adding 3 for the next terms.
It is indeed. Since f(x) = 3x-2 for f(1.5), everywhere you see an x, replace it with 1.5 and then do the math.
chemistry pls help me asap
.96g of O2 is .03 moles So, since it takes 2 moles of Y to combine with 3 moles of O, and we have .03 moles of O2 (.06 moles of O), we have .04 moles of Y. So, the molar mass of Y is 2.08/.04 = 52
4x+7 < 11 4x < 4 x < 1 1-x <= -2 -x <= -3 x >= 3 so, x<1 or x>=3 see at http://www.wolframalpha.com/input/?i=solve+4x%2B7%3C11+or+1-x%3C%3D-2
3 mi * 15 min/mi = 45 min
what you have done is calculate the first year's growth. Now you have to add the 2nd year: 1000(1+.08)^(2-1) = 1080.00 Then the third year: 1000 1166.40+1080.00+1000.00 = 3246.40 As you can see, for n years, you would have 1000(1+1.08+1.08^2 + ... + 1.08^(n-1)) = 1000(1.08...
(1/4) / 3 = 1/12 think about it. If you cut a yard into 4 pieces, and then cut each of those (1/4 yard) into 3 pieces, there are now 12 equal pieces, of 1/12 yard each.
17ft * 17ft * 4 ft = 1156 ft^3 Now to convert that to $, 1156 ft^3 * (1yd/3ft)^3 * $50/yd^3 = $2140.74
a little inspection (or drawing) will reveal that ABCD is a rectangle with width=3 and height=2 EFGH is a rectangle with width=6 and height=4 Since the width and height have both been scaled by 2, the two rectangles are similar.
Help me trig.
tan(t/2) - sint = 0 (1-cost)/sint = sint 1-cost = sin^2 t 1-cost = 1-cos^2 t cost(1-cost) = 0 cost = 0 or 1 t = pi/2,pi,3pi/2 see http://www.wolframalpha.com/input/?i=solve+tan%28t%2F2%29+%3D+sint+for+t%3D0..2pi
use the product rule y = sinx tan^3(x) y' = cosx tan^3(x) + sinx (tan^3(x))' for tan^3(x), use the chain rule and you get y' = cosx tan^3(x) + sinx(3tan^2(x) sec^2(x)) Now we can massage things a bit: sin^3/cos^2 + 3sin^3/cos^4 sin^3*cos/cos^3 + 3sin^3/cos^4 tan^3(...
first step: what does 4x7 mean?
well, we know that with center at (h,k) the circle's equation is (x-h)^2 + (y-k)^2 = 100 Since (20,10) is on the circle, at one end of the horizontal diameter, it is clear that the center of the circle is at (10,10). (x-10)^2 + (y-10)^2 = 100 Getting the triangle's dim...
solve for what? Also, is the denominator m, or (m+1)?
Hmmm. That 9 at the start is perplexing. For the other terms, each increases by 5, so the millionth term after the 16 should be 16+5million = 5,000,016. If you can fix the 9 issue, it becomes quite easy.
log(x^3) = 2
4√6 / √30 multiply top and bottom by √30 to get 4√6√30 / 30 4√180 / 30 4√36√5 / 30 4*6√5 / 30 4√5/5 Or, 4√6/√30 4√(6/30) 4√(1/5) 4/√5 4√5/5
just the chain rule y = u^2 where u = tan(v) and v = x^4 y' = 2u u' y' = 2u sec^2(v) v' = 2u sec^2(v) (4x^3) = 8x^3 tan(x^4) sec^2(x^4) and, as usual, you can massage trig functions in various ways.
x = 2z y = 2a x < y 2z < 2a z < a
raise both sides to the 3/4 power: z+2 = 4^(3/4) z+2 = 2^(3/2) z+2 = 2√2 z = 2(√2-1)
4v = (4,8) w = (3,-4) so, now just subtract them
Math, Please Help
since the terms are number an, then n is any integer from one onward. n>=1. since a4 = a1*r^3, 1024r^3 = -16 r^3 = -16/1024 = -2^4/2^10 = -2^-6 So, r = -2^-2 = -1/4 a6 = a4*r^2 = -16 * 1/16 = -1
We have a circle and a straight line. So, either the line intersects the circle in two points, or it is tangent at just one point, or it misses the circle entirely. Since y = 4-x, plug that in to get x^2 + (4-x)^2 = 10 x^2 + x^2 - 8x + 16 = 10 2x^2 - 8x + 6 = 0 Since b^2-4ac i...
easy way: sin2x/cos2x = tan2x so the derivative is just 2sec^2(2x) hard way, using the quotient rule: [2cos(2x)cos(2x) - sin(2x)(-2sin(2x))]/cos^2(2x) 2(cos^2(2x)+sin^2(2x))/cos^2(2x) 2/cos^2(2x) 2sec^2(2x)
assuming simple interest, 50000*(3/4)*r = 4500 r = 4/3 * 4500/50000 = .12 or 12%
since you add exponents when multiplying, you just need to find three ways to add numbers to get 11: 5^11 = 5^3 * 5^8 5^11 = 5^0 * 5^11 5^11 = 5^-4 * 5^15 There are lots of other ways; not quite so many if you insist on only positive powers.
solve just like regular equations, working both at once. -4 <= 3+7x < 24 subtract 3 everywhere to get -7 <= 7x < 21 now divide through by 7: -1 <= x < 3
Algebra - eh?
I just see one, and yes, -4 <= 10
this is just a simple arithmetic progression, with a = 19 d = 1 Since there are 27-9+1=9 rows, S9 = 9/2 (19+27) = 207