Thursday
December 8, 2016

Posts by STEVE

Total # Posts: 46,957

Math
each side will be ?216 If you can't figure that out, just start listing the cubes of integers: 1^3 = 1 2^3 = 8 3^3 = 27 ... and see where you get 216
November 14, 2016

Trigonometry
csc x < 0 in QIII,QIV cot x > 0 in QI, QIII So, all 180 < x < 270 satisfy the requirements.
November 14, 2016

Math
what is /25? -25 + -9 = -34 25 + -9 = 16
November 14, 2016

Geometry
looks good
November 14, 2016

Graphing Linear Equations and Inequalities
well, did you fill in the table? when x=0, you have 4y = -16 and so on
November 14, 2016

Maximal area and dimensions of a window
see the related questions below. It does get a bit messy.
November 14, 2016

Calculus - Word Problems
v = 4/3 pi r^3 dv/dt = 4 pi r^2 dr/dt Now just use your numbers
November 14, 2016

Calculus - Optimization
blah blah stop reposting and wasting everyone's time
November 14, 2016

Calculus
see related questions below
November 14, 2016

Algebra 2
Take a look at the graph and figure it out. http://www.wolframalpha.com/input/?i=x%5E3%2B3x%5E2-9x-8
November 14, 2016

math
cosines will work well here, since you have B,a,c b^2 = a^2+c^2-2ac*cosB Then you can use sines to get A,C,b
November 14, 2016

math
You have a and A, so use sines: a/sinA = b/sinB That gives you B. Now A+B+C=180 Having C, use sines to get c.
November 14, 2016

math
I could not get the image to come up, but you will find that the maximum area is achieved when it is equally split among the widths and lengths. So, 1050 will be divided among the vertical pieces, and 1050 will be split into horizontal pieces. Define the 2100 as the sum of *x...
November 14, 2016

math
I will assume you gave the correct numbers. Now, present them in a way we can understand. Copy/paste from spreadsheets and word processor files does not work well here.
November 14, 2016

Math
construct a segment of length 19.5 At each end, draw a circle of the same radius. Where the circles intersect above (or below) the line will be the third vertex of the triangle, since all three sides are the same. Get out your protractor and measure the angles.
November 14, 2016

Math
a set has individual members Usually finding part of a whole involves dividing a single unit into pieces. Not really so different, but I think of it as the difference between cutting up an apple and separating the pieces of a puzzle.
November 14, 2016

math
Looks like Heron's formula is best here to get the area. Then, divide that by 70m^2/gal to get the # gallons.
November 14, 2016

math
so, a total of 16 east 8 north Now just find the length of the hypotenuse.
November 14, 2016

Math
depends on how long it is to take. 51 mph will do the job in an hour.
November 14, 2016

Math
1 - 1/5 = ? What did he spend it on -- Capital Letters?
November 14, 2016

math
and ... ?
November 14, 2016

pascal programming
the only critical thing here is deciding the age of the division.
November 14, 2016

math
x[(1.12)^(3/2) - (1.12)] = 150 assuming compounding annually
November 14, 2016

math
Draw a diagram and review your basic trig functions. It should be clear that the height is 15 sin60° + 8 sin30°
November 14, 2016

Calculus
Looks good to me, but I'd write it as -7/12 ft/s
November 13, 2016

Calculus
x^2+y^2 = 25 x dx/dt + y dy/dt = 0 So, find y when x=7, and then just use your numbers to find dy/dt
November 13, 2016

Graphing Linear Equations and Inequalities
while in this case, the explanation gives the right area, technically, the area to the right of the line is x > y/2 Since the y-coordinates are measured vertically, you should be looking for the area below the line. In this case, it's the same area.
November 13, 2016

Math
x+y+z = 7900 .05x + .11y + .15z = 965 z = x+y + 500
November 13, 2016

Math
The two roots of 2 and 5 mean y = a(x-2)(x-5)(x-h) for some h. Since y(0)=10, a(-2)(-5)(-h) = 10 ah = -1 Now, fix the bogus (-4) point and see what a and h have to be.
November 13, 2016

Science (galaxies and universe)
since it takes light some time to arrive at earth, we see what was happening when it left the galaxy, not now. So, if the star is one light-year away, when we see the light, it shows what was happening one year ago. Time travel!
November 13, 2016

Math
y-k = f(x-h) translates the graph y=x by the amounts h right and k up. y = (x+2)^2-3 y+3 = (x+2)^2 y-(-3) = (x-(-2))^2 so, that is the graph y=x^2 shifted -3 up and -2 right. Or, more simply, 2 left and 3 down. Work the others the same way. You can verify your results at the ...
November 13, 2016

Stoichiometry
First, balance the equation: 2Al + 3Cl2 -> 2AlCl3 So, you need 3/2 as many moles of Cl2 as you do Al.
November 13, 2016

Math
42
November 13, 2016

Integral Calculus
The p+2 just confuses things. Let q = p+2. Then you have the series 1/1 - 1/2^q + 1/3^q - 1/4^q The alternating series test says this converges for q>0 That is p > -2
November 13, 2016

Math
which multiple of 3 is 10 more than the same multiple of 2? 3x = 2x+10 x = 10 So, 10 students, 30 pencils.
November 13, 2016

Math
101 102 ... 198 199 and so on up to 904
November 13, 2016

English
#10 should be: Whoa! Bogus, D00d!
November 13, 2016

PreAp Math - incomplete
a. no way to tell, without knowing how many members in the club, or how many times they went shopping in a year. All we know is that some people spent about $18*1.055 each. Big deal.
November 13, 2016

Science-please help
2 and 3 are both involved. If the moon stood still (like the sun) #2 would do it If the earth did not rotate, #3 would still cause the moon to appear to rise and set, but it would only do it once a month, instead of once a day. I think #2 is the best answer here.
November 13, 2016

Math
think about C. It differs from B only in the rate of growth. (100% vs 3%)
November 13, 2016

help me calculus
I'll just use t for ease of typing. Those big Øs just distract me from the math. And that's "pi" not "pai" or "pie" or a dozen other ways it gets misspelled! x = cos(2t) y = 1+sin(2t) dy/dt = 2cos(2t dx/dt = -2sin(2t) dy/dx = dy/dt...
November 13, 2016

NO
?7 is real, but not an integer.
November 13, 2016

Math
assuming you meant the line joining those two points, it is (y2-y1)/(x2-x1) = (6-(-5))/(-4-3) = 11/-7 or, more usually, -11/7
November 13, 2016

8th Grade Pre-Algebra
P' = 1/3 P reflection in the y-axis just changes the sign of all the x-values. Since P" ? P', and P' is smaller than P, P" cannot be ? to P It is, however, similar to P.
November 13, 2016

MATH
clearly not A. 1.5 is real, but not an integer.
November 13, 2016

another please help me check~calculus maths
see related questions below.
November 13, 2016

College algebra
if x at 10%, then the rest (2500-x) at 8%. So, add up the interest: .10x + .08(2500-x) = 2200 But before trying to solve that, think on the numbers. No way could $2500 produce $2200 in interest...
November 13, 2016

Calculus
I guess you did. y' = (8e^(8x))(e^(8x)+9)-(e^(8x))(8e^(8x)) -------------------------------         (e^(8x)+9)^2 = 72e^(8x)/(e^(8x)+9)^2 You can use wolframalpha.com to confirm your results: http://www.wolframalpha.com/input/?i=...
November 13, 2016

Calculus
f = x^3+8x-3 f' = 3x^2+8 f'(6) = 116 dx/df = 1/(df/dx) = 1/116 1/11 must be a typo. http://www.sosmath.com/calculus/diff/der08/der08.html
November 13, 2016

Algebra 2
the real solutions are where the graph crosses the x-axis. That is, where ax^2+bx+c = 0
November 13, 2016

need help calculus plz plz-sir steve
ln(ab+cd) is NOT lna +lnb + lnc +lnd
November 13, 2016

need help calculus plz plz-sir steve
y=3e^(2x)cos(2x-3) y' = 6e^(2x) (cos(2x-3)-sin(2x-3)) y" = -24e^(2x)sin(2x-3) y" - 4y' + 8y = -24e^(2x)sin(2x-3) - 24e^(2x)(cos(2x-3)-sin(2x-3)) + 24e^(2x)cos(2x-3) = 0 Note that the DE y" - 4y' + 8y = 0 has the solution y = e^(2x)(a cos2x + b sin2x...
November 13, 2016

Math
Clearly, k=0 will do the job, but I doubt that's what you want. the quadratic formula says x = (-8±?(64-144k))/72 So, any negative value of k which makes 64-144k a perfect square will work. SO, if we let v be 64-144k, we have k v -1 208 -2 352 -3 496 -4 640 -5 784...
November 13, 2016

Math
That's better. Recall that area = base*height/2 BC is the base, and AD is the height.
November 13, 2016

Math
you have serious notation problems.
November 13, 2016

trigonometry
convert to x-y, add the components, and convert back to compass bearing. 15 @ S40°10’W = <-9.675,-11.463> ...
November 13, 2016

algebraic expression
15-12 and 15+12
November 13, 2016

Tanis
Remember that the circumference is c = 2?r You can find c, and thus get r.
November 13, 2016

Maths
powers of the numbers end in 1: 1,... 2: 2,4,8,6,... 3: 3,9,7,1,... 4: 4,6,... 5: 5,... Note that all can be grouped in periods of 4. 2014 = 4*53 + 2 So, the 2014th powers end in 1,4,9,6,5 Their sum ends in 5 So, the remainder is zero.
November 13, 2016

math
Model using a Venn diagram. The numbers fall into (a) multiples of 6 (b) multiples of 9 (c) multiples of 6 and 9
November 12, 2016

Math
You can't choose both B and D! B grows by a constant 3% rate, or a factor of 1.03 D grows by a constant difference of just 12 Both cannot express the same model.
November 12, 2016

Math- HELP!
Depends on the base of your growth factor. Clearly, the relative amount after t days is 2^(t/3) But, if you want e^(kt), then since 2 = e^ln2, you have (e^ln2)^(t/3) = e^(ln2/3 t) = e^(0.231t)
November 12, 2016

math - typos
fix the typo(s) -/ is not a legal sequence of operators
November 12, 2016

Maths
the series is 132 ?(3k+2) = 3?k + 2?1 k=1 = 3*(132)(133)/2 + 2*132 = 26598
November 12, 2016

maths help sir steve
x^2+2xy+3y^2=1 2x + 2y + 2xy' + 6yy' = 0 (2x+6y)y' = -2(x+y) y' = -(x+y)/(x+3y) y" = -[(1+y')(x+3y)-(x+y)(1+3y')]/(x+3y)^2 You are correct so far. It can be simplified to y" = -2(x^2+2xy+3y^2)/(x+3y)^3
November 12, 2016

Calculus @Multiple Choice!
there you have three answers. Take your pick...
November 12, 2016

Calculus
x^2+y^2 = 20^2 a = xy/2 = x?(400-x^2)/2 da/dt = (200-x^2)/?(400-x^2) dx/dt at x=11, da/dt = (200-121)/?279 * 4 = 18.92 ft^2/s It would have been polite to show your work, so we could find the mistake. Or, of course, check my work to be sure I haven't goofed!
November 12, 2016

math
(x+x+...+x)+(2-1)+(4-3)+...+(100-99) = 0 100x + 50 = 0 x = -1/2
November 12, 2016

maths
we have 3(x-y)^2 (1-y') = A + Ay' 3(x-y)^2 - 3(x-y)^2 y' - A'y = A (3(x-y)^2 + A)y' = -(A+3(x-y)^2) y' = -1 so, y = -x and (2x+(-x))(-1) = (x + 2(-x)) -x = -x Kind of a strange problem. Now for the other one, I'm not sure I can improve on Damon'...
November 12, 2016

Math
You appear to mean "two" distinct real roots, since :tho" is just too weird to mean "one" or "three". SO, there is a repeated root. If the two roots are p and q, with p repeated, then (x-p)^2 (x-q) = x^3-kx+k-1 x^3 - (2p+q)x^2 + (p^2+2pq)x - ...
November 12, 2016

urgent math
In this case, Draw the horizontal ground Draw two vertical lines standing on the horizontal ground, one taller than the other. Label their tops A and B, and their bottoms C and D Draw a horizontal line from the top of the shorter building (A) to where it intersects with the ...
November 12, 2016

urgent math
Draw a diagram and review your basic trig functions. Then it will be clear that if the distance between the buildings is x and the height of the taller building is h, then 39/x = tan36° (h-39)/x = tan47° so, h = (39/tan36°)(tan 47°) + 39
November 12, 2016

math
The 8th term of (a+b)^12 is, according to the binomial theorem, 12C7 a^(12-7)b^7 12C7 ?x^5*(2/?x)^7 = 792 * x^(5/2) * 128/x^(7/2) = 101376/x
November 12, 2016

math
(x+x+x...+x) - (1+2+3+...+10) = 0 10x - 55 = 0 x = 55/10 = 11/2
November 12, 2016

maths too hard help
is that "men or doctors or both"? I assume so, since otherwise, all the doctors are women. It appears that 1 woman is a doctor, since there are only 23 men, 3 of whom are doctors.
November 12, 2016

math- Trigonometry
Draw a diagram. It should be clear that x/15.6 = cos54° If this is challenging, you need to review your basic trig functions.
November 12, 2016

maths sir steve plz reiny plz sir damon plz help
stop with the repeat postings already, ok?
November 12, 2016

maths sir steve plz reiny plz sir damon plz help
?1.21
November 12, 2016

Math
yes.
November 12, 2016

Math
check the slopes. If they are all the same, then the lines are parallel. If their product is -1 (as with -4 and 1/4) then the lines are perpendicular.
November 12, 2016

math
Your average is still 90. The 1.10 (not 1.10%) only matters when weighed in combination with other grades. And even then it might not make a difference. For example, if your other grades are 80 and 100 (with weight 1.00 each), then the average of the three is still 90, ...
November 12, 2016

maths help plz&plz
As you found, 31 play Football and Tennis. But there is no way to know how many play exactly which one sport. Clearly, n can be any multiple of 3. For example, if n=3, then there are 6 people who play exactly one sport, but there's no way to know how those six are ...
November 12, 2016

Maths
h/42 = tan36°
November 12, 2016

English
#1 is best choice. (#3 maybe in Britain) #5 is best match for meaning. #4 implies a lack of specific intent or destination. #6 is just bad usage.
November 12, 2016

English
#1. I don't think that's a good explanation. It just means that I agree. #2 nope - However, it's common to say "It's not raining much"
November 12, 2016

English
yes
November 12, 2016

mathematics
just put the words into math: Original fraction: x/(x+3) (x-2)/(x+3-2) = x/(x+3) - 1/8 Now just solve for x
November 12, 2016

Geometry
opposite angles are equal, and consecutive angles are supplementary, so 3x-20 = 5y-10 7x + 3x-20 = 180 x+y = 30
November 12, 2016

Physical Science
A 68.4-g sample of potassium chloride was added to 200.0 g of water at 20 C. Is the solution saturated, unsaturated, or supersaturated?
November 12, 2016

English
1 and 2 are both common, and mean the same. 3-6 are all grammatically correct, but the only way I'd say it is she is wearing makeup (all finished) she is putting on makeup (in the process) use of the word "cosmetics" in such a context seems stilted to me. The ...
November 12, 2016

math
?(6x-5)/x = 1 6x-5 = x^2 x^2-6x+5 = 0 x = 1 or 5
November 12, 2016

Physical Science
When iron metal reacts with oxygen, the reaction can form Fe203. The balanced chemical equation I think is right is 4 Fe + 302----2Fe203. So I have 4 moles of iron + 3 moles of oxygen creates 2 moles of iron oxide. I need to find the number of moles of oxygen that are needed ...
November 11, 2016

Algebra
the rule of signs says that there is at most one positive root, and 3 negative roots. rational zeros states that any rational root will be ±1 or ±1/2
November 11, 2016

MATH
If x was at 9%, then the rest (700-x) was at 6%. So, add up the interest: .09x + .06(700-x) = 57
November 11, 2016

Math
x = smaller. So, 4x = larger now what else do you know?
November 11, 2016

Linear Algebra
a-3c=0 2b+4c=0 -a+2b+7c=0 3v1 - 2v2 + v3 = 0 v3 = 2v2 - 3v1 ...
November 11, 2016

Math
the diagonal of the square is the diameter of the pizza. ?/4 d^2 - d^2/2 ---------------------- ?/4 d^2 = (?-2)/? = 0.3634 ? 37%
November 11, 2016

Math
look at the diagram. Drop a line from E to AB. E is in the center of the rectangle, so if angle AEB=?, tan(?/2) = (10/2) / (5/2) = 2 ?/2 = 63.4° ? = 126.8°
November 11, 2016

Math
Let the amounts invested at the three rates be x,y,z. Now just write down the facts as given: .04x + .05y + .08z = 5700 x = y + 20000 .08z = 8 * .05y Now just solve for x,y,z.
November 11, 2016

maths
since the terms of the sequence are all odd numbers (2k+1), and there are k^2 terms <= the kth odd number, look for something like 2[?n]+1 That sequence is 3,3,3, 5,5,5,5,5,5,5, ... Looks like we have to adjust it by 1 to get 2[?(n-1)]+1 So, b+c+d = 2 No, I don't have ...
November 11, 2016

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