# Posts by Steve

Total # Posts: 53,641

geometry
the value of x does not matter, if it is just the ratio of ares you want. Just draw the figure, and it should be clear that (x/2)^2 + (x/2)^2 = y^2 simplify, and then your ratio is just x^2/y^2

Math_sales tax_ discount
100 * 0.80 * 1.07 = ?

math
It is (x-5)(x+4) just having the problem given the way it was, you ought to have looked for a factor in common with the numerator. Don't let the teacher be cleverer than you!

Coordinate geometry
set it up so that the three vertices are at (0,0), (a,0), (0,b) Then the median to the hypotenuse has endpoint (a/2,b/2) So, its length ?((a/2)^2 + (b/2)^2) = ?(a^2/4 + b^2/4) = 1/2 ?(a^2+b^2) which is half the hypotenuse.

Math
clearly, infinity! extra credit: what if x -> 0 ?

Math-intergration
e^-? = 0 sin? and cos? are undefined, but lie between -1 and 1 multiplying by 0 leaves the result = zero

coordinate geometry
google is your friend. one definition is the locus of a point whose distances from a fixed point and a fixed line is the equal.

rationalizing
(a-b)(a+b) = a^2-b^2, so (?18-?17) * (?18+?17)/(?18+?17) = (18-17)/?(18+?17) A calculator has roundoff error. ?18 is very close to ?17. Not too close in this case, but ?188888 - ?188887 are very close, and (floating-point) precision will be lost when trying to include the ...

math
"of" means "times," so [(2/5)(2/3)]/(3/10) = (4/15)*(10/3) = 40/45 = 8/9 also, "division sign is divided by" is gibberish.

Order with fractions
you are right; I misread the words. Here is what you wrote, using only math symbols: 2/(2/3) + 3/4/(4/5) Now start inserting parentheses until it means what you think it should. If you use wolframalpha.com, it will show what your entered text really means: http://www....

Order with fractions
why all the words? 2/3 + 3/4/5 = 2/3 + 3/20 = 49/60 2/3 + 3/(4/5) = 2/3 + 15/4 = 53/12 without parentheses, multiplication and division are done left to right, before any addition or subtraction.

Maths
the inside space is a 6x6x6 cube. So, just subtract it: 8^3-6^3 = ?

composite functions
Assuming the usual carelessness with parentheses, I guess you have f(x) = 2/(3x-1) g(x) = (x+4)/x g(f) = (f+4)/f = (2/(3x-1)+4)/(2/(3x-1)) = 6x-1

Algebra 2
(b) as always, max height (the vertex) is at t = -b/2a = 1 (a) figure h(1) (c) solve -16t^2+32t+28 = 0

math
p((1+r)^2-1) = 220 p(2r) = 200 now just solve for p and r.

maths
well, we know that a/c = b/d, so a^3c/b^3d = (a/b)^3 * c/d = (c/d)^4 ac^3/bd^3 = a/b * (c/d)^3 = (c/d)^4 see what you can do with that.

math
the opposite direction: 120+180 = 300

Math
20% = 1/5 3/8 * 4/5 = 3/10 1/5 + 3/10 = 1/2 so, x/2 = 40 ...

Maths
the jeans cost \$30 less 30/280 = 0.107 or about 11% cheaper

Math
He sold 9 eggs at 4/egg = 36 His cost was 40 I don't see any profit there. Looks more like a 10% loss.

Math
98/7 = 14 lbs/day average 7/2 (2a+6*2) = 98 so, a = 8 The median is the 4th day, so he cooked 8+3*2 = 14 lbs on that day. So, the mean and median are the same. In fact, that is true for all arithmetic sequences. Sn = n/2 (a1 + an) the mean is thus Sn/n = (a1+an)/2 The median ...

Maths
1 1/2 hours = 90 minutes, or 15 doubling periods. So, there will be 3*2^15 bacteria

Math
If \$x is at 8%, then the rest (3500-x) is at 5%. So, .08x + .05(3500-x) = 238 Now just solve for x. Extra credit: How much did Moon Unit get to invest?

Math- Slope
of course not. You have to have two points.

Math- Slope
The line through (2,4) and (-2,1) has slope 3/4 The line through (2,4) and (4,0) has slope -2 Remember that the slope is y2-y1 ------ x2-x1

Math_ Geometry
actually, you divide by 180. A n-sided polygon's interior angles sum to (n-2)*180. So, here we have (n-2)*180 = 1260 n-2 = 1260/180 n-2 = 7 n = 9

Math_ Geometry
1260 = 180*7 So, a 9-gon fits the bill

Trigonometry
just convert everything to x-y values, add them up, and change back to headings. If his heading is ?, then we need 160sin? - 20sin310° = v*sin80° 160cos? - 20cos310° = v*cos80° solve that and you get ? = 74.5° v = 172.1 makes sense, since the wind is ...

Math
just put together what you know: horse: 5 round, 10 square cat: 24 round, 6 square dog: 0 round, 19 square rabbit: 11 round, 0 square so, now you can easily figure what fraction are round.

Physics
final location: 30 E, 20 S total travel: 110 now you can find the displacement, using the Pythagorean theorem. no idea what distance in FPS is. All distance quoted were in meters.

math
tan x/2 = (1-cosx)/sinx so, tan(1/2 cos^-1(a/b)) = (1-a/b)/(?(b^2-a^2)/b) = ?((b-a)/(b+a)) so, if we let z = 1/2 cos^-1(a/b) tan(?/4+z)+tan(?/4+z) = (1+?((b-a)/(b+a)))/(1-?((b-a)/(b+a))) + (1-?((b-a)/(b+a)))/(1+?((b-a)/(b+a))) putting all over a common denominator, things ...

math
(3/4 - 3/5)x = 9 3/20 x = 9 x = 60 check: 3/4 * 60 = 45 3/5 * 60 =36 45-36 = 9

math
you can play around with Z-table stuff here: http://davidmlane.com/hyperstat/z_table.html

Math
For x ft^2 of flooring, T = V1 + V2*x x = (T-V1)/V2

Physics
that's "estimate" not stamate. 3700km/5.1days = 725.5 km/day So, for 6200 km, it will take (6200/3700) * 5.1 days

math
to get what? If you want a perfect square, (x+5)^2 = x^2+10x+25

math
(a) as with all these, divide the fence so that the lengths (1) equal the widths(2). Thus the pen is 600x300 (b) same problem, but now there are 4 widths, so the same principal applies. To minimize the fence, each pen has dimensions x and 25/x, where 4x = 5(25/x). That is, x^2...

geometry
Drop altitudes of length a from the ends of the shorter base. This gives you two right triangles at the ends, with altitude a and base x. Since the figure is isosceles, the two base angles are equal. Now you have Each base angle is 70° a/7 = cos70° x^2 + a^2 = 7^2 Now ...

geometry
as you recall a = ?r^2 c = 2?r so, the pool with cover has a diameter of 21 ft. The radius is thus 10.5 Now just plug and chug.

physics
If you mean that the balls pass as they have both fallen 400m, then you have 4.9t^2 = 400 v(t-2)+4.9(t-2)^2 = 400 v(20/?4.9-2)+4.9(20/?4.9-2)^2 = 400 v = 22.39 m/s

MATH
1/x = 1/10 + 1/12 - 1/20 x = 15/2

Math
5/3 * 1/3 = 5/9

math
the areas are in the ratio 4:9, so 4/9 * 63pi = ? Note that's pi, not pie!

maths
how about 18 * 7 1/4 ?

Maths ( arthmetic )
find a and d using what they have told you: a+3d = 10 a+10d = 3(a+3d)+1 Then just evaluate S20 = 20/2 (2a+19d)

physics
y = h + 100t - 4.9t^2 and you know that y=0 at t=6, so h + 100*6 - 4.9*36 = 0 I suspect a typo...

math
well, what is 1/8 of 64? 64/8 = ? now just take 7 times that.

maths
well, you know that 1.05 p = 262.50 so, ...

Math
I assume you mean (9a^4)^2 = 9^2 (a^4)^2 = 81a^8

Math-college
Actually, it is correct for some values of x. Now, if you want to solve (x + 3)(x -4) = 7 you cannot just set one factor equal to 7, because that means that the other factor must be 1. That is why we always set the left side equal to zero, because then if the product is zero, ...

statistics
just multiply all the quantities together.

Calculus
Since I cannot see the graphs, I have no idea what the numeric values are...

Calculus
concave up means f" > 0 That means f' is increasing. inflection points are where f"=0 and f'?0

Math
well, (3b^4)^2 = 9b^8

Math
well, 48 = 16*3 see where that takes you.

Math
getting rid of the expressions inside the parentheses, you have 7x = 2(-3)^2 + 3(8) 7x = 2*9 + 3*8 ...

Math
3x = # dogs 2x = # cats 3x+2x = 30 ...

Chemistry
the valence of Na is always +1

Science
2kW = 2000 J/s = 2000 Nm/s Now just convert that to kg

math
the yard is 5750x2200 GCD(5750,2200) = 50 so, using 50x50 cm stones will use the fewest Now just figure how many that will be.

Math
looks like you just want the sum of all the numbers from 1 to 10. If you list the numbers, you get 1 2 3 4 ... 8 9 10 Now pair them up, starting from the ends. Each pair adds up to 11. There are 10 numbers, so 5 pairs, adding up to 11*5 = 55 Since it looks like you are going ...

math
there are 6 possible outcomes, and only one is a success, so P(5) = 1/6 Now you want two independent events, so just multiply their probabilities. Of the 36 possible outcomes, only 1 is a success...

math
see the related questions below

math
see related questions below

Physics
take a look at the formula which gives the pendulum's period. It involves g, right? Look what happens if you replace g by g/6

Math-college
if it has real coefficients, then its complex roots come in conjugate pairs, meaning f(x) = a(x-2i)(x+2i)(x-4i)(x+4i) = a(x^2+4)(x^2+16) Now just find a that makes f(-1) = 85

Math
a garden is 2x15 yards in size. what is its area, in ft^2?

Math
(44-4)/4 = 10 Hint: 4+2 = 6

building a stair system
what do you mean by "length"? The circumference is 360? inches. The size of the steps affects the "length" to the top, but the slant height is ?(180^2+77.5^2) ? 196 inches

MaTh
You can do this one by inspection, since you know that 5*20 = 4*25 = 100 Still, to solve this kind of problem in general, follow the steps. Write what they tell you, then work for a solution: vt = 100 (v+5)(t-1) = 100 (v+5)(100/v-1) = 100 (v+5)(100-v) = 100v v^2+5v-500 = 0 (v-...

science
which given calendar?

Math
so, how do you have a 12th row in a 3-by-3 array?

Math
they occur where the denominator is zero (and the numerator is not zero)

Vectors
the three vertices determine a plane. The 4th point must lie in that plane, but you can pick any of the three points to be the "origin" relative to the other two.

Algebra
we have b = kc/d^2 So, bd^2/c = k is constant That mean you want b such that 9b/20 = 45*2^2/40 ...

Math
b = j+9 6(b+8) = 7(j+8) now just solve for b and j.

math
x(1 - 7/13 - (2/3)(6/13)) = 6 now just find x.

maths
Pick two points, one near A and the other near B. You will find the order does not change.

science
the initial upward velocity is 80 sin 25° = 33.8 m/s So, the height y = 35 + 33.8t - 4.9t^2 (a) t = 7.8 So, use that to find the horizontal distance traveled at 80 cos25° = 72.5 m/s Finally, find the x- and y-components of the velocity at t=7.8 to get the answers to (b)

Angular motion
the circumference of the wheel is 0.6? so, since there are 2? radians per revolution, the angular speed is 36 / 0.6? * 2? = 120 rad/s

Physics
He clearly did not accelerate at 10 m/s^2 for the whole 10 seconds, or the distance covered would have been 1/2 at^2 = 500m and his top speed would have been 100m/s. So, if he accelerated smoothly from 0-12 m/s over t seconds, then a = 12/t m/s^2 So we have (1/2)(12/t)t^2 + 12...

@oops
I see I can neither factor nor count. Go with Reiny.

Maths
7056 = 2 * 3528 = 2^2 * 1714 = 2^3 * 857 Now factor 857. You know there are no more 2's in there, so start with 3, and so on. So, what do you get? Since there are only three 2's, the square root will not be an integer, but will have a radical left over.

Math - eh?
Is that (a^q)-r or a^(q-r) etc. And is that comma supposed to be a period? That is, are the three items all to be multiplied together?

math
recall that (u-v)(u+v) = u^2-v^2 Now let u = 2?b v = ?(3a) and it falls right out

geometry
see related questions below

math
42

Math
don't know. some probably can do polar coordinates, but the implicit definition makes it tricky. They wouldn't look as nice as the online ones, that's for sure.

Math
first step: use real math notation (x^2+y^2-1)^3 = x^2 y^3 As with any function, just start plugging in values for x (or y) and solving to get the other coordinate. Not easy, in this case, since high powers are difficult to solve except in special cases. The other, easier, way...

math
not even close. That 25 in there doesn't just disappear...

math
(30*25*14)/42 = ?

calculus
I guess that would just be ?[-5,5]?[0,?(25-x^2)] y dy dx = 250/3

maths
the job is 12*6 = 72 man-hours of work. In 1 hour, the 12 men have done 1/6 of the work, leaving 60 man-hours to do. That will take 20 men 3 hours to finish up.

math
if you mean 16% is 832, then .16x = 832 ...

Math
hmmm. You need to review just what "isosceles" means ...

math
any situation where one quantity changes steadily. All you need are two pairs of data relating the items

math
the 25% + 2/9 of the remaining 75% add up to 1/4 + (2/9)(3/4) = 9/36 + 6/36 = 15/36 = 5/12 So, if he started out with x limes, then 7/12 x = 280 and so on

math
since the only difference is an ice cream, it clearly cost \$10 That means that the cake was \$200 ...

algebra
If you set up the curves as described, you have x^2/25^2 + y^2/20^2 = 1 x^2/125 - y^2/100 = 1 They intersect at (±25?5/3,±40/3) so pick P to be one of those points and figure your answer.

algebra
you need to review your material. The mode is the value which occurs most often. So, what do you think?