# 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?