Monday
October 20, 2014

Posts by STEVE


Total # Posts: 25,943

Urgent geometry help
Since there is no conditional specified, there can be no converse. However, given your interpretation, your converse is correct. The "will" isn't really necessary at all, if you consider coming and leaving as sort of chronic events, one conditional on the other.
September 25, 2014

Algebra 1
|n-34| <= 8
September 25, 2014

Algebra
|p-53| <= 5
September 25, 2014

algebra
clearly the minimum cost is at the vertex of the parabola, which is at x = -b/2a = 18.1/1.8
September 25, 2014

AP Physics
28 @ S45W = (-19.8,-19.8) 56 @ E = (50,0) 84 @ E53N = (50.5,67.1) Add them up to get (80.7,47.3) So, we need (-80.7,-47.3) to get back to (0,0), a displacement of 93.5 m
September 25, 2014

Physics
Speedboat A negotiates a curve whose radius is 100 m. Speedboat B negotiates a curve whose radius is 221 m. Each boat experiences the same centripetal acceleration. What is the ratio vA/vB of the speeds of the boats?
September 25, 2014

Math-please check
#1 of course not: |-6|=|6| but -6≠6 #2 same reasoning. y could be -8. You can say, therefore that if |a|=|b|, then a^2 = b^2.
September 25, 2014

math...
I think you meant b-9 > 20 Now add 9 to both sides to get b by itself: b > 29
September 25, 2014

Math Help.
clearly, x <= 1, so 3x <= 3 3x+1 <= 4 Looks like D to me. C would have an open circle on the 1, rather than a filled dot.
September 25, 2014

geometry
oldv = 1/3 pi r^2 h Now replace r with 4r and h with whatever fraction of h, say, 1/n, it has become. new v = 1/3 pi (4r)^2(1/n * h) = 1/3 pi * 16r^2 * h/n = oldv * 16/n
September 25, 2014

Please math help
A n n-10 10-n 7-n n-7 n-7 = -3, so n=4 B yes, it always works, as shown above
September 25, 2014

Algebra
7p^2+16=2151 7p^2 = 2135 p^2 = 305 p = √305
September 25, 2014

Math
Things would be a lot clearer if you wrote CN^2 = 13^2 + 18^2 - 2*13*18 cos 45 = 169 + 324 - 468*√2/2 = 162.07 CN = 12.73
September 25, 2014

trignometry
y^2*sin(x)*sin(z)/2*sin(y) area = z/2 * y sinX but, z/sinZ = y/sinY, so z = ysinZ/sinY area = ysinZ/2sinY * y sinX = y^2 sinZ sinX / 2sinY
September 25, 2014

algebra
(5.1*10^3)*(3.2*10^3) (5.1)(3.2)*(10^3)(10^3) 16.32 * 10^6 But that's not scientific notation, so you need to shift the decimal point to 1.632 * 10^7
September 25, 2014

Algebra 2
a = 2pi r h + 2 pi r^2 = 2pi((3x-2)(x+3) + (3x-2)^2) = 2pi(3x^2+7x-6 + 9x^2-12x+4) = 2pi(12x^2-5x-2)
September 25, 2014

MATH
#1 ok #2 First, recall that ALL |x| are positive. So, make sure all the plain old negative values come first, then the positives. For example, D is obviously not it, because the numeric values are 7,4,3,0,-3,-7 In fact, it's exactly the reverse of what you want. #3 ok #4 |...
September 25, 2014

Math
4x + 2x = 15 x = 2.5 So, 5 cups of nuts, 10 cups of chips.
September 25, 2014

maths
26*(48)+(-48)*(-36) 26*(48)-(48)*(-36) Now factor out the 48 (48)(26-(-36)) (48)(62)
September 25, 2014

ALGEBRA 2
1-x >= -3 x <= 4 5x-1 >= 19 5x >= 20 x >= 4 Looks like all real numbers.
September 25, 2014

ALGEBRA 2 - Oops
Oops - mangled that one, eh? -1 <= 3+2x < 11 -4 <= 2x < 8 -2 <= x < 4
September 25, 2014

ALGEBRA 2
-1 <= 3+2x < 11 -4 <= 2x <= 14 -2 <= x <= 7
September 25, 2014

TRIANGLE
hard to solve without knowing which angle is 59°. If A or C, 8/sin59° = 12/sin(C or A), so then you can figure B and use law of sines again to get AC. If B, AC^2 = 8^2 + 12^2 - 2*8*12 cos 59°
September 25, 2014

Maths
x+y = cscA+cosA+cscA-cosA = 2cscA x-y = cscA+cosA-(cscA-cosA) = 2cosA 2/2cscA = sinA 2cosA/2 = cosA All clear now?
September 25, 2014

math
Assuming he started at the pole, after 5 seconds he is 7.5 m away. So, if the shadow has length s, use similar triangles to get (s+7.5)/3.8 = s/0.95 Now just solve for s.
September 25, 2014

Math
correct. Just as 47 is in between 36 and 49, the root is in between 6 and 7.
September 24, 2014

Algebra, Please Help!
no way to tell. There are lots of circles with a given center. Just think of a target with a bulls-eye. You will need some other piece of data, such as a point on the circle.
September 24, 2014

Math
cube has volume 4^3 = 64 sphere has volume π/6 * 4^3 = 64π/6 Now just subtract the volumes: 64(1 - π/6) Actually, the wording is a bit vague. Since the sphere has replaced some of the cube, the space is still occupied, so the whole cube constitutes the souvenir...
September 24, 2014

calc 3
(a) study your text, or (b) google for examples, such as http://www.math.ucla.edu/~ronmiech/Calculus_Problems/32A/chap12/section6/812d55/812_55.html and follow the same steps.
September 24, 2014

Algebra II Honors
Any line in the yz plane becomes a plane perpendicular to the yz plane, in xyz space. Think of the point y=3. When propagated parallel to the x-axis (perpendicular to the y-axis), it becomes a line. Same for a line propagated through space. x+y=0 is the same thing, parallel to...
September 24, 2014

Math-calculus
what don't you get? You have the equation for d(t). Just do the math. For the graph, see http://www.wolframalpha.com/input/?i=40%2B60cos%28%28pi%2F2%29%28t-2%29%29 For the rest, just solve for t under the given conditions: (b) 40+60cos(PI/2(t-2)) = 76 (c) is d(t) on its ...
September 24, 2014

math-pre calc
To average 48 mi/hr, you need to cover 106 miles in 2.208 hours. The first half took 53/36 = 1.472 hours So, how fast do you need to go to cover the other 53 miles in (2.208-1.472) hours?
September 24, 2014

SAT Math
how about (A)? 3 is not divisible by 2.
September 24, 2014

Pre-Calc
clearly, y = a(x+5)^2 - 2 Now just plug in the point and solve for a. But, you want y=ax^2+bx+c, so just expand and collect terms to wind up in that format.
September 24, 2014

Algebra 2
You are correct
September 24, 2014

Calculus
y = 3x^2 - x - 5 y' = 6x-1 So, at (1,-3), the slope of the normal is -1/5, and the line there is y+3 = -1/5 (x-1) y = -1/5 x - 14/5 So, where does the line intersect the parabola? -1/5 x - 14/5 = 3x^2-x-5 -x-14 = 15x^2-5x-25 15x^2-4x-11 = 0 (15x+11)(x-1) = 0 So, the line ...
September 24, 2014

Geometry
R+S = 90 U+V = 90 so, y-2 + 2x+3 = 90 2x-y + x-1 = 90 2x+y = 89 3x-y = 91 5x = 180 x = 36 and now you can take it from there.
September 24, 2014

Pre-Calculus
the slope is 5/2, so y+3 = 5/2 (x-2) Now rearrange the terms as needed
September 24, 2014

Math 112
equal has many meanings, most of them to do with numbers. Maybe equal area, equal perimeter, etc. congruent is for geometric properties, not numeric values. For instance, we say two angles are congruent when they have equal measures.
September 24, 2014

geometry
v = (40)(20*8 + 20*7/2)
September 24, 2014

Math 112
since both your expressions are identical, I think there's a typo. If you meant for the operators to be "equal" and "congruent", then the answer is that AB and CD are geometric figures. As such, they can be congruent, not equal. They are congruent if ...
September 24, 2014

algebra 2
Just draw the line 3x+y = 5 then, shade the area below the line, where, naturally, 3x+y < 5 See http://www.wolframalpha.com/input/?i=3x%2By%3C5
September 24, 2014

Math--Teach me?
work your way from the inside, to get rid of parens and brackets: 2[4(9 – 7) + 1] ÷ 3 2[4(2) + 1] ÷ 3 2[8+1]÷3 Now do the multiply and divide, left to right: 2[9]÷3 18÷3 6
September 24, 2014

Pre-Calculus
correct
September 24, 2014

Pre-Calculus
correct
September 24, 2014

Algebra
just recall that orthogonal means that u•v = 0. So, (a) (1,2)•(k,k) = k + 2k = 0, so k=0 (b) (1,2,1)•(k,2k,4) = k+4k+4 = 0, so k = -4/5 Kind of boring examples, IMO.
September 24, 2014

Pre-Calculus
Ummm, y = mx+b is called the slope-intercept form because you can just read them off: slope = m y-intercept = b Now can you pick the correct choice?
September 24, 2014

Algebra
you just need to d a lot of these problems. Look for common factors. 9w-w^3 clearly w can be factored out, so w(9-w^2) Now you have to recall the difference of squares is x^2-y^2 = (x-y)(x+y), so w(3-w)(3+w) As for the rest, I have no idea what 3h2 the 2 power + 1+3a even ...
September 24, 2014

calculus
z = √(x^2+y^2)+xy ∂z/∂x = x/√(x^2+y^2) + y ∂^2z/∂x^2 = y^2/(x^2+y^2)^(3/2) ∂^2z/∂x∂y = 1 - xy/(x^2+y^2)^(3/2) Since z is symmetric in x and y, the y derivatives are the same, just using y instead of x. As usual, check my ...
September 24, 2014

trig
review your basic trig definitions, and draw a diagram. You will see that (h-1.6)/50 = tan 36° Now just solve for h.
September 24, 2014

Calculus I
Since T(t) is the temperature after t hours, N(T(t)) is the number of bacteria after t hours
September 24, 2014

calculus
f(x) is decreasing when f'(x) < 0, so just solve 6x^2+6x-12 < 0 x^2+x-2 < 0 (x+2)(x-1) < 0 The roots are at -2 and 1, and the parabola opens upward, so f'(x) < 0 between the roots. f(x) is decreasing on (-2,1) Note that it is not [-2,1] because at the ...
September 24, 2014

math,algebra
3^-1 = 1/3, so you have (x^3/3)^2(12x^5) = (x^6/9)(12x^5) = 4/3 x^11
September 23, 2014

calculus
(6x^2+4y^2)/(3x+7y)=3 we know that (u/v)' = (u'v-uv')/v^2, so ((12x+8yy')(3x+7y)-(6x^2+4y^2)(3+7y'))/(3x+7y)^2 = 0 36x^2 + 84xy + 24xyy' + 56y^2y'-18x^2-12y^2-42x^2y'-28y^2y' = 0 because the denominator is not zero y'(24x+56y^2-42x^2-28y...
September 23, 2014

Trigonometry
this is just (1-cos^2)^2 = (sin^2)^2 = sin^4
September 23, 2014

MATH ASAP!!
1/(1-√7+√5) multiply top and bottom by 1-√7-√5 (1-√7-√5)/((1-√7)^2 - 5) = (1-√7-√5)/(1-2√7+7-5) = (1-√7-√5)/(3-2√7) now multiply by 3+2√7 (1-√7-√5)(3+2√7)/(9-28) (1-√7...
September 23, 2014

Math
since sine = y/r, and r is always positive, sine is positive where y is positive.
September 23, 2014

algebra
recall the point-slope form for a line. #1 the slope is 3, so y-3 = 3(x-4) Similarly for #2, except the slope is 1/3. (why?)
September 23, 2014

Vector
measuring from P, (s-p)+(r-s) = (q-p)+(r-q) = r-p = (2,6,2)-(1,2,-1) = (1,4,3) the area is |(s-p)x(q-p)| = |(0,2,4)x(4,-3,5)| = |22,16,-8| = √804
September 23, 2014

Vector
The angle between a and b is α = θ-Ø a•b = |a| |b| cosα a•b = (xa*xb)+(ya*yb) xa = |a| cosθ ya = |a| sinθ ... Carry on, and you will see the result fall right out.
September 23, 2014

Math Help
How about you tell us what you think are the correct answers? Even better, show how you got them. Then we can help you fix the mistakes, if any. For #7, recall that |x| is always positive. So, |-27| = 27 Thus, -|-27| = -(27) = -27
September 23, 2014

Precalculus
tan .836 = 1.1071 tanθ > 0 in QI, QIII So, θ = 1.1071 or 1.1071+π sin 1.080 = 0.8818 sinθ < 0 in QIII and QIV So, θ = π+0.8818 or 2π-0.8818
September 23, 2014

Algebra
175 = 5*5*7 so, you can use 35 5" tiles or 25 7" tiles, if you don't want to cut any tiles. Not counting grout!
September 23, 2014

Fractions
trim+style needs 1/4 + 1/6 = 5/12 hour each day she can do (10/3) / (5/12) = 8 appointments. So, that makes 40 appointments during the week.
September 23, 2014

algebra
If you mean what is the solution to the system of equations, just start working things through. I find it easy to get rid of the fractions first: 1/2 x - 2/3 y = 4 2x + 1/3 y = 7 multiply to get 3x - 4y = 24 6x + y = 21 Now get rid of one of the variables, say y. 3x - 4y = 24 ...
September 23, 2014

algebra
consistent
September 23, 2014

Fractions
(5 1/2) / (3/4) = 11/2 * 4/3 = 22/3 = 7 1/3 So, she has enough for 7 servings, with 1/3 serving left over. For 10 people, she needs to have only 11/2 * 1/10 = 11/20 cup per serving 10 servings of 3/4 cup each is 30/4 = 7 1/2 cups
September 23, 2014

math
If the numbers are relatively prime, then x(x-7) = 60 x^2 - 7x - 60 = 0 (x-12)(x+5) = 0 So, the numbers are 12 and 5
September 23, 2014

Math
To use the quadratic formula, you need to arrange things so that you have y = ax^2 + bx + c So, (x - 10 )(x + 9 ) = 2 x^2-x-90 = 2 x^2 - x - 92 = 0 Now just apply the formula.
September 23, 2014

math
(-a,b)
September 23, 2014

Math
x^2 + 4 x = 4 x^2 + 4x - 4 = 0 Now just apply the formula.
September 23, 2014

Maths
The cylinder has radius r The cone has radius 2r So, the ratio of volumes is (πr^2h)/(π(2r)^2h/3) = (πr^2h)/(4πr^2h/3) = 3/4
September 23, 2014

College Pre-Calculus
m(f) = f/5280
September 23, 2014

Math
27/3 + 5*2 = 19
September 22, 2014

math
1kg/(4.8g/cm^3) = 208.333 cm^3 So, now you know that 4π/3 r^3 = 208.333
September 22, 2014

math
There is no GCM. There is no greatest number which is a common multiple.
September 22, 2014

Algebra1
either or both
September 22, 2014

physics
F = ma -1.50*10^4 = (1.96*10^4/9.81)(a)
September 22, 2014

math
same as what?
September 22, 2014

Math
77 = 11*7, so (6+5)*(9-2)
September 22, 2014

algebra
Just work it step by step: 105/(-20+15) ------------------- 45/(-9)+12 105/(-5) ------------ -5+12 -21 --------- 7 -3
September 22, 2014

Math
r(x) = (600-4x)(250+4x) Now plug and chug.
September 22, 2014

Algebra
If x lbs at $7, then 7x + 5(50-x) = 5.79(50)
September 22, 2014

math
what difference does it make how far the sun is from earth? Unless the distance to Mars is measured in a.u.
September 22, 2014

Advance Algebra
v(x) = x(12-2x)(10-2x) Since the sides must have positive length, we need 10-2x > 0, or x<5 Since the cuts must also have nonzero length, x>0, so the domain is 0 < x < 5
September 22, 2014

math
After t minutes, the positions are (if P=(0,0)) turtle: (0,4t) snail: (50,-2t) So, the distance d can be found from d^2 = 50^2 + (6t)^2
September 22, 2014

Algebra 2
just expand as you normally would a polynomial, and you get 30i^3 + 125i^2 + 120i But, once you recall that i^2 = -1 i^3 = -i, you have -125 + 90i
September 22, 2014

Geometry
Hard to parse the garbled sentence, but if the hill slopes at a 30 degree angle, then the tree makes angles of 60 and 120 with the hill. To explain, just draw a diagram and label all the angles.
September 22, 2014

algebra 2
First, that's equal to, NOT too! It's a lot easier just to write x >= 2. With that said, let's proceed. #1: ok #2: ok #3: Hmmm. This one is no harder than the first two, just a bit longer. 4(1-3n)-14>4(2n+3)-9n 4-12n-14 > 8n+12-9n -12n-10 > -n+12 -11n &...
September 22, 2014

trigonometry
A wheel with a 15-inch diameter is turning at the rate of 60 revolutions per minute. To the nearest inch per minute, what is the linear speed of a point on the rim?
September 22, 2014

Maths
start factoring: 2*2198 4*1099 4*7*157 = 28*157 What's with "using the numbers 1-9"? Seems like a stupid condition.
September 22, 2014

Math
(b) no angles provided
September 22, 2014

algebra
clearly, when 50.00 + 3.50x = 75.00 + 2.25x Now just solve for x.
September 22, 2014

algebra
5n+10d+25q = 325 n = d+2 q = n+1 Now just start substituting in to solve for the variables.
September 22, 2014

Math
What's the trouble? Just start writing the words as equations. We are told: a+b+c = 18 a = 2(c-b) (because c > b) b = (a+c)/2 Now just go through the usual procedures to solve several equations.
September 22, 2014

Math
correction on #1. What I gave was the solution for a particular radius. Since we have to consider all possible such circles, the locus is the perpendicular bisector of the line joining centers of the circles. All points on that line are equidistant from the two centers.
September 22, 2014

Math
since |z-c|=r is a circle of radius r, |z+1| = |z+i| is the intersection of two circles. If z = x+yi, Re z = x |z-1|^2 = (x-1)^2 + y^2 So, you need x^2 = (x-1)^2
September 22, 2014

math
If there are x,y,z of each cost, we have x+y+z = 20 4.00x + 0.25y + 0.50z = 20.00 Since we have only two equations, there are multiple solutions. Let's work with knowing x. Then we have y = 14x-40 z = 60-15x Since y and z must be positive, we need x >= 3 and x < 4. ...
September 22, 2014

math
(150*15)/500 = 4.5 so, now you can figure it out, right?
September 22, 2014

Math Help Please
just solve 16t^2 = 1614
September 22, 2014

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