Wednesday
October 1, 2014

Posts by Steve


Total # Posts: 25,411

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

Math
how are the 6 fields to be arranged? 2x3: 9x+8y = 1200 a = 6xy = 6x(1200-9x)/8 max area at x = 200/3 1x6: 12x+7y = 1200 a = 6xy = 6x(1200-12x)/7 max area at x = 50 Note that the fencing is divided equally among lengths and widths.
September 22, 2014

math
Ben takes time t = (d/2)/r + (d/2)/w = d/(2(r+w)) Bob covers distance w(t/2) + r(t/2) = d so Bob's time is 2d/(r+w) So, which time is less?
September 22, 2014

Algebra
9-c < 2 c > 7 -3c > 15 c < -5 so, c < -5 or c > 7 See http://www.wolframalpha.com/input/?i=solve+9+-+c+%3C2+or+-3c+%3E+15+
September 22, 2014

Precal
sec θ = r/x = √218/-7
September 22, 2014

Math
3^2-12/(6-3)*8 9-12/3*8 9-4*8 9-32 -23
September 21, 2014

Math - Madison the Mooch
The equation describes an ellipse. There is no inverse, because each value of x corresponds to 2 values of y (the vertical line test). There is no such thing as an inverse equation. If you want to find x as a function of y, then 2x^2 = 4 - 3y^2 x^2 = (4-3y^2)/2 Now, there is a...
September 21, 2014

Math
False even without doing the math, the left side is odd and the right side is even.
September 21, 2014

AP Calc. AB
correct.
September 21, 2014

algebra
(2,10,5)
September 21, 2014

Math
(6-6)/(6x6+6)=0
September 21, 2014

Algebra
as usual, first just clear fractions: (n+9)(7) = 6(d+9) (n-7)(3) = 2(d-7) 7n+63 = 6d+54 3n-21 = 2d-14 7n-6d = -9 3n-2d = 7 Now can you solve for n and d?
September 21, 2014

Algebra
Just put the words into symbols. If the original fraction is n/d, then (n+9)/(d+9) = 6/7 (n-7)/(d-7) = 2/3 Now just solve for n and d.
September 21, 2014

math
If the base of the rectangle has length 2x, and height y, the area is a = 2xy = 2x√(1-x^2/16)(4) = 2x√(16-x^2) da/dx = 4(8-x^2)/√(16-x^2) so, max area occurs at x=√8, and the rectangle is 2√8 by √2
September 21, 2014

AP Calc. AB
Clearly A is not continuous at x = -1, since the denominator is zero. The domain of √u is u >= 0. So, we need x+6 >= 0 The domain of sin x is all reals, so it doesn't affect the result. we know that lim sin(x)/x = 1, so sin(2x)/(2x) is 1. So, lim sin(2x)/x = 2...
September 21, 2014

Algebra
The only question I see is whether x^3-2x^2-1+2 = 0 For some values of x, it is. I suspect a typo, since you have no x term, and two constant terms. Why not fix the typo and then ask your real question?
September 21, 2014

Math.
x - 8.77 = 23.40
September 21, 2014

math
2.3x = 48.00
September 21, 2014

Math
20*27 = ?
September 21, 2014

Math
100/200 = x/53.40
September 21, 2014

Math
what is the difference between 10 and 6? It is 10-6, or 4. So, the difference here is just x = 39.50 - 23.50
September 21, 2014

math
clearly (0,5) is is a set of x values, since x is in that interval. I'm sure it is just to restrict us to a single period of 2π. 1+x <= f(x) <= 3+sin πx as x->2, 1+2 <= f(x) <= 3
September 21, 2014

math
#1: c = 9.95 + .10m #2: c = 12.95 + .08m
September 21, 2014

maths
In triangles adb and adc, angle adb = angle adc bd = dc ad = ad So, the triangles are congruent, meaning ab = ac so abc is isosceles.
September 21, 2014

Algebra
correct
September 21, 2014

math
If the digits are a and b then 10a+b = 8(a+b) 10a+b - 45 = 10b + a The number is 72
September 21, 2014

Algebra 2 (Please, help me!)
well, it just means that all points have become 1/3 as far away from the origin as they were. Just divide all the coordinates by 3: (9,-6) -> (3,-2) and so on
September 21, 2014

math
the area grows as the square of the length ratio. So, the sides are in the ratio √9:√4 = 3:2. So also are the perimeters.
September 21, 2014

trigonometry
as usual, draw a diagram, and review your basic trig function definitions: tan θ = 5100/12000 So, θ = arctan(51/120)
September 21, 2014

Physics help ASAP
Suppose you are visiting a planet in a distant part of the galaxy.To determine the acceleration due to gravity on this planet, you drop a rock from a height of 55 m. The rock strikes the ground 1.9 s later.How many times greater is the acceleration due to gravity on this ...
September 20, 2014

Physics
A baseball is thrown upward with an initial speed of 35 m/s. What is the speed at t = 2 s?
September 20, 2014

physicas
A baseball is thrown upward with an initial speed of 35 m/s. What is the speed at t = 2 s?
September 20, 2014

Physics
A basketball is shot from an initial height of 2.4 m with an initial speed (v0 = 12 m/s) directed at an angle (35 degrees) above the horizontal. Additional information: Height of the basket is 3.05 m Find how far away the player is standing.
September 20, 2014

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