Sunday
December 21, 2014

Posts by steve


Total # Posts: 27,665

easy geometry
For the trapezoid, all we really need is the altitude. You can surely then find the area and perimeter. The long base is 10 cm longer than the shorter one. So, draw altitudes at the end of the short base and you will see two right triangles with base 5 and hypotenuse 10. So, ...
December 14, 2014

Math
AD = AE-DE BE = AE-AB AB=DE, so AD = AE-AB = BE You can reword that using all the "congruents" instead of = signs.
December 14, 2014

Physics
initially, all the energy is KE = 1/2 mv^2 At the peak, all the KE has become PE = mgh So, with 2v at first, there's 4 times the KE. That means 4 times the height at the peak.
December 13, 2014

Calculus 1
As usual, draw a diagram. If the angle subtended by the arc walked around the lake is θ, then the distance traveled on foot = 4θ by boat = √(32(1+cosθ)) = 8cos(θ/2) Use the law of cosines to get this. So, the total time t is t = 4θ/10 + 8/5 cos...
December 13, 2014

algebra 2
x^2+2x-35 x = (-2±√(4+140))/2 = (-2±12)/2 = 5,-7 Not sure how you got your answers, since you declined to show your work... x^2+10x+24 (x+4)(x+6) or, using the QF, (-10±√4)/2 x^2-11x+24 (x-8)(x-3) or, via QF, (11±√25)/2
December 13, 2014

Algebra
If a4a5 means a4*a5, then clearly a4=1 and a5=13, making d=12. So, a3a6 = (-11)(25) = -275
December 13, 2014

algebra 2
if you are aiming for a perfect square, then you are correct.
December 13, 2014

Math
Sorry, make that the long multiplication button.
December 13, 2014

Math
(2x-1)(3x-7) = 6x^2-17x+7 go to calc101.com and click on the long division button. Enter 6x^2-17x+7 and 4x+3 as your polynomials, and watch the fun! I'm sure you will find where you went wrong.
December 13, 2014

precalculus
(A) The denominator never zero, so the domain is all real numbers. So, of course F(x) is continuous, since there are no places where it is undefined. As x gets large, F(x) ≈ 3x^2/x^2 = 3. For the zeros of rational functions, they occur where the numerator is zero (as ...
December 13, 2014

Math
If the ladder of length z touches the ground x feet from the fence, and touches the building at height y, then z^2 = (x+2)^2 + y^2 Using similar triangles we see that x/12 = (x+2)/y y = 12(x+2)/x z^2 = (x+2)^2 + (12(x+2)/x)^2 So, find dz/dx and set it zero, to see that the ...
December 13, 2014

physics
the answer, of course, is 10.0-6.14 = 3.86 kg have been removed.
December 13, 2014

physics
since PV=nRT and RT and V are to remain constant, P/n = RT/V must be constant. n is usually in moles, but we can just as easily call it grams, since the ratio of moles to grams is constant for O2. We have reduced P by a factor of 26.4/43.0, so we must reduce the quantity of O2...
December 13, 2014

physics
1.8 (1 - 5.80/21.6) = 1.32 moles
December 13, 2014

precalculus
holes occur where the numerator and denominator are both zero. #16 x^2+2x+1 = (x+1)(x+1) 2x^2-x-3 = (x+1)(2x-3) So, f(x) = (x+1)/(2x-3) everywhere except at x = -1. At that point, f(x) = 0/0 which is not defined. The only vertical asymptote is at x = 3/2, and at x = -1 there ...
December 13, 2014

Algebra 1
2 units down sorry
December 13, 2014

Algebra 1
2 units down sorry
December 13, 2014

Algebra 1
what kind of translation? To shift the graph up k and right h, you need y-k = f(x-h) So, to shift f(x) = |x| up 2 and right 3, you have y-2 = |x-3| or, y = |x-3|+2 h and k may be negative, for shifting down and left.
December 13, 2014

Algebra 1
Write an equation for then translation of y = IXI
December 13, 2014

algebra 2
both correct
December 13, 2014

Algebra
⌊t⌋ = 2t+3 Clearly, t must be a multiple of 1/2 If an odd multiple, then we have t = (2k+1)/2 ⌊t⌋ = k 2t = 2k+1 k = 2k+1+3 k = -4 t = -7/2 If t is an even multiple of 1/2, then ⌊t⌋ = 2k/2 = k 2t = 2k k = 2k+3 k = -3 t = -3 See the graphs at ...
December 13, 2014

Algebra 1
Thank you from a 68 hear old Grandfather trying to help his Grandson
December 13, 2014

Algebra 1
What does the graph y = - absolute value of X -4 look like.?
December 13, 2014

Algebra 1
Yes I can. Thank you from a 68 year old Grandfather helping his Grandson
December 13, 2014

Algebra 1
What does the graph of y = absolute X-2 look like?
December 13, 2014

Algebra 1
Thank you -- A Grandfather trying to help his Grandson.
December 13, 2014

Algebra 1
Describe how the graphs of y = absolute value of x,and y = absolute value of X -15 are related. 1- Them graphs have the same shape. The y intercept of y = absolute x is 0, and them x intercept of the 2nd graph is -15. 2-m The graphs have the same y intercept. The second graph ...
December 13, 2014

math
Assuming the robot is completely submerged, then the water will rise by (20m^3)/(5m*4m) = 1m Doesn't really matter how tall the tank is, or how much water is already there, as long as the entire volume of the robot is submerged.
December 13, 2014

math
(-5/10)(-5/4) (-17/13)(-65/136)
December 13, 2014

algebra
A = Pe^(rt)
December 13, 2014

algebra (please help)
If $x is at 4.25%, the rest (22000-x) is at 5.75% So, just add up the interest received: .0425x + .0575(22000-x) = 1085
December 13, 2014

algebra (please help)
you are told that 2c+f = 1120 3c+2f = 1870 Now just solve for c and f.
December 13, 2014

algebra
the cost for x items is 4000+2.19x the income for x items is 4.59x Breakeven is where income and cost are equal: 4.59x = 4000 + 2.19x For 5500 profit, you need 4.59x = 4000 + 2.19x + 5500
December 13, 2014

math
πr^2h = 512 So, h = 512/(πr^2) area a = 2πr^2 + 2πrh = 2πr^2 + 2πr (512)/(πr^2) = 2πr^2 + 1024/r Assuming you have calculus, we see that da/dr = 4πr - 1024/r^2 da/dr=0 when r = 4∛(4/π) Now you can find h.
December 13, 2014

Math
f(x) = sin(x) df = cos(x) dx So, since sin(30°) = 1/2 sin 27° = 1/2 + (√3/2)(-π/60)
December 12, 2014

Algebra
can't be both. For floor, round down to next integer for ceiling, round up to next integer
December 12, 2014

Algebra
1 sometimes 0^0 is undefined 2 never 3 never 4 sometimes .3^1 < 1
December 12, 2014

Algebra
well, just solve 46 + .024x = 1558
December 12, 2014

Math
5r(13r+3s-5s^2) = 65r^2+15rs-25rs^2 -6s(13r+3s-5s^2) = -78rs-18s^2+30s^3 s^2(13r+3s-5s^2) = 13rs^2+3s^3-5s^4 Add them up to get 65r^2 - 63rs - 12rs^2 - 18s^2 + 33s^3 - 5s^4
December 12, 2014

geometry
google the number of segments determined by n points is and you will find many discussions of the topic. Find the one you like and use n=4.
December 12, 2014

Grade 9 Science
the orbit is not a circle, but an ellipse. The planet is not always exactly the same distance from the sun. Read up on Kepler's laws of planetary motion.
December 12, 2014

physics 1
This is just the same as figuring the time it takes for an object to fall 2cm on earth, except that the gravitation acceleration is not 9.81 m/s^2, but GM/r^2 where you have the values for G,M and r. Once you have that evaluated, s = 1/2 at^2 and you can just plug in s=0.02m ...
December 12, 2014

Calculus - Correction
Oops. The part from 0 to 0.0667 is not included, because it's all inside r=1. So, the real area is just 2∫[0.0667,π/2] 1/2 ((15sinθ)^2-1^2) dθ
December 12, 2014

Calculus
The area inside a polar curve is ∫1/2 r^2 dθ The circles intersect where 15sinθ = 1 θ = 0.0667 So, from 0 to 0.0667, we have r = 15sinθ From 0.0667 to π/2, we have to subtract the area inside r=1 from r=15sinθ, so the area is twice the area ...
December 12, 2014

calculus (check)
f(x) looks good No idea what F(n) is. If you mean the sequence of partial sums, it's just the normal sum formula for A.P.'s.
December 12, 2014

calculus (Series)
You just want the sum of the series where a = -2.02 d = -0.09 n = (-4 +2.02)/-.09 = 22 S22 = 22/2(-2.02 + -4) = -66.22
December 12, 2014

Calculus
You just want the sum of an arithmetic series where a = 4 d = 1/2 S28 = 28/2(2*4 + 27(1/2)) = 301
December 12, 2014

Math
That's what I get
December 12, 2014

Physics
Assume the heavier satellite is traveling in the +x direction. Conserve momentum, so the final velocity (xi+yj) is the solution to 1000*500i + 400*700(.707i+.707j) = (1000+700)(xi+yj) That will give the x- and y-components of the final velocity, which you can then express as ...
December 12, 2014

math
(n-2)180 / 360 = 4 So, find n to determine the number of sides, and that will let you find the angles.
December 12, 2014

algebra
I'd guess from previous posts that we want y > -5/3 x + 3 But what we are to do with it I don't know.
December 12, 2014

algebra 2
2√3+√27-√1/3 2√3+3√3-1/√3 5√3 - 1/√3 (5*3-1)/√3 14/√3 √1/2•(√8+√2) 1/√2 * 2√2 + 1/√2 * √2 2 + 1 3 √18-√3/√6 3√2 - √3/(√3√2) 3&#...
December 12, 2014

physics
BCE potential and kinetic energy depend on mass.
December 12, 2014

Geometry
tanθ = 1.89/50
December 12, 2014

Sequences
a10 = 6 + 9*8
December 12, 2014

Math
(13.69 + 3.96)/6
December 12, 2014

Math - Sooyong
vertical lines have no y-intercept horizontal lines have no x-intercept (unless these lines are in fact x=0 or y=0) #2 ok #3 also yes. Pick any point on the line (and there are an infinite number of points) and you can draw a perpendicular line through it.
December 11, 2014

Math
the minimum cable length occurs where f'(x) = 0 So, you need 2x/√(x^2+16) - 1 = 0 2x - √(x^2+16) = 0 2x = √(x^2+16) 4x^2 = x^2+16 3x^2 = 16 x = 4/√3 So, the minimum cable length is f(4/√3) = 10+4√3
December 11, 2014

Math
As usual, draw a diagram, and it is clear that f(x) = (10-x) + 2√(x^2+16) f'(x) = -1 + 2x/√(x^2+16) f"(x) = 32/(x^2+16)^3/2 Now the answers are easy to provide
December 11, 2014

algebra
When the car starts, the truck is 56/4 = 14 miles ahead. the car is going 8 mi/hr faster. So, how long will it take to make up the 14 miles? Add that to the 1/4 hr the truck already traveled.
December 11, 2014

Physics
300rev/min / (1/120 min) = 36000 rev/min^2 Now you can convert that to whatever units you like. Remember: 2pi radians/rev
December 11, 2014

math
2(w + 2w) = 72
December 11, 2014

math
xy=20 x+y = x + 20/x minimum occurs where x=2√5 (same as the problem for finding maximum area for a given perimeter: a square) So, pick two integers near √20. They would be 4 and 5, with sum=9 The only other sums are 1+20=21 2+10=12
December 11, 2014

Pre-Calc
Note that if you multiply on the left inside the radical, by (1-sinx)/(1-sinx), you have √((1-sinx)^2/(1-sin^2(x)) That should get you most of the way there, since √x^2 = |x|
December 11, 2014

trig
well, the perimeter is the sum of the sides, so 3n-4 + 3n+9 + 4n+5 = 114 10n = 104 Now it's easy to find n, and then figure the actual side lengths.
December 11, 2014

statistics finding the shaded region
enter your data here. http://davidmlane.com/hyperstat/z_table.html It's a great Z table site.
December 11, 2014

Algebra 2
well, note that f(x) = 5(x^3-2^3) = 5(x-2)(x^2+2x+4) That help?
December 11, 2014

statistics probability
P(-1.39<=Z<=1.69) = 0.8722 You can play around with Z table stuff at http://davidmlane.com/hyperstat/z_table.html
December 11, 2014

Math
If the mother's age is x, x/2 - 10 = 12 x = 44
December 11, 2014

maths
log_2(a) = 2log_4(a) = 3log_8(a) So, you have 2/(1/3 log_2(a)) - 4/log_2(a) = 1/(1/2 log_2(a)) 1/log_2(a) (6 - 4) = 2/log_2(a) 6-4 = 2 Or, recall that log_b(a) = 1/log_a(b) So, you have 2log_a(8) - 4log_a(2) = log_a(4) But, since 8=2^3 and 4=2^2, that means 6log_a(2) - 4log_a(...
December 11, 2014

algebra
log_8(2)+log_8(4x^2) = 1 1/3 + log_8(4) + log_8(x^2) = 1 1/3 + 2/3 + log_8(x^2) = 1 log_8(x^2) = 0 x^2 = 1 x = ±1 ln2 - ln(3x+2) = 1 ln (2/(3x+2)) = 1 2/(3x+2) = e 2/e = 3x+2 x = (2/e - 2)/3 = 2(1-e) / 3e ln(x-3) - ln(x-5) = ln 5 (x-3)/(x-5) = 5 x-3 = 5x-25 x = 11/2
December 11, 2014

algebra
well, clearly the spacing indicates -e^(-3.9n-1) -1 = -3 e^(-3.9n-1) = 2 -3.9n-1 = ln2 n = -(1+ln2)/3.9 Of course, I could be way off...
December 11, 2014

Math
since 36=6^2 its exponents are only half as big as powers of 6 to get to the same value. That is, log_36(n) = 1/2 log_6(n) So, 1/log_36(a) = 1/ (1/2 log_6(a)) = 2/log_6(a)
December 11, 2014

Algebra 2
remember the difference of cubes, and you see that you have (2x)^3 - (10y^2)^3 (2x-10y)((2x)^2+(2x)(10y^2)+(10y^2)^2) = 2(x-5y)(4x^2+20xy^2+100y^4) = 8(x-5y)(x^2+5xy^2+25y^2)
December 11, 2014

Middle School Math
Not at all. 3g+5 = 17 3g+5-5 = 17-5 3g = 12 3g/3 = 12/3 g = 4 I'd be interested to see how you arrived at -20.
December 11, 2014

math
If the ratio is 2:3, then games won = 2/5 of 120 = 48 So, games lost is 3/5 of 120 = 72 The correct proportion would be x/120 = 3/5 Consider. If the ratio is 2:3, the won/lost = 2/3 won = 2/3 lost lost+won=120 lost + 2/3 lost = 120 5/3 lost = 120 lost = 120 * 3/5 = 72
December 11, 2014

math show work please
You just need 2^(t/7) = 3 (t/7) log2 = log3 t = 7log3/log2 = 11.1 hours
December 11, 2014

algebra
that would be the cost per ride, since the only thing that changes is the number of rides.
December 11, 2014

Math
You are correct. 4 was indeed the solution to the equation, but you correctly went on to realize that that meant the actual price was $8/mug. Good work. Still, just plugging x=4 into the equation would have given the same answer for the income, since that accounted for the ...
December 11, 2014

Math
It would surely help if you showed how you got there. What you provide is not much help. If x is the number of price increases, then we have price p = 6.00 + 0.50x quantity sold q = 200 - 10x revenue is price * quantity, so r(x) = (6.00 + 0.50x)(200-10x) = 1200+40x-5x^2 This ...
December 11, 2014

Math
no, the amplitude is the coefficient out front: 37 You know the amplitude of sin(x) is 1 5 in this case isn't really anything. It might look like a phase shift, but it's not even that. And you still have a typo, since there's no t anywhere on the right side. You ...
December 11, 2014

Trig
so, since when is 1/2 pi not the same as pi/2?
December 11, 2014

Math
diameter is 35, so radius is 17.5 -- that is the amplitude of f(t) f(t) is like 17.5 sin(t) Since the max height is 50, that means the axle is at 50-17.5 = 32.5 f(t) is like 17.5 sin(t) + 32.5 The period of sin(kt) is 2pi/k, so we need 2pi/k = 13 k = 2pi/13 f(t) = 17.5 sin(2pi...
December 11, 2014

Algebra
well, just plug in the numbers and see whether it's true. 5(-2) - 2(-1) + 1 > 0 -10 + 2 + 1 > 0 -7 > 0
December 11, 2014

Math
since the range of sin(x) is [-1,1] that is the domain of sin^-1(x).
December 11, 2014

Math
In no way! 3/12 = 25% 50% is 6/12 !
December 10, 2014

Math
there were 12 plants in all 3 had no fertilizer. 3/12 had no fertilizer. Is C your final answer? ...
December 10, 2014

trigonometry
A. 4.5/x = tan 25° B. 4.5/x = sin 25°
December 10, 2014

math
121 = 7+2x
December 10, 2014

Math 6th grade
3 1/4 = 15/4 pizzas each person got 1/4 * 15/4 = 15/16 of a pizza Joe ate 1/4 of his portion, so he ate 1/4 * 15/16 = 15/64 of a pizza Extra credit: who stole the other 3/4 of a pizza? No one buys 3 1/4 pizzas!!
December 10, 2014

Math
Actually, since -(-(-x)) = -x we have |-x| = -x which is true for all x <= 0 Still the correct answer, though.
December 10, 2014

Math solve the equation
7x = 72 7x/7 = 72/7 x = 72/7 9p = 30 p = 30/9 or 10/3
December 10, 2014

German
yes, but it is incorrect. das Kind ein Kind no "eine" allowed. And, since Kind is a noun, it is always capitalized. Now, with adjectives, following a definite article, they are all ending in e. Otherwise, they are inflected by gender: das kleine Kind ein kleines Kind...
December 10, 2014

Algebra2
I'd be interested in seeing your work. I get (h-6)/150 = tan 46.2° (h-6)/150 = 1.04 h-6 = 156.42 h = 162.42
December 10, 2014

Algebra2
If the height is h, then (h-6)/150 = tan 46.2°
December 10, 2014

pre-algebra
5n >= 300*1.25 + 500 5n >= 375+500 n >= 175
December 10, 2014

Calculus
y = e^-x^2 y" = (4x^2-2)e^-x^2 y"=0 when x = ±√2 y(±√2) = e^-2 = 1/e^2 = 1/e^a Looks like a=2
December 10, 2014

math
The first train travels 16(6 37/60) = 96 592/60 = 105 13/15 min = 105'52" or 1 hr 45 min 52 sec do the other similarly
December 10, 2014

Math
y' = 7x^3+28x^2-63x-252 = 7(x+4)(x+3)(x-3) Now things should be easy. You know y is increasing when y' > 0...
December 10, 2014

Algebra
even-root radicals have domain only positive reals, since even powers of all numbers are positive odd powers can be negative or positive, so odd-root radicals have domain all reals.
December 10, 2014

Pages: <<Prev | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | Next>>

Search
Members