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March 27, 2017

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Posts by steve

Total # Posts: 49,627

Calc
dy = (2x-7) dx so, ?x ? (2x-7) ?x
February 26, 2017

Maths, triangle trigonometry
draw a diagram. If the two lighthouses are at S and N, and the ship moved from A to B, then let the east-west distance moved by the ship be x. x = 5cos20° SN = x tan50° - x tan10°
February 26, 2017

Maths, triangle trigonometry
It's handy to think of P,R and Q as complex numbers, with P=(0,0). Find Q-R and then convert to polar form.
February 26, 2017

Physics
the horizontal speed is constant: 20 cos39° The vertical position is (20 sin39°)t - 4.9t^2 so, figure how long it takes to go 55m, then use that to get the relative height at that time.
February 26, 2017

Physics
If the height is h, then the vertical position y at time t is y = h - (9.4 sin21°)t - 4.9t^2 y(6) = 0, so you can find h. the horizontal speed is constant: 9.4 cos21° Now you can answer the questions.
February 26, 2017

math
First off, your distance is wrong. You must have used some bogus formula. d^2 = (5+3)^2 + (2+4)^2 = 100 d = 10 Since that is the distance from the center to a point on the circle, it is the radius. ...
February 26, 2017

math NEED HELP ASAP
add up the juice amounts: .65x + .90(150-x) = .75(150) ...
February 26, 2017

math
add up the vinegar in each part: .06x + .11(250-x) = .09(250) ...
February 26, 2017

Math
the coefficient of x^5 is negative. So, for x large negative, f(x) is large positive for x large positive, f(x) is large negative The lower powers don't matter for end behavior.
February 26, 2017

math
make a table for t=1 to 5. The annual cost is 1: 300-5 = 295 2: 300-10 = 290 3: 300-15 = 285 4: 300-20 = 280 5: 300-25 = 275 just add them up. Hmm. Maybe you just use t=5 for all 5 years. In that case, the annual cost is 275, so the total would be 5*275 = $1375 How did you ...
February 26, 2017

Math
recall that cos^2 x = (1+cos2x)/2 so, cos^4 x = (1+cos2x)^2/4 now cos^2 2x = (1+cos4x)/2 and so on. In the end, you get sin^8(x) = 1/128 (cos8x - 8cos6x + 28 cos4x - 56cos2x + 35)
February 26, 2017

Pam
x^2 is never less than zero, so f(x) is never less than -3. The vertex is at (0,-3) In general, f(x) = ax^2+bx+c has its vertex at x = -b/2a f(x) = a(x-h)^2 + k has its vertex at (h,k). In this case, h=0 and k = -3, so the vertex is at (0,-3)
February 26, 2017

Pam
The 3 is tiny, but the curve does not approach the line y=x. It gets arbitrarily close to the line y=x+3.
February 26, 2017

Pam
While the asymptote is a sloping line, and it looks like it ought to be x+11, it is not. (x^2+11x+16)/(x+8) = x+3 - 8/(x+8) So, the asymptote is actually the line y=x+3
February 26, 2017

Pre-algebra
If the cut is x inches, then the length and width are reduced by 2x, and the height is x. So the volume is v = x(40-2x)(20-2x) = 4x^3-120x^2+800x I can't believe that finding the maximum value of such a function is a topic for pre-algebra! It requires either analysis of a ...
February 26, 2017

math
?r^2h = 2800, so h = 2800/(?r^2) So, the cost function is c = 2*3?r^2 + 4*2?rh = 6?r^2 + 22400/r now just find r when dc/dr=0 and use that.
February 26, 2017

@Ms algebra
No "|" key on your keyboard, Ms?
February 26, 2017

Algebra
well, start with time = distance/speed
February 26, 2017

math
L(L-2) = 20
February 26, 2017

math
clearly, r = 2/5 now just use your formula.
February 26, 2017

Maths
If you meant to solve 18m^2-8m = 0 just factor out 2m: 2m(9m^2-4) = 0 2m(3m-2)(3m+2) = 0 your steps make no sense; you have discarded factors, changed signs, etc. Pay attention to what you're doing!
February 26, 2017

maths
find the angle between the headings (not bearings!) use the law of cosines for the third side.
February 26, 2017

Maths
sorry, that's n(n+1)/2 So, you have (n+1)(n+2)/2
February 26, 2017

Maths
I expect the differences are 3,4,5,6,7,... Did you know that 1+2+3+...+n = n(n-1)/2 ?
February 26, 2017

MATH NEEDS HELP NOWw
Did you take a look at the terms? 1, 1, 0, 0, ...
February 26, 2017

maths
consecutive angles add to 180. Looks to me like the two acute angles are 70° each.
February 26, 2017

physics
h(t) = 5t - 4.9t^2 max height at t=5/9.8 so, figure h at that value of t. Total distance is that height up, then back down.
February 26, 2017

maths
If you have a protractor, this should be easy.
February 26, 2017

calculus
arctan x = x - x^3/3 + x^5/5 - ... so, x-arctan(x) = x^3/3 - x^5/5 + x^7/7 - ... divide by x^3 and you get 1/3 - x^2/5 + x^5/7 - ... as x->0, that -> 1/3
February 26, 2017

calculus
surely you recognize the sequence 1, 3, 6, 10, ... as n(n+1)/2 it is the sequence of partial sums of 1+2+3+4+...
February 26, 2017

Calculus
a = xy da/dt = y dx/dt + x dy/dt d^2 = x^2+y^2 Now just plug in your numbers (I used x and y instead of w and l, since the l looks like a 1)
February 25, 2017

Calculus
xy = 12 y dx/dt + x dy/dt = 0 Now just plug in your numbers and solve for dy/dt
February 25, 2017

Algebra 2
Since the domain of ?x is x>=0, you will need (x-3) >= 0. That is, x >= 3. So, plug in some values of x and plot the points for y=-?(x-3): x y 3 0 4 -1 7 -2 12 -3 ... It will look like the bottom half of a horizontal parabola with vertex at (3,0). The equation could ...
February 25, 2017

Algebra
well, 7.5 is 3/4 * 10, so ...
February 25, 2017

College Algebra
if x at 5% then the rest (10000-x) is at 6%. So, add up the interest: .05x + .06(10000-x) = 550
February 25, 2017

math
24 = 8^(log_8(24)) 24^x = 8^(x log_8(24)) = (8^x)^(log_8(24)) = 12^(log_8(24)) = 12^1.52832 = 44.6
February 25, 2017

Algebra 2
geez, what's with all the words? f(x) = x^2 + 3x + 6 g(x) = (x-3)/2 g(1) = (1-3)/2 = -1 f(-1) = (-1)^2+3(-1)+6 = 1-3+6 = 4 or, f(g(x)) = g^2+3g+6 = ((x-3)/2)^2 + 3(x-3)/2 + 6 = (x^2+15)/4 f(g(-1)) = ((-1)^2+15)/4 = 16/4 = 4
February 25, 2017

math
well, is f(1)=19? yes. So, f-1(19) = 1
February 25, 2017

math
sorry - not much specific information here.
February 25, 2017

Math
A: If the red line has slope m1, then your line is y-5 = m1(x-3) B: If the blue line has slope m2 then your line is y = (-1/m2)(x+4) So, use the needed slopes, and massage the equations into the form y = mx+b
February 25, 2017

math
drop an altitude to KM. Note that you now have two 5-12-13 right triangles. ...
February 25, 2017

Maths
just use your GP sum formula. You have a/(1-r) = 243 a (1-r^5)/(1-r) = 242 Now divide and you have 1-r^5 = 242/243 = 1 - 1/243 . . .
February 25, 2017

math
the student walked on a heading, not a bearing. use the law of cosines. The distance d is found via d^2 = 50^2 + 200^2 - 2*50*200*cos115°
February 25, 2017

math
you should have remembered the 5-12-13 right triangle. The altitude is 12. So, the area is 5*12 = 60
February 25, 2017

High School Geometry
If SU?TP, SU=8 (think 3-4-5 triangle) Since the area is 1/2 bh using any side as a base, the other two altitudes can be found via 8*12 = 10h
February 25, 2017

High School Geometry
AC=BC = ?(3+9) = ?12 so, the perimeter is 6+2?12 or 6+4?3
February 25, 2017

Math
(68+72)/2 = 70 Or, since 70 is the average, 72 = 70+2 68 = 70-2
February 25, 2017

maths
well, 2b-3a = -(3a-2b) so you have 4(x+y)(3a-2b)-(6x+y)(3a-2b) ...
February 25, 2017

math
so, where does the slope begin, and does it drop lower when moving away from the tower, or what?
February 25, 2017

Math
The numbers in your LaTeX don't seem to agree with the "regular" section, so I'll ignore them. You want A with rows (a b) and (c d) such that 6a-b = 13 6c-d = -26 a+4b = 23 c+4d = 4 I get rows (3 5) and (-4 2) Check: http://www.wolframalpha.com/input/?i=%7B%...
February 25, 2017

math
g = b+25 b+g = 101
February 24, 2017

MaTHS
think of tan(A-B)
February 24, 2017

Algebra 2
I agree. I assume you did some math to get that idea...
February 24, 2017

Maths
L1: y = 2x+1 L2: y = (bx+5)/7 assuming that b/7 > 2, we have, using tan(A-B) = (tanA-tanB)/(1+tanAtanB) we want to find b such that (b/7 - 2)/(1+(b/7)(2)) = 1 b = -21, and we have L2: -3x + 5/7 or any parallel line with slope -3. check: arctan(-3) = 108.43° arctan(2) = ...
February 24, 2017

Math
hello ?? kitty
February 24, 2017

MATHS
well, one way is (x-h)^2 + (y-k)^2 = r^2 now plug in your values and solve for (h,k)
February 24, 2017

math 4th grade
to find the average, add up the total points and divide by the number of students: (6*100 + 4*90 + 3*80 + (26-6-4-3)*80)/26 = 86.15 I suspect a typo, since a score of 80 appears twice in the description. If so, just fix it in the expression above, and recalculate.
February 24, 2017

Algebra
x^4 = 1 = 1 cis 2? x = 1 cis 2?/4 = 1cis ?/2 Now add multiples of 2?/4 to that till you get all 4 roots. You can verify, knowing that 1^4 = (-1)^4 = i^4 = (-i)^4 = 1 Do the others in like wise.
February 24, 2017

Calculus
k is an odd name for a variable, but your answer is correct. Way to watch the integration limits.
February 24, 2017

Math
f(x) = 8-4x A f(2) = 8-4(-2) B 8-4x = 8 C Now you have two points. Draw the line connecting them D all real numbers. Think about it. Pick any x you want, and y is defined. A line goes out forever in both directions. E,F now use the graph. If it's you who has posted this ...
February 24, 2017

Math
#1. |z-1|=|z+3| |z-i|=|z+3| are both straight lines. This can be seen since |z-(a+bi)|=|z-(c+di)| |(x+yi)-(a+bi)|=|(x+yi)-(c+di)| |(x-a)+(y-b)i|=|(x-c)+(y-d)i| (x-a)^2 + (y-b)^2 = (x-c)^2 + (y-d)^2 x^2-2ax+a^2+y^2-2by+b^2 = x^2-2cx+c^2+y^2-2dy+d^2 (2c-2a)x + (2d-2b)y = c^2+d^2...
February 24, 2017

Calculus II
nope. consider {an} = 1/n The harmonic series diverges.
February 24, 2017

Science
well, you surely know that the moon is a choice. If only one choice is allowed, that must be it. If you really aren't sure about the others, you need to do some reading. google is your friend.
February 24, 2017

math
well, 2^-2 = 1/4, so -3x = -2
February 24, 2017

Mathematics
uh, which square?
February 24, 2017

Math- Outcomes and Probability
the question is the same as asking how many ways can 5 of 6 items be arranged. You will recall that that is 6P5 = 720
February 24, 2017

math
.10+.66+.08+.035 = .875 or 7/8 so, they have 1/8 left. 1/8 * 300000 = ?
February 24, 2017

Math
for angle x, the complement is 90-x: comp(x) = 90-x for angle x, the supplement is 180-x: supp(x) = 180-x So, supp(comp(x)) = supp(90-x) = 180-(90-x) = 90+x
February 24, 2017

Math Word Problem
Yes its 297 Thank you Reiny, I had a hard time understanding that one.
February 24, 2017

Math Word Problem
199 is also wrong :/
February 24, 2017

Math Word Problem
I am trying to find the exact number of male employees, thats where I am having troubles at. Like I tried, x = the number of employees x - 603 = the number of males x = 603 - x 2x = 603 x = 301.5 and it show that its wrong
February 24, 2017

Math Word Problem
67% or 603 employees in a company are female. How many are male?
February 24, 2017

Mat8
(2000*1500*1000)/(10*5*5) = 12,000,000
February 24, 2017

Math
A. f(-2) = 8-4(-2) B. 8-4x = 9 You have two points now. plot them and draw the line between them A line goes forever in both directions, both horizontally and vertically, so ... now look up the points for E and F
February 24, 2017

maths(rational numbers)
1/3 + 1/4 + 3/8 = 23/24 so, 9 hectares is 1/24 of the total...
February 24, 2017

engineering mathematics
8t + 1/2 t^2 = 18 t = 2 ?v = a * t
February 24, 2017

engineering mathematics
(300-200) = 500a
February 24, 2017

engineering mathematics
F = ma plug in your numbers
February 24, 2017

Pre Calculus 30
#1 what about zero? 9*10*10*5 #2 ok #3 as in #1, 1*10^4 #4 1000..9999 = ? #5 6P3 #6 4! * 3! #7 6 (assuming a win means matching a picture to the chosen name)
February 24, 2017

cal
There are several ways to do this. I'd google the topic. You might start here: http://whistleralley.com/torus/torus.htm
February 24, 2017

K
Using discs (washers) of thickness dx, v = ?[0,2] ?(R^2-r^2) dx where R=6-y and r=3 v = ?[0,2] ?((6-3e^(-x))^2-3^2) dx = 9?(5e^4+8e^2-1)/(2e^4) using washers of thickness dy, v = ?[3/e^2,3] 2?rh dy where r=6-y and h=2-x v = ?[3/e^2,3] 2?(6-y)(2+ln(y/3)) dy = 9?(5e^4+8e^2-1)/(...
February 24, 2017

Algebra
first, check the discriminant. If it's negative, there are no real factors. If the discriminant is a perfect square, then there are rational factors, so you can then work on finding them. 2x^2-5x+2 discriminant is 25-16=9, so we can work to find (2x-1)(x-2) the others ...
February 24, 2017

Trigonometry
you are correct so far. Of course, you have not provided any choices for selection, but the equation you need is tan? = 200/80 ? = tan-1 2.5 ? 68°
February 23, 2017

Math
#1: 20 + 4x = 140 #2: GCD(24,64,56) = 8 #3: I suspect you meant that there is a remainder of 4 when it is divided by 5. If sol, just list the numbers with these two properties: 2,5,8,11,14,17,... 4,9,14,19,... 14 = 4*3+2 = 2*5+4 #4. There are only 4 such numbers: 105,150,501,510
February 23, 2017

Math
there are 3 pairs of faces, each a rectangle. So, the area is 2(3.5*1.5 + 3.5*2 + 1.5*2) Of course, that does not include any overlap for taping things shut...
February 23, 2017

Math
the domain of all polynomials is all real numbers. f(x) = 8-4x. So, for f(-2), replace every x with -1: f(-2) = 8-4(-2) = 8+8 = 16 To graph the function, you just need two points. You already have (-2,16). So, pick any other value for x (0 is an easy one!) and plot (0,f(0)). ...
February 23, 2017

Math ; Algebra
-2x-6=-12 add 6 to both sides: -2x = -6 divide by -2: x = 3 or, -2x-6=-12 add 2x to both sides: -6 = -12+2x add 12: 6 = 2x divide by 2: 3 = x or, -2x-6=-12 divide by 2: -x-3 = -6 ... Follow the same logic for the other one and see what you get.
February 23, 2017

Precal
for this kind of problem, draw the right triangle. cos? = 2/3 means that the adjacent side is 2 and the hypotenuse is 3. sin? = ?5/3 means that the opposite side is ?5 and the hypotenuse is 3. But, then you knew that already, since the opposite side would be ?(3^2-2^2) = ?5 Si...
February 23, 2017

math
For each item, its total cost is unit-cost * no-units. So, in this case, the total cost is 6000*4 + 0.5*2050 + 5*3600 = 43025
February 23, 2017

trigonometry
recall that cos(x+y) = cosx cosy - sinx siny so, ...
February 23, 2017

Math
?PRT is isosceles ?PRT is 180-30 = 150 So, ?P and ?T are (180-150)/2 = 15° PT^2 = 1^2 + 1^2 - 2(1)(1)cos150° = 2+?3 Consider ?PQT and you can get tan T
February 23, 2017

Algebra
Try writing it as f(x) = -x(x-5)(2x-3) Now you can see that the coefficient of x^3 is negative. So, for x very large negative, say, -100, f(x) is positive. So, the graph comes down on the left, crosses the x axis at 0,3/2,5, and then continues on down to the right. So, f(x) &...
February 23, 2017

Sequences Math
x: up 1 y: down 5 so, start with y = -5x But, y(0) = -1, so y = -5x-1
February 23, 2017

Geometry
this is the other problem backwards. You need to find three numbers which add up in pairs to the given sides.
February 23, 2017

Geometry
draw the figure. Each side is the sum of the two touching radii.
February 23, 2017

Physics
PE = mgh
February 23, 2017

Math
7*8 = 5.6h
February 23, 2017

Math
The area of a parallelogram with a side of 5.6 in is equal to the area of a rectangle with sides 7 in and 8 in. Find the altitude to the given side in the parallelogram.
February 23, 2017

Mathematics
since time = distance/speed, 22.5/(x-6) + 22.5/(x+6) = 9 1/x + 1/(x+1) = 17/72 hint: 17 = 8+9 To get rid of the fraction in the denominator, invert and multiply. Then you have (x^2-16)/(x^2+5x+6) * (x^2-2x-8)/(x^2+5x+4) = (x+4)(x-4)(x+2)(x-4) ------------------------------- (x...
February 23, 2017

Math
since 15+25 = 40% did not get all correct, 24 = 60% of the class. so, ...
February 23, 2017

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