# 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*