# Posts by Steve

Total # Posts: 49,729

**Math (Semicircle)(Pre-calc)**

a circle with center at (4,0) and radius 4 is (x-4)^2 + y^2 = 16 or, y = ?(16-(x-4)^2) The left semicircle has center at (-4,0) and radius 4, but lies below the x-axis, so So, f(x) = -?(16-(x+4)^2) for -4 <= x <= 0 ?(16-(x-4)^2) for 0 <= x <= 4

*January 17, 2017*

**Math**

If the meet after x hours, then 1.5 + 4.5x = 10x

*January 17, 2017*

**Recursive Sequence and its Limit**

A little work shows that the nth term a<n> = 3/(2^(n+1)-1) Now, do you want the limit of the terms, or the limit of the sums? a<?> = 0 S<?> = 3(sum 1/(2^(n+1)-1) I thought that would be relatively simple, but you can see below that it is not: http://www....

*January 17, 2017*

**Math**

7P3 = 210

*January 17, 2017*

**Math**

the vertical distance moved is 12 sin25° = 5.07 ft Work = PE lost = 5.07 * 180 ft-lb

*January 17, 2017*

**math**

37A-A = 36A 36A/4A = 9 36A is the 10th term.

*January 17, 2017*

**math**

yes

*January 17, 2017*

**Math**

100 coffee a 50% solution ???

*January 17, 2017*

**math**

42 is the answer to The Ultimate Question of Life, the Universe, and Everything. So it is surely the answer to whatever puny question you have in mine.

*January 17, 2017*

**Maths factorise**

note that the fits two terms are 3p(x-y) and then use grouping.

*January 17, 2017*

**Science**

well, 1 mole fills 22.4L 28cm^3 = 0.028L So, you have .028/22.4 = 0.00125 moles (1/800 moles) Thus, if the mol wt is x grams, x/800 = 0.4 x = 320

*January 17, 2017*

**Algebra**

I assume the usual sloppiness with parentheses, and that your original equation was x/(x-2) + (x-1)/x + 1 = 0 If you found x=0 as one solutions, you need to exclude it. (x-1)/x is undefined when x=0 So, while it may appear that x=0 is a solution, it is not acceptable as a ...

*January 17, 2017*

**Algebra 2**

What you have is already in recursive form. Each An depends on the previous term. Now, if you want an explicit formula, An = 5*3^(n-1) + 2

*January 17, 2017*

**Algebra 2**

If you meant (2?(3x^5) - 2?y)^2 = 4(3x^5) - 8?(3x^5y) + 4y Not sure how that's any simpler, though...

*January 17, 2017*

**Maths**

Huh? If ABCD is a parallelogram. AB∥CD and has the same length.

*January 17, 2017*

**Maths**

recall that the area of a rhombus is 1/2 the product of its diagonals.

*January 17, 2017*

**Mathematical Induction**

you need to show that a<n+1> > a<n> (increasing) or a<n+1> < a<n> (decreasing) If you expand the expression from the recursion, you can clearly see that it is. Once you can show that each term is greater (or less) than the previous one, then you ...

*January 17, 2017*

**riddle**

Guys! This is easy! The answer is NEW MOON! The new moon is old and also 'new' at the same time!

*January 17, 2017*

**math;);)**

draw a side view. Draw a circle Mark a vertical diameter Draw a horizontal radius from the center O The radius has length 3 Draw another vertical line 1 unit away from the center. On that vertical line, mark its intersections with the horizontal radius (A) and the circle (B). ...

*January 16, 2017*

**Calculus**

Looks good to me.

*January 16, 2017*

**calculus**

f(x+3) = 2^(x+3) = 2^x * 2^3 = 8*2^x f(x-1) = 1/2 * 2^x PI, not PIE! G(0) = sin(2*0) = sin(0) = 0 similarly, just plug in the other values for x. These are some of your standard angles, whose trig functions you should know. They come up so often, it's better if you just ...

*January 16, 2017*

**calculus**

just look at the graph of sin(x). Clearly, it is defined everywhere, so its domain is all real numbers. sin(2x) gets to each x value twice as fast, but has exactly the same domain: all real numbers.

*January 16, 2017*

**maths**

make the two colors anything except black.

*January 16, 2017*

**Math**

tan(x) = 45/60 x = 36.87° As for the time of day, since you don't give any information on location, assume sunrise is at 6:00 am and sunset is at 6:00 pm. In that case, 180° of arc covers 12 hours. Use that to find how many hours after 6 am (or before 6 pm) it is.

*January 16, 2017*

**9th grade algebra (sequences)**

If you have an explicit formula, coming up with a particular term is easy. If not, you have to use the recursion several times. #1. try (-2)^(n-1) #2. You can use the explicit formula, but showing how to handle it as a general arithmetic sequence is also nice. Naturally, any ...

*January 16, 2017*

**Math**

what, you can't solve 4x+8 = 0 ??

*January 16, 2017*

**Math**

momentum is not measured in kg.

*January 16, 2017*

**Algebra**

(0.8-3.4)/(2007-1972) = -2.6/35 = -0.074 (hc/mile)/year if you want a % yearly rate, then that would be -0.77%/year

*January 16, 2017*

**Math**

Not quite sure what the "at 50m" means. Also, knowing the other stake is 65m from the end of the pond does no good. Now, if the two stakes are at the ends of the pond, and the given distances are as measured from the observation point, then the distance between the ...

*January 16, 2017*

**Algebra**

use the number of tickets, and the total income: s = 2a 10a+6s = 3300

*January 16, 2017*

**math**

because there was no bounce at first - just a drop. When it hits the ground for the 5th time, it has made a single 3-foot drop, and then 4 round-trip bounces.

*January 16, 2017*

**maths trigonometry**

you have the formulae. What do you get?

*January 16, 2017*

**Math**

yes, except 30*100 = 3000

*January 16, 2017*

**math**

n = k/(y^2-1) So, n(y^2-1) = k, a constant. You want n such that n(5^2-1) = 24(10^2-1) 24n = 24*99 n = 99

*January 16, 2017*

**Math**

Newton's method converges rapidly. If you don't have calculus, then there are other methods, such a bisection. f(x) = 6x + 12 + 2cosx Start off with the interval (-3,-1) and find f at the midpoint: -2 f(-2) = 6(-2)+12+2cos(-2) = -0.832 So, f=0 occurs in (-2,-1). f(-1.5...

*January 16, 2017*

**Math**

As I recall, (a) ?x P(x) means "there exists an x such that P)x) is true. So, in this case, that wold be P(-2) V P(-1) V P(0) V P(1) V P(2) Hmmm. Not sure what (c) ? ¬P(x) means. There exists "not P(x)"? Is that the same as ?x ¬P(x), that is there exist ...

*January 16, 2017*

**Vector Calculus**

Take a look at your previous post. See whether my solution makes any sense, and whether I interpreted things correctly.

*January 16, 2017*

**Calculus**

Just a note on #3 even though ?x^2 dx = x^3/3 ?cos^2(x) dx is NOT cos^3(x)/3 cos^2(x) = 1/2 (1+cos(2x)) since cos(2x) = 2cos^2(x) - 1 Thus, ?cos^2(x) dx = x/2 + 1/4 sin(2x)

*January 16, 2017*

**Calculus**

using discs of thickness dx, v = ?[0,2] ?r^2 dx where r=y=x^3 v = ?[0,2] ?(x^3)^2 dx = ?[0,2] ?x^6 dx = 128?/7 using shells of thickness dy, v = ?[0,8] 2?rh dy where r=y and h=2-x = 2-?y v = ?[0,8] 2?y(2-?y) dy = 128?/7

*January 16, 2017*

**Calculus**

#3 3. Use the washer method to find the volume of the solid that is generated by rotating the region in the first quadrant bounded above by y = cosx and on the right x = pi/2 about the line y=2 My work: pi((4(pi/2) - ((2-(cos(pi/2))^3)/3) My Answer: 11.36 v = ?[0,?/2] ?(R^2-r^...

*January 16, 2017*

**Calculus**

#2 This time, our discs are of thickness dy, so v = ?[0,2] ?r^2 dy where r=x = 3y/2 v = ??[0,2] (3y/2)^2 dy = 6? checking with shells, v = ?[0,3] 2?rh dx where r=x and h=2-y = 2 - 2x/3 v = ?[0,3] 2?x(2 - 2x/3) dx = 4?/3 ?[0,3] 3x-x^2 dx = 6? Your answer, 72?/12 = 6? is correct.

*January 16, 2017*

**Calculus**

#1 Zero? Really? That did not see strange to you? Too bad you didn't show your original integral. The graphs intersect at (-1,1) and (1,1). Since the area of a disc is ?r^2, the volume of a disc of thickness dx is ?r^2 dx. So, your integral should be v = ?[-1,1] ?(R^2-r^2...

*January 16, 2017*

**Algebra**

Nice work. I'd have changed things a bit here: Your system become: a * ( r ^ 2 - 1 ) = 12 a * r * ( r ^ 2 - 1 ) = 36 Divide the bottom by the top to get r = 36/12 = 3 a*8 = 12 a = 3/2

*January 15, 2017*

**Algebra**

ar^2 = a+12 ar^3 = ar+36

*January 15, 2017*

**calculas**

well, (a)(i) 4/(6-6.9) = 4/-.9 = -4.44 mPQ = (-4-(-4.444))/(7-6.9) = .444/.1 = 4.444 similarly for the other points (b) I expect you will guess m=4 (c) now you have a point and a slope, so the line is y+4 = 4(x-7)

*January 15, 2017*

**vector calculus**

The unit vectors are just the vectors perpendicular to the cylindrical surface. r^ points radially outward ?^ points tangent to the planar circle z^ points upward To convert to Cartesian vectors, r^ = cos? i + sin? j ?^ = -sin? i + cos? j z^ = z^ You have V = rrˆ + r^3 ...

*January 15, 2017*

**vector calculus**

Not sure what the R 3 means, but the transformation is just the usual polar-Cartesian we all know and love: x = r cos? y = r sin? z = z

*January 15, 2017*

**Math**

Hmmm. The statements are an exercise to see whether you can correctly evaluate and compare the expressions. Note that once a true condition has been found, the value of x changes, and the following statement works with a new value. There is no positive number such that x^2 = 5...

*January 15, 2017*

**Math**

Just work them. For example (a) is 3^2 = 5^3? No Some of the conditions will match, and then you can do the assignment. The last assignment done will be the new value for x.

*January 15, 2017*

**Math**

no idea. what was his cost? But, 2000/3600 = 5/9 So, he would have lost 4/9 of his previous sale value.

*January 15, 2017*

**Pre Calc**

This is a typical 3-circle Venn diagram. When you fill in the areas, the question should be easy. Start with the central 3-circle intersection. That is 4. ...

*January 15, 2017*

**Math**

10x+12=32

*January 15, 2017*

**math**

that's "lead" not led. The area of a disc of diameter d is pi/4 d^2. So, the area of the lead cross-section is pi/4 (2.4^2 - 2.2^2) = 0.723 cm^2 So, the mass of the lead is volume * density, or 0.723cm^2 * 350cm * 4g/cm^3 = 1012.2g

*January 15, 2017*

**mathematics**

hey! where's john? If you did the question and can find the value of x, then what do you want? As for me, I can find no value of x which works.

*January 15, 2017*

**mathematics**

and . . .

*January 15, 2017*

**Algebra2**

If you mean f(x) = 2x^2+x-3 then f(g) = 2g^2+g-3 = 2(x-1)^2+(x-1)-3 = 2x^2-3x-2

*January 14, 2017*

**Algebra2**

f(x)2x^(2)+x-3 g(x)=x-1 Perform the indicated operation, then find the domain (f*g)(x)

*January 14, 2017*

**Education**

Thank you very much

*January 14, 2017*

**Education**

The single best way to increase your income is to get an education. Why? 1- You automatically make more money if you are educated. 2- You automatically get promotions if you are educated. 3- You can obtain jobs that have higher starting salaries. 4- You will automatically ...

*January 14, 2017*

**Calculas**

x?¹-1 = 1/x - 1 = (1-x)/x So, your fraction is just (1-x)/x ---------- = -1/x x-1

*January 14, 2017*

**Physisc**

A 12 kg mass initially moving at 4 m/s is acted upon by a 120 N constant force. What is the final speed of the mass?

*January 14, 2017*

**Applied calculus**

the other dimension is (2000-2x)/2 = 1000-x I assume you know how to express the area of a rectangle.

*January 14, 2017*

**Calculus**

see related questions below.

*January 14, 2017*

**Math**

looks ok to me.

*January 14, 2017*

**math**

W = kL That is, W/L is constant. So, you want W such that W/14 = 105/7

*January 14, 2017*

**math**

what do you mean by A=50? A is an angle of ABC. Same for P P is a point. What do you mean by "find P"? If you want lengths of sides given the lengths of bisectors, then review the angle bisector theorem.

*January 14, 2017*

**Arithmetic progression**

"sum" not "some" Assuming you meant had she got 3 more in maths and 4 marks less in science I tried m+s = 28 (m+3)(s-4) = 180 If that's what you meant, then just solve for m and s.

*January 14, 2017*

**Maths**

the length+width must be 8. So, how many pairs of numbers add to 8? 1+7 2+6 ...

*January 14, 2017*

**physics**

The somewhat vague requirements give rise to the following equations of motion: a = 2/3 v + (2/3)t = 25 vt + (1/3)t^2 = B-A or 25t - 1/3 t^2 = B-A Without knowing how long it took to get from A to B (only knowing that it is less than 75/2 seconds - why?), that's all we can...

*January 14, 2017*

**Algebra**

-1375 + 450 = ?

*January 13, 2017*

**Algebra**

you should recognize those numbers as perfect squares.

*January 13, 2017*

**Calculus**

well, f'(Ø) = 2secØ tanØ + sec^2Ø = sec^2Ø(2tanØ cosØ + 1) = sec^2Ø(2sinØ+1) f'(Ø)=0 when sinØ = -1/2 Now, what else is a critical number?

*January 13, 2017*

**Calculus**

Think about what you know about the shape of |x| functions. They have a cusp, where the slope is discontinuous.

*January 13, 2017*

**Precalc**

when cos(pi/6 (t+2)) = -1 That is, where pi/6 (t+2) = pi

*January 13, 2017*

**Algebra 1**

try this: http://calc101.com/webMathematica/long-divide.jsp

*January 13, 2017*

**Calculus**

check your text or google to review what differentiable means.

*January 13, 2017*

**Algebra**

1 ok 2 is 7 < 3? 3 "<" means less

*January 13, 2017*

**math**

2x-4 = x+11

*January 13, 2017*

**maths**

well, there will be two days that occur 53 times. So, ...

*January 13, 2017*

**dynamics of rigid bodies**

I'll assume you meant s = 5t^2 + 1/3t^3 -1/50t^4 so, v = 10t + t^2 - 2/25 t^3 max v occurs when v'=0, so a = 10 + 2t - 6/25 t^2 So, find t when a=0, and then figure v at that value of t. max acceleration is when a'=0 a' = 2 - 12/25 t

*January 13, 2017*

**math**

15% of original, (.15*24000) or 15% off original ((1-.15)*24000) ??

*January 12, 2017*

**Calculus**

h = u/v h' = (u'v-uv')/v^2 Now just let u = 3x+2 v = x^2-5 Now each step is easy.

*January 12, 2017*

**Riddle**

well, you said her mom kept 6

*January 12, 2017*

**pre-algebra**

depends on what you mean by solve the question. Drawing a graph is one way to illustrate the relation between x and y. Another way is to fill in a table of matching values. Pick values for x and calculate the matching y values. Other questions might be to determine the axis ...

*January 12, 2017*

**math**

it is an odd function, so it is symmetric about (0,0)

*January 12, 2017*

**Geometry**

just use the distance formula.

*January 12, 2017*

**Precalculus**

well, every 2pi brings theta back to the same point, so ...

*January 12, 2017*

**math unit 7 test**

it should be clear that the inside of the arch cannot be covered by another arch.

*January 12, 2017*

**math**

ask google many many discussions

*January 12, 2017*

**Math**

5 ...

*January 12, 2017*

**Graphing in the coordinate plane unit test**

try google on some key topics...

*January 12, 2017*

**algebra**

try here. It shows all the steps. http://calc101.com/webMathematica/long-divide.jsp

*January 12, 2017*

**Mathematical measurement**

sure looks like 5:12 to me

*January 12, 2017*

**Computing**

n=1 s=1 for (i=1;i<=5;i++) { print s; n += 2; s += n }

*January 12, 2017*

**Computing**

depends on what information you want No idea what the "output of a triangle" is

*January 12, 2017*

**C**

add the numbers and divide by 10. If they are in an array called n, then sum=0 for (i=0 to 9) sum += n[i] avg = sum/10

*January 12, 2017*

**math**

4x-6 = x+15

*January 12, 2017*

**Physical science**

use the lengths as the legs of a right triangle. But, if the are not acting perpendicularly, you're out of luck.

*January 12, 2017*