# Posts by steve

Total # Posts: 49,531

**Algebra2**

let f (x)=x-3,and g(x)=x^2 find f(g)(4)

*January 29, 2017*

**Calculus**

true, since sin(0) = 0 1+cos(0) = 2 That is, the left limit is 0 The right limit is 2

*January 29, 2017*

**Trigonometry**

draw a diagram. At first sighting, the distance d1 is d1/12000 = tan 10.4° The second distance d2 is d2/12000 = tan 25.6° Since speed is distance/time, s = (d1-d2 ft)/(2 min) That will be in ft/min.

*January 29, 2017*

**Math**

f = 3+2j f+j = 48 ...

*January 29, 2017*

**Math-Geometry**

yes. study as many similar proofs as you can find. Lots are online. Do as many exercises on your own as you have time for, especially those where you can check your answer. This skill, like all others, improves with practice.

*January 29, 2017*

**Geometry**

Try this discussion: https://www.math.toronto.edu/mathnet/questionCorner/miter.html

*January 29, 2017*

**Geometry**

Draw diagonals AD and AC Now you have two isosceles triangles AED and ABC with vertex angle 120° and equal sides of 2. Those can easily be solved. Now triangle CAD is isosceles, with base CD=2 and the equal sides the base of the other two triangles. Now just add up the ...

*January 29, 2017*

**algebra**

Not sure just what your f(x) is, but for any inverse function g(x) = f^-1(x), (f?g)(x) = (g?f)(x) = x

*January 29, 2017*

**Algebra**

Your syntax is cockeyed Correct the typos and try again a^b4^c6^ is gibberish a8^b2^c3^ is gibberish What does 6^ mean? Ah. Maybe you mean -3a^8 b^2 c^3 (5abc^9 -11a^ b^4 c^6) At this point I have to stop. I can't parse the 2nd factor.

*January 29, 2017*

**calculus**

you know that lim(u->0) sinu/u = 1 let u = 2/5 x lim sin2x/5x = lim sinu/(5/2 u) = lim sinu/u * 2/5 = 1 * 2/5 = 2/5

*January 29, 2017*

**des school**

tsa is total surface area. r=8 v = pi r^2 h = 288pi so, h = 288pi/64pi = 4.5 tsa is two circles plus the curved sides: 2pir^2 + 2pi r h = 2pi*r(r+h) = 2pi*8(8+4.5) = 200pi cm^2

*January 29, 2017*

**math**

using Taylor series, sinx-x = -x^3/3! + x^5/5! - ... x-tanx = -x^3/3 - 2x^5/15 - ... divide both by x^3 and you have -1/3! + x^2/5! - ... -1/3 - 2x^3/15 - ... now divide and let x->0 and (-1/3!)/(-1/3) = 1/2

*January 29, 2017*

**calculus**

That is, http://www.jiskha.com/display.cgi?id=1485688337

*January 29, 2017*

**calculus**

see your other post for the method.

*January 29, 2017*

**calculus**

lim(x -> -1+) x^2 = 1 ax+b = -aa+b when x=-1, so lim(x -> -1-) = -a+b So, we need -a+b = 1 f(-2) = -2a+b = -1 So, now we have two equations for a and b, giving us a=2 and b=3 So, f(x) = 2x+3 for x > -1 Now the limit from both sides at x = -1 is 1 and f(x) is ...

*January 29, 2017*

**calculus**

lim (x->1) = -2 g(1) = 0 So, there is a jump discontinuity. It is not removable, since g(1) is defined, but is not the same as the limit from both sides.

*January 29, 2017*

**calculus**

ok. there is certainly a break at x=1.

*January 29, 2017*

**Math**

1.06 * 0.97 = 1.0282 so, it grew by 2.82%

*January 29, 2017*

**Math**

a+2d = 20 a+13d = 64 11d = 44 d=4 a=12 Tn = 12 + (n-1)*4 = 8+4n

*January 29, 2017*

**math**

s+t = 27 t-7 = 3+(s-7)/4 ...

*January 29, 2017*

**math**

n = -2m, so m+2(-2m) = 3 -3m = 3 m = -1 n = 2

*January 29, 2017*

**Math**

3x-4=29

*January 29, 2017*

**Precalculus**

since cos(4t) has period pi/2 and sin(6t) has period pi/3 the LCM is pi

*January 29, 2017*

**math**

36/720 = 1/20 = 5% absent. So, ...

*January 29, 2017*

**Math**

this is just a right triangle with longest leg length 4. (Hypotenuse is 5) 5+3+4 = 12 180/12 = 15 So, scale it up by a factor of 15, and its sides are 75:45:60

*January 29, 2017*

**math2**

just use the power rule. For example, a. v(t) = 2t+3 v(2) = 2*2+3 = 7

*January 29, 2017*

**Math**

?(-3/2 * 81) = 9?(3/2) i ?(-3/(2*81)) = 1/9 ?(3/2) i = 1/(3?6) i = 1/18 ?6 i

*January 29, 2017*

**maths**

how far have you gotten using Reiny's suggestion? For #2, you might also look at it as involving the translation of one line onto a parallel line. The line from (-2,3) to (3,4) is one side of the parallelogram. If you translate (-2,3) to (-3,-2) then you have moved it by...

*January 28, 2017*

**Pre Cal 12**

900(1+r/4)^(4*12) = 1400 r = .0369 ? 3.7%

*January 28, 2017*

**Pre Cal**

f(x) = (x-3)^2(x-2)+c Note that 3^2*2 = 18 But that will be -18 (why?), so c=36 and that's "constant" not constance.

*January 28, 2017*

**Calculus can you please show me the step by step s**

As Tom showed you, I = A/s^2 + 8A/(600-s^2) Actually, that is not quite right. It should be 1/s^2 + 8/(600-s)^2 You should have caught that. In any case, The A is just a constant, so it does not affect the solution, and we can say I = 1/s^2 + 8/(600-s)^2 dI/ds = -2/s^3 + 16/(...

*January 28, 2017*

**Math**

|T-88| <= 7.5 88-7.5 <= T <= 88+7.5 ...

*January 28, 2017*

**Maths**

well, 2x = 25-5y So, use that: 4x-3y = 11 2(2x)-3y = 11 2(25-5y)-3y = 11 50-10y-3y = 11 -13y = -39 y = 3 Now use that to find x.

*January 28, 2017*

**Math show work**

Using convenient units of 1 AU for earth orbit and mass of sun=1, and P=1 earth year, you know that R^3 = P^2 using 11.1P, (11.1P)^2 = 123.21P^2 = (4.976R)^3 So, the distance is 4.967 AU

*January 28, 2017*

**Math**

recall that cot -x = -cotx = -1/tanx

*January 28, 2017*

**Math**

well, ? radians = 180 degrees 4.5 rad * 180deg/? rad = ? deg

*January 28, 2017*

**Mean (Average) Question**

How come you have only 9 values, if you have ten lions? Surely the 10th litter is also zero? In any case, the mean is the sum divided by the no. of values being measured.

*January 28, 2017*

**Geometry and shape**

Or, any regular n-gon with more than 4 sides and n an even number.

*January 28, 2017*

**math**

ar^3/ar^11 = 1/256 1/r^8 = 1/256 r = 2 Now you can find a, so the sum S8 = a(2^8-1)/(2-1) = 127a

*January 28, 2017*

**math**

r^2 = 2^2+9^2 = 85 so, if the unknown chord is 2x in length, 6^2+x^2 = r^2

*January 28, 2017*

**Maths**

If x is the son's age, 9x+15 = 3(x+15)

*January 28, 2017*

**Math**

#2 Huh? The planetary radius is equal to the separation? Do the planets touch, or is the separation between planetary surfaces? If so, then a cube with side 5r contains about 9 planets of radius r. So, the void ratio would be ((5r)^3 - 9*4/3 ?*r^3)/(9*4/3 ?*r^3) = (125-12?)/12...

*January 28, 2017*

**Math**

#1 You know that the weight is GMm/r^2 = 100 Replace M by 7M and r by 2r, and you have the new weight of G(7M)m/(2r)^2 = 7/4 GMm/r^2 = 175

*January 28, 2017*

**Math**

not quite sure what you're after, but d/dx (x^3) = 3x^2 d/dx (x^2+x) = 2x+1 If you want x where they are equal, then 3x^2 = 2x+1 3x^2-2x-1 = 0 (3x+1)(x-1) = 0 x = -1/3 or 1

*January 28, 2017*

**Math**

You have not asked a question. Clearly, to wrap all 80 boxes, you need 80 * 2 3/4 = 220 ft of ribbon. Now you have to decide just what it is you want to know...

*January 28, 2017*

**Math**

which region is shaded? Are the circles concentric? The area of the larger circle is 81?. The smaller circle has area 121?/4 = 30.25?

*January 27, 2017*

**Math -**

8x + 14y = 24 6x + 7y = 10 double the 2nd equation and you have 8x + 14y = 24 12x + 14y = 20 Now if you subtract the top from the bottom, the 14y cancels and you have 4x = -4 x = -1 Now use that in either original equation to find y: 8x+14y = 24 8(-1)+14y = 24 -8+14y = 24 14y...

*January 27, 2017*

**Basic math**

42.42

*January 27, 2017*

**basic calculus**

dA = 8?r dr dr = -1/2, so dA = 8?*200*(-1/2) = -800? m^2 so, the area is approximately 4?*200^2 - 800? = 159200?

*January 27, 2017*

**Pre Cal**

You know A, since A+B+C=180 a/sinA = b/sinB ...

*January 27, 2017*

**Math**

A\B is all x in A but not in B x not in A\B is all x in A&B or in B. So, A\(A\B) is all x in A and in (A&B or B) so, it is all x in A&B ? B

*January 27, 2017*

**Math**

The legs add up, but the eyes do not. You are correct that there are 19 animals. But then you go on to finish wrong. If there are m cows (moo) and c hens (cluck), 4m+2c = 52 2m+2c = 38 2m = 14 m = 7 7 cows and 12 chickens 7*4+12*2 = 28+24 = 52 legs 2*(7+12) = 2*19 = 38 eyes

*January 27, 2017*

**Math**

90 by 60

*January 27, 2017*

**Math**

Not sure how to parse your expression. B(A\B) is not correct syntax, since B is a set (A\B) is a set, call it C So, what does BC mean? Similarly, (A\B) is a set, so call it D. Again, what is DC? two set names juxtaposed has no meaning.

*January 27, 2017*

**Algebra - units**

Damon makes a good point. You know that you can always multiply by 1 without changing anything. If 6 meters = 1 minute, then 6m/1min = 1 1min/6m = 1 Those "conversion factors" are just different ways of writing 1! If you pick the correct expression, the unwanted ...

*January 27, 2017*

**Maths**

p+g+c = 100 100p+30g+5c = 1000 A little checking will show that he bought 94 chickens 1 goat 5 pigs

*January 27, 2017*

**ALGEBRA MATRICES HELP**

Turn to the section in your text. Start reading.

*January 27, 2017*

**algebra**

sounds good to me.

*January 27, 2017*

**Math**

well, four pounds more than three times the weight of his sister becomes 3w+4 so, now what do you think?

*January 27, 2017*

**Math**

well, each side is ?6.25 = 2.5 km, so since there are 4 sides, ...

*January 27, 2017*

**Maths**

see related question below

*January 27, 2017*

**math**

draw a diagram, including a diameter perpendicular to the chords. You will find a couple of 8-15-17 right triangles.

*January 27, 2017*

**Precalculus**

I think I can read this as z^7 = 1/?2 - 1/?2 i so, that means z^7 = cis 315° z = cis(315/7)° = cis45° + k*360/7 for k=1..6

*January 27, 2017*

**Maths**

If they work 3/2 as fast, it will take 2/3 the time.

*January 27, 2017*

**algebra**

clearly, when -16t^2 + 156t + 105 = 0

*January 26, 2017*

**Math**

h * h/2 * 1/2 = 100 h = 20

*January 26, 2017*

**Math**

well, 8 pts = 1 gal, so ...

*January 26, 2017*

**trig**

sin? = y/r cos? = x/r tan? = y/x tan? is the slope, so you have tan? = 5 r^2 = x^2+y^2 = 26

*January 26, 2017*

**Math**

it appears so.

*January 26, 2017*

**Trig**

csc^2 ? = 1+cot^2 ? so, ...

*January 26, 2017*

**Algebra**

a = 7 d = 3 Now you can answer the questions: T8 = a+7d Sn = n/2 (2*7 + (n-1)*3) > 425

*January 26, 2017*

**formal language**

ok. and ... ?

*January 26, 2017*

**8th grade math**

hmmm. I don' see no steenking triangles!

*January 26, 2017*

**math**

t = 2s k = t-3 t+s+k = 37

*January 26, 2017*

**Math**

so, we have (1,9) -> (3,-3) (3,12) -> (5,-6) (4,4) -> (6,2) x -> x+2 y -> 6-y = 3-(y-3) So, shift right 2 reflect across the line y=3.

*January 26, 2017*

**Math**

time = distance/speed, so time for sound to return: d/c time to fall: t = T-d/c d/c + gt^2/2 * d/t = T now just solve for d

*January 26, 2017*

**algerbra**

Looks like A to me. The prices are in the ratio 1:3:5:7, just like the times.

*January 26, 2017*

**Math**

450/(600+450+270) = 15/44

*January 26, 2017*

**math**

12^2 + L^2 = 20^2 L = 16 It's just a 3-4-5 triangle scaled up by a factor of 4.

*January 25, 2017*

**Trigonometry**

sin? = 1.2/4.4

*January 25, 2017*

**Calculus**

#1 correct ?[1,4] ?(1 + 1/4x) dx ?[1,2] ?(1+4y^2) dy where did you come up with [16,1]? The curve goes from (1,1) to (4,2) Note that ?(1+4y^2) is NOT (1 + 2y) ?(a^2+b^2) is not a+b !! #2. looks ok. For C, the radius is just x+2 For D, the radius is just 3-y

*January 25, 2017*

**Math**

use your standard conversion factors for gal/L and mi/km

*January 25, 2017*

**Measurement**

u = 10^-6 p = 10^-12 you surely have a list of prefixes - use them.

*January 25, 2017*

**Algebra**

you know that x = 3y-6 So, use that in the other equation: 20y + 35(3y-6) = 3795 20y + 105y - 210 = 3795 125y = 4005 y = 32.04 Now use that to find x. Odd, I expected an integer answer. Check for typos.

*January 25, 2017*

**Algebra 1**

just evaluate at x=5

*January 25, 2017*

**Trigonometry with right triangles**

you can always get a book on geometry and study it. I learned calculus on my own from my teacher's textbook. But I suggest you finish Algebra I before trying geometry or trig. It will give you a good foundation to work with.

*January 25, 2017*

**Trigonometry with right triangles**

what, you can't figure 90-25 ?

*January 25, 2017*

**Trigonometry with right triangles**

cos(x) = sin(90-x) That's what the co- in cosine means: sine of the complement.

*January 25, 2017*

**Algebra 2**

I get B. What did you do? Maybe we can figure what went wrong.

*January 25, 2017*

**Calculus**

sin = y/r cos = x/r sinx = 1/5 cosx = -?24/5 = -2?6/5 cosy = 1/8 siny = ?63/8 = 3?7/8 I'll do sin(x+y) and you can apply the formulas for the rest. sin(x+y) = sinx cosy + cosx siny = (1/5)(1/8)+(-2?6/5)(3?7/8) = 1/40 - 6?42/40 = (1-6?42)/40 makes sense, since x+y is in QIII

*January 25, 2017*

**Algebra**

If the walkway has width w, then 2(6+2w + 10+2w) = 60.8

*January 25, 2017*

**maths**

a = 31 1/4 = 125/4 ar^(n-1) = 2 r^(n-1) = 8/125 Now, 8/125 = (2/5)^3 Looks to me like r = 2/5 and n=4 and the sequence is thus 125/4, 25/2, 5, 2 I think you'll find it adds up to 203/4

*January 25, 2017*

**Algebra**

Draw a diagram. Set the center of the ellipse at (0,0). Then we have semi-axes a = 74 b = 48 x^2/74^2 + y^2/48^2 = 1 Now plug in y=10 and find x. The distance d is then d^2 = x^2 + 10^2

*January 25, 2017*

**calculus**

3xy^3+4xy=63 3y^3 + 9xy^2 y' + 4y + 4xy' = 0 y'(9xy^2+4x) = -(3y^3+4y) y' = -(3y^3+4y)/(9xy^2+4x) So, at (9,1) y' = -7/117 Now you have a point and a slope, so the line is y-1 = -7/117 (x-9) Refer to http://www.wolframalpha.com/input/?i=plot+3xy%5E3%2B4xy%...

*January 25, 2017*

**Math 114**

so, did you check? 3+9=12 so, ok.

*January 25, 2017*

**MATH**

well, 4 for each kg, so ...

*January 25, 2017*

**math**

72/4 = 18 So, multiply all the lengths by 18 to get 54+72+36 = 162

*January 25, 2017*

**Math**

-8+3 = -5

*January 25, 2017*

**math**

1/5 boys absent means 4/5 present 4/5 boys = 160 = 4*40 So, there are 5*40 = 200 boys 2/5 of the students are boys 200 = 2/5 * 500 So, there are 500 students in all. Now you can see how many are girls.

*January 25, 2017*