# Posts by steve

Total # Posts: 49,586

**Math**

T13/T6 = ar^12/ar^5 = r^7 (3/16)/24 = 1/128 = (1/2)^7 so, ...

*March 25, 2017*

**maths**

506 base 6 does not exist, since base 6 numbers consist only of the digits 0-5.

*March 25, 2017*

**Math**

use the law of sines to show that the base is divided into equal lengths. Then that will imply that the angles at the base of the altitude are also equal, so they are both 90 degrees.

*March 25, 2017*

**math**

50 * (1788/3725)

*March 25, 2017*

**algebra**

just solve the equation x^2 + (1/2 x + 11)^2 = (2x+1)^2 x = 8

*March 25, 2017*

**college algebra**

C(x) is just a parabola. Its minimum value is at the vertex, where x = -b/2a = 7

*March 24, 2017*

**college algebra**

Sorry, that -3072 means its initial height (at t=0) is 3072 feet below ground.

*March 24, 2017*

**Math**

since |y| > y, y < 0, so |y| = -y x>|y|, so x+y>0 ==> |x+y| = x+y |x+y|-|x|+|y| = x+y-x-y = 0

*March 24, 2017*

**Math**

4^x = 6 2^x = ?4^x = ?6 8^x = (2*4)^x = 2^x * 4^x = 6?6 or, 8^x = (4^(3/2))^x = (4^x)^(3/2) = 6^(3/2) = 6?6

*March 24, 2017*

**Math**

(A+B)/2 = A + B/10 A/2 + B/2 = A + B/10 A/2 = 2/5 B A = 4/5 B A.B = 4.5

*March 24, 2017*

**Calculus**

2?r^2 + 2?rh = 20 so, h = 10/?r - r the volume is v = ?r^2h = ?r^2(10/?r - r) = 10r-?r^3 so, find r when dv/dr=0

*March 24, 2017*

**Math**

If the walk has width w, then since the parkland occupies 80% of the area, (30-2w)(5-2w) = 0.80*30*5 w = 0.4396m

*March 24, 2017*

**Calculus**

h+4s = 14 v = hs^2 = (14-4s)s^2 so find s when dv/ds = 0

*March 24, 2017*

**Physics**

since V is constant, and PV=kT, P/T = k/V is constant. So, you want P such that P/(273+25) = 7/(273+15)

*March 24, 2017*

**math**

because 1/c = c^(-1)

*March 24, 2017*

**Math**

check your prior post in the related questions below ...

*March 24, 2017*

**Calculus please help!**

consider f'(1) where f(x) = ?x where you should have written the limit as (?(1+h) - ?1)/h

*March 24, 2017*

**Pre calculus**

p(x) = (x-11i)(x+11i) = x^2 - (11i)^2 = x^2+121

*March 24, 2017*

**Physics**

distance = speed * time so, time = distance/speed

*March 24, 2017*

**Math(PLEASE HELP ME ASAP)**

22.50 * 1.15 = 25.875

*March 24, 2017*

**Math(PLEASE HELP ME ASAP)**

well, how did you figure it out?

*March 24, 2017*

**Math**

well, the base has area 132/11 = 12 so ...

*March 24, 2017*

**Calculus**

(a) c = 13(4x+y+4x+y) + 5(3y) = 112x+41y (c) xy=9, so y=9/x, and c(x) = 112x + 369/x now find x where dc/dx = 0

*March 24, 2017*

**Math**

huh? Just solve (75+x)(225-5x) = 16000 x = 5 so, ...

*March 24, 2017*

**Precalculus**

a) ok b) The average cost is the cost per unit, or c?(x) = c(x)/x So, c?(x) = 0.02x + 0.5 + 40/x The marginal average cost is thus c?'(x) = 0.02 - 40/x^2

*March 24, 2017*

**Algebra - rats**

I see other typos. The final answer is correct, but let me just do it right: Since the vertex and focus both lie on the line x = -2, the axis of symmetry is vertical, meaning the equation is (x-h)^2 = 4p(y-k) Since the focus above the vertex, p is positive. You know that the ...

*March 24, 2017*

**Algebra - typo**

As you noticed, the axis is vertical, on he line x = -2

*March 24, 2017*

**Algebra**

Since the vertex and focus both lie on the line x = =2, the axis of symmetry is horizontal, meaning the equation is (x-h)^2 = 4p(y-k) Since the focus above the vertex, p is positive. You know that the parabola x^2 = 4py has the vertex at a distance p from the focus. Here, that...

*March 24, 2017*

**Math, Algebra**

If you drop an altitude to the center of the base, then looking from the side you have a right triangle with legs 4 and 22. So, the hypotenuse of the triangle (the slant height of the pyramid, and the altitude of each triangular face) is h = ?(4^2+22^2) = ?500 = 10?5 That ...

*March 24, 2017*

**MAth help connexus**

c - review the section on functions, esp. the vertical line test.

*March 24, 2017*

**math - trigonometry**

one walks on a heading, not a bearing. a) Note that angle Q is 90 degrees, so you have a right triangle. Easy... b) This is the correct use of "bearing." If the bearing is x, then tan(x+25) = 18.7/11.4 A diagram will show you why.

*March 24, 2017*

**Math Measurment unit test**

1. A = bh 2. A = bh/2, so looks good.

*March 24, 2017*

**math**

2/s = 1/4 + 1/5

*March 24, 2017*

**math**

well, the volume of water flowing in every second is 1.2cm * 350cm/s = 420 cm^3/s Now divide the volume of the tank by the inflow rate to get the time (in seconds)

*March 24, 2017*

**calculus**

The 13 is just a scale factor, and has no bearing. You know that ? ? 1/10^n = 0.11111111 = 1/9 n=1

*March 24, 2017*

**Maths**

If the 5th is 4 times the 3rd, then r=2 a+ar = -4 a+2a = -4 a = -4/3 now take it from there.

*March 23, 2017*

**math**

Let the man run to point P, which is x meters upstream from the line AB. He swims across, being swept y meters downstream, and then runs to B. We know that he is in the water for d/(v/3) = 3d/v seconds, so y = 3d/v * v = 3d. His path is thus ?(d^2+x^2) meters on land, d meters...

*March 23, 2017*

**math**

again c? aa

*March 23, 2017*

**math**

before: 00AF

*March 23, 2017*

**math**

before: AFc after: cAF

*March 23, 2017*

**math**

c-bar ̅

*March 23, 2017*

**Math**

well, the last digit is 5 start there.

*March 23, 2017*

**Physical science**

2Na + 2H2O = 2NaOH + H2 now just multiply everything by 3/2

*March 23, 2017*

**Math**

y = x-12

*March 23, 2017*

**Math**

write them as 4x-6y = -48 x+6y = 18 add them together and you get 5x = -30 ...

*March 23, 2017*

**chem**

assuming a constant temperature, PV = kT is constant. So, you want P such that P*2.94 = 0.988*3.35

*March 23, 2017*

**Math**

y = 1+2x 3x+(1+2x) = 11 ...

*March 23, 2017*

**chem**

assuming a constant temperature, PV = kT is constant. So, with 5/4 the pressure, you get 4/5 the volume

*March 23, 2017*

**Math**

square both sides write cos^2 = 1-sin^2 Then you have a quadratic in sinx

*March 23, 2017*

**physic**

how long does it take to fall 160m? The horizontal speed does not affect that. 4.9t^2 = 160 Now, the horizontal speed does not change, so the body travels 20t meters

*March 23, 2017*

**Math1**

You want t years, where 2100(0.95)^t = 600 0.95^t = 2/7 t = log(2/7)/log(0.95) = 24.42

*March 23, 2017*

**Pre-cac**

well, even without completing the square, you know the vertex is at x = -b/2a = 3/2a So, a(3/(2a))^2 - 3(3/(2a)) + 5 = 15 5 - 9/(4a) = 15 a = -9/40 But, in the spirit of completing the square, ax^2-3x+5 = a(x^2 - 3/a) + 5 = a(x^2 - 3/a + (3/2a)^2) + 5 - a(3/2a)^2 = a(x - 3/2a...

*March 23, 2017*

**Maths**

4000*1.015^2 = 4120.90

*March 23, 2017*

**Math**

a. correct b. The volume with the cuts made and the sides folded up is v = (12-2x)(18-2x)x = 4x^3-60x^2+216x If you have calculus, then dv/dx = 12(x^2-10x+18) dv/dx=0 when x=5-?7 ? 2.35 If no calculus, then a graphical or numeric method is needed.

*March 23, 2017*

**Math**

(x,y)-> (x-4,y+1) is correct. But you still botched it: (-3,1) -> (-3-4,1+1) = (-7,2) + means ADD: 1+1 = 2, not 0! same for subtracting: -3-4 = -7 -3+4 = 1 -1 is just plain bogus, man.

*March 23, 2017*

**Math**

left 4 means subtract. as you said, up 1 means add. But even if your translation were correct, you did not do the math right 1+1 ? -2 Try again. You're getting the +'s and -'s mixed up some.

*March 23, 2017*

**Math**

naturally, we can see no graphs here. What are your choices for the others?

*March 23, 2017*

**Math**

(a) trés simples, non? (b) 2x cosy - x^2 siny y' - cosy y' = 0 y' = (2x cosy)/(cosy + x^2 siny) So, at (0,?), y'=0 (c) so, the tangent is a horizontal line, and the normal is a vertical line through (0,?).

*March 23, 2017*

**Pre-calculus**

I will assume a typo, and work with x^2+10x+4y+9 = 0 That may not be what you had in mind, but you can follow the method using your corrected equation. x^2+10x+4y+9 = 0 4y = -x^2-10x-9 y = -1/4 x^2 - 5/2 x - 9/4

*March 23, 2017*

**Math 120**

6+2 + 2 (conversion+safety) 6+1 + 3 6+2+2 (two safeties) 3+3+2+2 2+2+2+2+2

*March 23, 2017*

**math**

the nice thing about Ø is that Ø-1 = 1/Ø

*March 23, 2017*

**math**

sinx = cos^2x sinx = 1-sin^2x sin^2x + sinx - 1 = 0 now solve for sinx, and pick the positive solution.

*March 23, 2017*

**Calculus - Newton's Method**

well, f'(x) = 1-sinx So plug that into Newton's method. Here is a nice web site: http://keisan.casio.com/exec/system/1244946907

*March 23, 2017*

**calculus**

you will need to use integration by parts, twice. 1st step: u = t^2 dv=sin(2t) dt du = 2t dt v = -1/2 cos(2t) That makes the first integration by parts: ?u dv = uv - ?v du ?t^2 sin(2t) dt = -1/2 t^2 cos(2t) + ?t cos(2t) dt Then repeat, letting u = t dv = cos(2t) dt You should ...

*March 23, 2017*

**Calculus**

I suspect a typo, since what you have written is just f(x) = x/(x+x^2) = 1/(1+x) f' = -1/(1+x)^2 f" = 2/(1+x)^3 Anyway, fix that, find f", and recall that f"=0 means an inflection point f" > 0 means concave up f" < 0 means concave down

*March 23, 2017*

**calculus**

use integration by parts. That is just the product rule in reverse. d(uv) = u dv + v du u dv = d(uv) - v du ?u dv = ?d(uv) - ?v du ?u dv = uv - ?v du So, here we just let u = (lnx)^2 dv = dx du = 2lnx * 1/x dx = (2lnx)/x v = x ?(lnx)^2 dx = x(lnx)^2 - ?2lnx dx Now repeat, this...

*March 23, 2017*

**math**

x >= 15000/12 = 1250 So, consider how long a ride might take, and how long the park is open each day.

*March 23, 2017*

**math**

5 divides evenly any multiple of 5. Not sure what you mean by "5 divide into equaly" [sic]

*March 23, 2017*

**Help please I am lost, algebra**

if g(14) = -6, then that means you have the point (14,-6) on the graph. Using the point-slope form, then, you get y+6 = -5/4 (x-14) Now massage that to the slope-intercept form: y+6 = -5/14 x + 35/2 y = -5/14 x + 23/2

*March 23, 2017*

**Math**

The first model is linear because the changes are constant. In fact, y = x/2 - 1 For the second, check the differences: 1st: 5.1, 20.4, 81.6, 326.4 2nd: 15.3, 61.2, 244.8 If t were quadratic, the 2nd differences would be constant. Since they are also growing rapidly, you ...

*March 23, 2017*

**Functions, please help**

2700x+21000 = 83400 just solve for x 2010 is 7 years after 2003, so just plug in x=7 for P(x)

*March 23, 2017*

**Physics**

Let the man run to point P, which is x meters upstream from the line AB. He swims across, being swept y meters downstream, and then runs to B. We know that he is in the water for d/(v/3) = 3d/v seconds, so y = 3d/v * v = 3d. His path is thus ?(d^2+x^2) meters on land, d meters...

*March 23, 2017*

**Physics**

Let the man run to point P, which is x meters upstream from the line AB. He swims across, being swept y meters downstream, and then runs to B. We know that he is in the water for d/(v/3) = 3d/v seconds, so y = 3d/v * v = 3d. His path is thus ?(d^2+x^2) meters on land, d meters...

*March 23, 2017*

**Math**

p(red) = (#red)/(#total)

*March 23, 2017*

**Math**

start with 7.2 Since 10^0, that is just 7.2x10^0 Now, lowering the power of 10 moves the decimal place to the left, so 7.2x10^0 = 7.2 7.2x10^-1 = 0.72 7.2x10^-2 = 0.072 and so on The number of leading zeroes after the decimal point is 1 less than the negative power of 10.

*March 22, 2017*

**Calculus**

every polynomial is continuous and differentiable everywhere. At the midpoint, x = (a+b)/2 f'(x) = 2?x+? So, show that f'((a+b)/2) = (f(b)-f(a)/(b-a)

*March 22, 2017*

**calculus**

One way: Theorem of Pappas If the edge goes from (0,0) to (0,1), then the center is at (?3/2,?3/2). The area of the hexagon is 3?3/2. The radius of rotation is ?3/2, so its path has length ??3. So, the volume of the solid is ??3 * 3?3/2 = 9?/2 Another way: calculus. Using ...

*March 22, 2017*

**Maths**

I worked it out, and also got a 4th-degree equation in x. So what? Just solve it for x using whatever method works best. I did get z=x rather than z = -2x, but maybe I made a mistake.

*March 22, 2017*

**math**

A10-A7 = 3d = 15 Now you know d, so you can get a, and then the terms.

*March 22, 2017*

**Math1**

2^24 - 1

*March 22, 2017*

**algebra 1**

well, did you check it? -16*36 + 46*6 + 6 = -294 So, stop guessing and do the math! h = -2(8t^2-23t-3) = -2(8t+1)(t-3) So now what do you think?

*March 22, 2017*

**calculus review please help!**

#1 ?[0,4] arcsin(x/4) dx = 2?-4 To do this one, let x = 4sin(u) arcsin(x/4) = arcsin(sin(u)) = u dx = 4cos(u) du Now you have ?[0,4] 4u cos(u) du That you can easily do using integration by parts. Note that in changing variables, ?[0,4] f(x) dx = ?[0,?/2] g(u) du #2 Using ...

*March 22, 2017*

**Math**

x(?/4) = ?2 y(?/4) = 1 dy/dx = (dy/dt)/(dx/dt) = sec^2(t)/(sect tant) = sect/tant = csc t so at t=?/4, y' = ?2 and the tangent line is y-1 = ?2 (x-?2) y = ?2 x - 1 Note that x^2 = 1+y^2. So, to check the graphs, see http://www.wolframalpha.com/input/?i=plot+x%5E2-y%5E2%3D1...

*March 22, 2017*

**Precalculus**

|x| is a tricky one, since it changes at x=0. Consider it a |x| = ?x^2. Then, using the chain rule, d/dx ?x^2 = 2x/(2?(x^2)) = x/|x| Note that this correctly captures the change of slope at x=0. d/dx[5(x^2 + 3|x|)] = 5(2x + 3x/|x|) Also, the function is not differentiable at x=0.

*March 22, 2017*

**Math**

you don't say whether the radius, diameter, circumference is 28. Anyway, just plug in the formula: A = ?r^2

*March 22, 2017*

**maths**

remember the 3-4-5 right triangle? Just scale it up by 2.

*March 22, 2017*

**math real and complex numbers lesson**

(7+3,-9+5) = (10,-4)

*March 22, 2017*

**Maths**

x-28 = 42-x

*March 22, 2017*

**math**

It is true that Anna is not 1000mm taller, but in this case, the "times" indicates a multiplicative factor, and almost no one would interpret it as you have indicated.

*March 22, 2017*

**physics/maths help damon or steve or scott**

s(t) = s0 + v0t + a/2 t^2 so, s0 + 6v0 + 18a = 246 s0 + 9v0 + 81/2 a = 246+69 Solve for v0

*March 22, 2017*

**trigonometry**

draw a diagram, and you can figure angle T. Then, use the law of sines.

*March 22, 2017*

**trigonometry**

use the law of sines.

*March 22, 2017*

**math**

x-y = 1/10 y = 4/7 x - 4/7 = 1/20 x = 4/7 + 1/10 = ?

*March 22, 2017*

**Maths**

P = R-C break-even when R=C (P=0)

*March 22, 2017*

**Maths**

If all were bikes, there would be 70 tyres. There are 9 extra tyres, so that means 9 bikes were replaced with trikes...

*March 22, 2017*

**Math**

f(14) = 2*14-2 = 26 26 = m so the first letter is m and so on

*March 22, 2017*

**Calcalus**

ln(x^2-15y)=x-y+5 1/(x^2-15y) * (2x-15y') = 1-y' 2x-15y' = x^2-15y - (x^2-15y)y' Now just collect terms and solve for y' to get y' = (x^2-2x-15y)/(x^2-15y-15) So, at (-4,1) that is y'(-4) = (16+8-15)/(16-15-15) = -9/14 Finally, using the point-slope...

*March 22, 2017*

**Geometry**

8 * (8 + 1/24) * 34 = ? Or, considering the possibility of a typo, 8 * 8.5 * 34

*March 22, 2017*