# Posts by STEVE

Total # Posts: 54,334

Math
in a triangle, it is the line from a vertex to the midpoint of the opposite side.

Math
How long does it take the water to hit the ground? 4.9t^2 = 0.75 t = 0.3912 seconds so, the horizontal speed = 2m/.3912s = 5.11 m/s

calculus
First plot the curves. They intersect at (3/2,?/3) and (3/2,-?/3) So, let's just take twice the area for ? in [0,?/3] Now just plug in the functions. The area is ?[0,?/3] (1+cos?)^2 - (2-cos?)^2 d? = ?[0,?/3] 6cos?-3 d? = 3?3 - ?

Math
well, 120 = 2*2*2*3*5 Just pick 3 sets of factors from those combinations

Small changes differentiation
taking derivatives, you have dT = ?/?(gL) dL Now, to find the % change of T, you take dT/T You would expect it to be about 1/2 the change in L, since you have roughly T^2 = kL 2T dT = k dL

4 Calculus Related-Rates Problems
These are all just applications of the chain rule. If y is a function of u, and u is a function of t, then dy/dt = dy/du * du/dt So, now we see what do do: #1 v=4/3 ? r^3 dv/dt = 4?r^2 dr/dt dr/dt = 15/(4?r^2) As expected, if the volume changes at a steady rate, the bigger the...

Math
1x(4) - 8x9/-3 1*4 - 72/-3 4 - (-24) 28

when a problem says "of" that means multiply 1/2 of a dozen = 1/2 * 12 = 6

physic
just do the usual derivative: v(t) = z'(t) = -16.2tk and evaluate at t=3 and t=6 works the same if there are i and j components as well.

Math
there are two lengths and two widths, so the perimeter is 13+7+13+7 = 40 2(13+7) = 40 inches

Java
can't draw flowcharts here. However, the logic might look like this: define n as a 10-number array sum = 0 i=1 ask for number assign it to n(i) add it to the sum increase i i <= 10? yes, go back to ask again no, print the sum quit

Maths - huh?
you wanna try that again so it makes sense?

Math
31 are boys so, 31/50 are boys. Just turn that into a %

Math
he makes it 2 meters forward every second. So, after 29 seconds, he has gone 58 meters. He makes it out in the 30th second. (29 2/3 seconds, actually)

Math
I assume you mean the 5th term is 5. You don't even have to find the 1st term, a; just start at 5 and go backwards, adding 3 each time: 17,14,11,8,5 If you want to do it algebraically, of course, just realize that the 5th term is a+4d = a+4(-3) = 5 a-12 = 5 a = 17

MATH8
If by 25/2% you mean 12.5%, then 500 * 1.125 * 1.15 = ?

math
since the ratio of sides is the same, 9/5 = x/4

maths
I think this will be a good place to start. The answer is given, and you can surely find your way there. https://books.google.com/books?id=uwDfHbyl1IMC&pg=SL22-PA420&lpg=SL22-PA420&dq=Find+the+equation+to+the+cone+whose+vertex+is+the+point+(a,b,c)+and+whose+generating+lines+...

maths
probably the intersection of the first two planes.

Maths
m+r = 338 m+49 = r/2 m+49 = (338-m)/2 m = 80 check: Minah had \$80 and Rohana had \$258 Later, Minah had 80+49 = \$129 and Rohana had 258/2 = \$129

Math
42

math
p = 2g g = p-20 now just solve for p and g.

algebra 2
f(x)=3.8cos(?x20)+2.2 cos(x) has a minimum value of -1 so, f(x) has a minimum value of 2.2 + 3.8(-1) = -1.6

Educational Technology and Online Learning 7
copyright is for published material. which of the choices does not fit that category?

math
no way to tell what is his mass? what is his weight on earth? something, eh?

Physics
time for the carbon would be dilated, or slowed by the usual relativistic factor. So, multiply the half-life by that.

Pre calc
Draw the triangle in QIV so that r = 3 x = 2 y = -?5 tan? = y/x = -?5/2 ...

MATH
well, your equation has a typo (it has two = signs, and that 84x cannot be right!). Aha -- it appears that you have duplicated the equation 4x-3y = 8 Clearly (1,4/3) does not fit, but (1,-4/3) does work, since 4(1)-3(-4/3) = 4+4 = 8 4(3/2)-3(-2/3) = 6+2 = 8 4(-4)-3(-8) = -16+...

physic
It's easy if you (a) draw a diagram (b) review your trig functions Then it's clear that if the height is h, h cot17° - h cot20.9° = 928 Now just find h.

math
because (a+b)^2 ? a^2 + b^2 sqrt is not a linear operator

algebra
correct, if ?5 is one of two bisectors of ?1. Of course, you don't give much context, do you?

Math
Of course, it is not possible to make a "complete" graph of a parabola on finite graph paper. If y = x^2-2x-8 then clearly the y-intercept is -8, since that's what you get when x=0 x^2-2x-8 = (x-1)^2 - 9 So the vertex is at (1,-9), which is the lowest point on ...

Trigonometry
draw the triangle. Review your basic trig functions: opposite = ?11 adjacent = 5 hypotenuse = 6 csc = hypotenuse/opposite

Physics
if you mean the recoil speed, then just conserve momentum (mv) 6v = 0.025*615

math
check to be sure you don't want 3 + 9 + 27 + 81 + 243 4 + 16 + 64 + 256

Geometry

Physics
work = force * distance so, how far did he move?

Algebra
Well, revenue must equal costs, so if they sell t tickets and f fans get free bats, we have 4t + 1200 = 2100+1900+3f

calc 3
s = ?[0,2] ?((18t)^2 + (18t^2)^2) dt = ?[0,2] 18t?(1+t^2) dt = 6(5?5 - 1)

Calculus
if the interval is [a,b] and there are n equal subintervals, then the ith x value is a + i times the subinterval width, less 2/3 of that width. xi = a + (b-a)/n * i - (b-a)/n * 2/3 = a + (b-a)/n * (i - 2/3) and the sum is as usual n ? f(xi)*(b-a)/n i=1

math
6n + 4*2n = ?

MATHS
(a) ?x | A(x) any ideas on the others?

math
1/2.5 = 15/x x/2.5 = 15 x = 2.5 * 15 ...

L.A 8TH
the triangles are congruent. This is in fact almost the definition of congruent. Take a look at your text. two triangles are similar if their angles are equal. Also, they are congruent if their sides are equal, as described above.

Math
I'll work with a vertical axis, just because it makes me more comfortable with the derivatives. For y = x^2/4 (x^2 = 4y), at x=a, the slope is x/2, so the normal has slope -2/a For y = x^2+k, at x=b, the slope is 2b, so the normal has slope -1/(2b) So, the equations of our...

Math
Eh? How can two parabolas with a common vertex and a common axis of symmetry have two distinct normals? This should get you started... https://math.stackexchange.com/questions/524130/common-normal-parabola-problem

math
The four points are (0,b),(?b,0),(0,-b),(-?b,0) Now use your favorite method to find the base length and altitude, or sides and angles, etc. to find the area of the rhombus.

Math
what you do is translate so that the desired point becomes the origin. Then rotate as usual, and undo the translation afterwards. Each of these operations can be described using a matrix, and the whole shebang can be performed at once by using the product of the three matrices...

Math
correct. y = -x^3, which is a polynomial, not an exponential.

Algebra
since PV=kT, if T is constant, then P and V are inversely proportional. Halving the pressure doubles the volume.

Math
|x| + 5 = 18 |x| = 13 x = ±13 |x+3| < 5 x+3 < 5 if x >= -3 x < 2 so, -3 <= x < 2 or x+3 > -5 if x < -3 x > -8 so, -8 < x < -3 result: -8 < x < 2 |-3n|-2 = 4 |-3n| = 6 |3n| = 6 since |-3n|=|3n| 3n = ±6 n = ±2

mathematics
(e + 1/e)^4 = e^4 + 4e^3/e + 6e^2/e^2 + 4e/e^3 + 1/e^4 = e^4 + 4e^2 + 6 + 4/e^2 + 1/e^4 for the 2nd one, since the terms alternate in sign, every other term cancels out, leaving just 2(e^4 + 6 + 1/e^4)

mathematics
if wire 2 is 9, and wire 3 is x, then we have 9 = 2x-3 x = 6 the perimeter is just 5 + 9 + 6 = ?

math - trig/pythagoras
x^2 + (2b)^2 = (6b)^2 x^2 + 4b^2 = 36b^2 x^2 = 32b^2 x = 4b?2 Now recall that area = bh/2 and just do the multiplication

Math
1) m = 6t m+20 = 2(t+20) 6t+20 = 2t+40 t=5 So, Mary is 30 in 20 years she will be 50, which is 2*25 2)5W = 2*10W = 4*15W = 8*20W 3) makes no sense, either the question of the answers

Math
taxes: 40% of 50000 = 20000 So, they had 30000 left to spend In 1994 they spent of their \$40000 Others-10000 Food- 4000 Housing- 10000 Total: 24000 That leaves 6000 for savings

Math - Need Pattern
ummm, which pattern?

If the points given are those of P(x), then f(x) has the same values, with the exception of (1,-3). f(x) contains (1,3) since |-3|=3, and the range of f(x) is all the distinct values of y.

Math
ah, actually I misspoke. Since 3+2i is also a root, we have p(x) = (x-(3-2i))(x-(3+2i))(x-a) = (x^2-6x+13)(x-a) So, now just solve for a: p(0) = -13a = -52 a = 4 p(x) = (x^2-6x+13)(x-4) = x^3-10x^2+37x-52

Math
peter is 30 lbs lighter than john. So, j + j-30 = 235 Odd; I expected an integer answer... as for the polynomial, who knows? I see no question there. And LaTex doesn't do well here. And p(x) cannot be monic with real coefficients and have a complex root.

maths
x^(3/2) = x^(1 + 1/2) = x * x^(1/2) = x?x so, 20^(3/2) = 20?20 = 40?5

physics
1200rev/min * 2?/rev * 1min/60s = 40?Hz 40?Hz * 3s = 120?*6cm = 720?cm

MATH
or, convert all to decimals. Then it is easy to see.

Calculus
So, with limits a and b, that will be n-1 ? f(a+(i + 1/3)*(b-a)/n)*(b-a)/n i=0

math
one way is to check the lengths of the sides. Call the longest c, and the others a and b. If c^2 = a^2+b^2 then you have a right triangle. For example, GH^2 = (3+2)^2 + (-1-1)^2 = 29 Now fin the other side lengths Another way is to find the slopes of the sides. If two of the ...

mtap
assuming the diagonals are equal, 3x+2 = 5x-8 x = 5

Math
r^6 = 39366/54 = 729 = 3^6 a = 54/3^2 = 6 ... for the factorials, just use any online calculator. geez.

Algebra II
Note that since 8 = 2^3, 8a^-3 = 2^3/a^3 = (2/a)^3 so, (8a^-3)^-2/3 = (a/2)^2 = a^2/4 You are done, and you are correct.

Math
well, you know that 1 ft = 12 in 1 yd = 3 ft = 36 in So, just do the math

maths
the nth term is (1 + .07/12)^n after 5 years, the balance is thus 25000(1+.07/12)^(12*5)

You want |f(x)-1| < 0.1 |2-(1/x)-1)| < 0.1 |1 - 1/x| < 0.1 Now, let x = 2+? |1 - 1/(2+?)| < 0.1 |2+?-1| < 0.1(2+?) |?+1| < 0.2 + 0.1? we know that ?+1 > 0, so that means ?+1 < 0.1 + 0.1? 0.9? < -0.9 ? < -1 This makes no sense. Since f(1/2) = 0, I ...

49% is about 1/2, so ...

Joanne and Bill are financing \$305,500 to purchase a house. They obtained a 20/6 balloon mortgage at 5.75%. What will their balloon payment be? \$206,311.68 \$401,524.25 \$152,285.77 \$249,295.69 My answer is the 4th one.

Math
oranges/800 = 9/40 = 180/800

Math
.0175*68000 + .118x = .075(68000+x)

math help asap
the degree is the sum of the exponents. So, -x^4y^3 is degree 7 and yes, the 1st one is a monomial. polynomials have terms separated by + and - signs.

Algebra
D = 0.40A A = D+E = 0.40A+E so E = 0.60A N = 0.75E = 0.45A S = 5.2A N/S = 0.45/5.2 = 45/520

Math
since AD=15 and AB=12, I'd say you have A-12-B-3-D Now, if C is 4 to the left of B, we have A-8-C-4-B-3-D So, choice (D)

Algebra 1
There are lots of useful calculators online, such as this one: https://ncalculators.com/statistics/linear-regression-calculator.htm

Math
Heck. Just draw any triangle, and label one side 5.6 I suspect there is more to this little problem ...

Math
Nah. Where did you get the 40? 50 * 5/6 = 250/6 = 125/3 so, you have a genuine GP, with a = 72 r = 5/6 So, S = 72/(1 - 5/6) = 72*6 = 432

math
I'd say 5 * 3/8 = 15/8 lbs or, ...

maths
since two sides are equal, you must have one of 4b=6b-2a+1 4b=a+2b 6b-2a+1=a+2b which can be simplified to 2b-2a = -1 a-2b = 0 3a-4b = 1 also, using the perimeter, 4b + 6b-2a+1 + a+2b = 28 12b-a=27 so, see how the perimeter equation can be matched with one of the others to ...

Math
312.5/625 = 0.5 = 50%

Math
5/8 + 1 7/9 + 3 45/72 + 1 56/72 + 3 4 101/72 5 29/72

Math
since f and g both have positive leading coefficients, f+g has degree 4. If a is positive, the same holds true. If a = -2, f+a*g has degree 3. So, f+ag can have max degree 4.

Math
across y=-5: (x,y)->(x,-5-(y- -5)) = (x,-10-y) across x=1: (x,y)->(1-(x-1),y) = (2-x) now just use them both; they are independent. Check using some graph paper.

Geomery
draw one line. Mark its midpoint. Draw the bisector through the midpoint. You have not said it is the perpendicular bisector, so the angle does not matter.

Math
311 km/hr * .625mi/km = ? mi/hr 347 euro * 1.25 \$/euro = ? \$

Math
well, she walks 3 trips of 600m each, so ...

Math
just calculate the interest on \$x -- (.063/12)x = 250 Now just find x.

Math
packets of flour: 24*2000 / 500 = 96 packets of sugar: 36*1000 / 250 = 144 so, what next? Did they hand out packets of both as long as they had both, or did they just give one or the other to anyone?

Further mathematics
just divide successive pairs of terms. r = (-1/2)/1 = (1/4)/(-1/2) ...

Further mathematics
20 = 8+4d, so d=3 Now use that to find x,y,z.

calculus
f'(x) = -sinx e^cosx since e^cosx is never zero, f' has zeroes where sinx has zeros. I'm sure you remember enough trig to figure that out.

math
get all the x stuff on one side, by adding 4 to both sides of the equation: 3x+x = 32+4 Now collect all the x stuff into one term: 4x = 36 Now divide both sides by 4, to get x all alone: x = 9

Trigonometric functions
geez - you know how to draw a sine curve, right? So, draw your generic sine curve, but instead of -1 to 1 on d, label it -10 to 10 and on the t axis, instead of a period going from 0 to 2?, label the axis so it goes from 0 to 2. Sine curves all look the same. Just label the ...

Trigonometric functions
what don't you like about what I wrote?

Trigonometric functions
I can't see the figure, but if A and B are both 10 cm from the center line, then the maximum value of d is 10. This is the amplitude of the sine function desired, so since the period is 2 seconds, d = 10sin(?t)

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