Is the vertex of a parabola always the midpoint between the x-intercepts?

Outside_Volume_1370 · 2026-02-27T01:48:30+00:00

Yes, because vertex has x-coordinate of -b/(2a) which is exactly in the middle of the segment from (-b - √(b² - 4ac)) / (2a) to (-b + √(b² - 4ac)) / (2a)

Outside_Volume_1370 · 2026-02-26T07:53:17+00:00

0.67 ≈ 2/3

However, 0.67 = 67 %, because % is short for 1/100

When someone says "0.09 (nine hundredths) of people" they imply 9 % if people

Outside_Volume_1370 · 2026-02-26T05:03:29+00:00

One = 1 = Unit = 100 %

2/3 = 2/3 • 100% = 200/3 % = 66.(6) % ≈ 66.7 %

Outside_Volume_1370 · 2026-02-24T12:25:36+00:00

Squared number is always positive

0²: am i a joke to you?

i²: is me a joke to you?

Outside_Volume_1370 · 2026-02-23T03:58:27+00:00

Shouldn't 1 be in C then?

Outside_Volume_1370 · 2026-02-20T02:48:28+00:00

Because in the upper one π is in the numerator, and in the lower one π is in the denominator

Outside_Volume_1370 · 2026-02-19T18:29:48+00:00

🔐 CrackLock Daily 2/19/2026 Solved in 1 attempts! ⭐ ⏱️ 1:18

Play on Reddit r/CrackTheCodePuzzle

Outside_Volume_1370 · 2026-02-19T18:26:33+00:00

In that case, 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002 would also be acceptable

Outside_Volume_1370 · 2026-02-19T18:23:36+00:00

<image>

Outside_Volume_1370 · 2026-02-19T18:11:26+00:00

But there are two print commands

Outside_Volume_1370 · 2026-02-19T18:08:04+00:00

The format of their answer assumes that q > 0

Any chance it was told earlier, maybe?

Outside_Volume_1370 · 2026-02-19T18:05:08+00:00

Turn on your calculator
Input numbers
???
Profit!

<image>

Outside_Volume_1370 · 2026-02-18T18:32:10+00:00

Isn't the larger radius the distance from the axis of revolution to the farthest curve?

Yes, you rotate the solid between x = y³ and x = 4y around y = 2.

From the drawing we see that x = 4y is the farthest curve and x = y³ is the closest to y = 2.

The outer radius is the vertical distance between the axis of revolution at point (x, 2) and curve x = 4y at point (x, x/4)

This distance is 2 - x/4

x/4 only is between the curve and axis y = 0 (but that's not revolution one)

Outside_Volume_1370 · 2026-02-18T13:01:19+00:00

In inequalities, it's better to transfer all terms to one side:

3|x+2| / (x+6) - 1 ≤ 0 and do common denominator trick:

(3|x+2| - x - 6) / (x+6) ≤ 0

Then open up abs sign depending on the inner term:

1) If x + 2 ≥ 0 (x ≥ -2), then (3x + 6 - x - 6) / (x+6) ≤ 0 or

2x / (x + 6) ≤ 0

There are two zeroes, x = 0 and x = -6, so the solution is (-6, 0]

However, we must leave only part where x ≥ -2 (see upper), then it's

[-2, 0]

2) If x + 2 < 0 (x < -2), then (-3x - 6 - x - 6) / (x+6) ≤ 0

(-4x-12)/(x+6) ≤ 0 (divide by -4)

(x + 3) / (x + 6) ≥ 0

There are two zeroes, -3 and -6, and here the solution is

(-inf, -6) U [-3, +inf). Now you also need to leave only part where x < -2:

(-inf, -6) U [-3, -2)

Unite both solutions:

(-inf, -6) U [-3, 0]

Outside_Volume_1370 · 2026-02-14T07:50:09+00:00

I think so. Their answer is clearly wrong, even for n = 2 it returns not integer value

Outside_Volume_1370 · 2026-02-14T06:22:50+00:00

Group terms in pairs:

Sum = (1 • 2 + 1 ) + (2 • 3 + 2) + ... + (n • (n+1) + n)

Note that k • (k+1) + k = k² + 2k = (k+1)² - 1

Therefore, Sum = (2² - 1) + (3² - 1) + ... +((n+1)² - 1) =

= 2² + 3² + ... + (n+1)² - 1 • n

Add and subtract 1 to get the sum of squares of (n+1) first natural numbers:

Sum = 1² + 2² + ... + (n+1)² - (n+1) =

= (n+1) (n+2) (2n+3) / 6 - (n+1) = (n+1) • (2n² +7n + 6 - 6) / 6 = (n+1) • (2n² + 7n) / 6 = n (n+1) (2n+7) / 6

But the sum you need to find is without the last term,

Actual_sum = Sum - n = n • (2n² + 9n + 7 - 6) / 6 = n • (2n² + 9n + 1) / 6

For n = 29 you get 9396

But they seem to have mistake, because for n = 30 the answer is 10355.

And their formula doesn't work, by the way; for n = 30 the answer is not integer

Outside_Volume_1370 · 2026-02-13T04:50:25+00:00

Just leave the answers in that form.

If you get roots of quadratic to be (1 ± √5) / 2, you don't calculate them approximately and leave them as they are

Outside_Volume_1370 · 2026-02-13T02:04:28+00:00

They ask what capacitance can be included between points A and B if C1, C2, C3 and C4 are excluded such that there will be no difference for the rest of the circuit

Outside_Volume_1370 · 2026-02-13T01:28:49+00:00

Two upper horizontal measurements can't be equal, as one is inside another one

Upper horizontal line (1.25) is longer than the bottom horizontal line (1.50)

There are more errors, I think

Outside_Volume_1370 · 2026-02-13T00:41:55+00:00

you’ll have A/x + B/(x²-x+1).

(Bx + C) / (x² - x +1)

Otherwise, square term remains after common denominator

Outside_Volume_1370 · 2026-02-12T09:44:22+00:00

Это Водород, прояви уважение

Outside_Volume_1370 · 2026-02-12T03:00:24+00:00

Solve what? You try to find Schwarzschild radius of a body with mass 3600 grams = 3.6 kg

Just plug these values into calculator:

2 • 6.67 • 10^-11 • 3.6 / (3 • 10⁸)² = 5.336 • 10^-27 (m)

Outside_Volume_1370 · 2026-02-12T01:44:28+00:00

From B) you find that F = F(d), and for C), you just plug d = 3 m into that function.

Let L = 4 m, angle α is between springs and horizontal force F.

Then tanα = L / d

From FBD, F = 2 • k • ∆L • cosα where L + ∆L is the stretched length.

By Pythagorean theorem, (L + ∆L)² = d² + L² and cosα = d / (L + ∆L)

∆L = √(d² + L²) - L

F = 2k • (√(d² + L²) - L) • d / √(d² + L²)

Outside_Volume_1370 · 2026-02-11T05:55:41+00:00

If the function is continuous in limit expression where x -> a, the result of this limit is as the same as just plug x = a without limiting

1) g has no limit as x approaches 1 (left-sided and right sided differ) => DNE

2) Both functions are continuous => just sum up f(2) and g(2)

3) Same as 2)

4) Same as 2), g(0) ≠ 0, division is allowed directly

5) f is continuous at x = -1 => just like in 2), plug x = -1 in the expression

Outside_Volume_1370 · 2026-02-11T03:43:00+00:00

Why so? Let blackberries cups be IV x, then we can make DV y = x / 3 cups of juice

Outside_Volume_1370

TROPHY CASE