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- ...more than a pink pill, and Al's pills cost a total of 546 dollars for the two weeks. How much does one green pill cost? ...) = 8</math> and <math>\clubsuit(123) = 1 + 2 + 3 = 6.</math> For how many two-digit values of <math>x</math> is <math>\clubsuit(\clubsuit(x)) = 3?</math>13 KB (1,987 words) - 18:53, 10 December 2022
- ...{C}) 75+100\pi \quad (\mathrm {D}) 100+100\pi \quad (\mathrm {E}) 100+125\pi</math> ...a display of cans in which the top row has one can and each lower row has two more cans than the row above it. If the display contains 100 cans, how many13 KB (2,049 words) - 13:03, 19 February 2020
- ...e for <math>2</math> dollars. They sell all the candy bars at the price of two for <math>1</math> dollar. What was their profit, in dollars? \mathrm{(A)}\ 80-20\pi \qquad12 KB (1,781 words) - 12:38, 14 July 2022
- ...math>\frac{14^2}{2}-\frac{4^2}{2}-(\frac{5\sqrt{2}}{2})^2\pi=98-8-\frac{25\pi}{2}</math>, which is approximately <math>51</math>. The answer is <math>\bo2 KB (262 words) - 21:20, 21 December 2020
- ...i\theta_n}</math>, where <math>\theta_n=2^n(\theta_0+\frac{\pi}{2})-\frac{\pi}{2}</math>. ...\frac{iz_k}{\overline {z_k}}=i e^{i\theta_k} e^{i\theta_k}=e^{i(2\theta_k+\pi/2)}4 KB (660 words) - 17:40, 24 January 2021
- ...math> is cut into two congruent hexagons, as shown, in such a way that the two hexagons can be repositioned without overlap to form a square. What is <ma How many sets of two or more consecutive positive integers have a sum of 15?13 KB (2,028 words) - 16:32, 22 March 2022
- ...e have that <math>\left(\sin\left(\frac\pi2 - u\right) + i \cos\left(\frac\pi 2 - u\right)\right)^n = \sin n \left(\frac\pi2 -u \right) + i\cos n \left(\ ...left(\cos u + i \sin u\right)^n = \cos nu + i\sin nu</math>. We know that two [[complex number]]s are equal if and only if both their [[real part]] and [6 KB (1,154 words) - 03:30, 11 January 2024
- Setting these two expressions for <math>(OF)^2</math> equal and solving for <math>x</math> (i ...equation yields <math>a^2+b^2 = 290000</math>. We now finish by adding the two original stewart equations and obtaining: <cmath>2(450\sqrt{2})^2 = (500-x)13 KB (2,080 words) - 21:20, 11 December 2022
- ...ruent]] [[circle]]s form a ring with each circle [[externally tangent]] to two circles adjacent to it. All circles are [[internally tangent]] to a circle ...ath>. <math>K = 30^2\pi - 6(10^2\pi) = 300\pi</math>, so <math>\lfloor 300\pi \rfloor = \boxed{942}</math>.1 KB (213 words) - 13:17, 22 July 2017
- ...ation are <math>x = 1 + i^n r</math> for <math>n = 0, 1, 2, 3</math>. The two non-real members of this set are <math>1 + ir</math> and <math>1 - ir</math ...a quadratic, then <math>((x-1)^2+\sqrt{2006})</math> is bound to hold the two non-real roots since the other definitely crosses the x-axis twice since i4 KB (686 words) - 01:55, 5 December 2022
- ...ed. A [[plane]] [[parallel]] to the base of the cone divides the cone into two solids, a smaller cone-shaped solid <math> C </math> and a [[frustum]]-shap ...the [[Pythagorean Theorem]], we get <math>\ell = 5</math> and <math>A = 24\pi</math>.5 KB (839 words) - 22:12, 16 December 2015
- ...sides of the square determined by the vertex <math>(0,0)</math>. Let the two endpoints of the segment have coordinates <math>(x,0)</math> and <math>(0,y ...ed by all of the midpoints is <math>4-4\cdot \left(\frac{\pi}{4}\right)=4-\pi \approx .86</math> to the nearest hundredth. Thus <math>100\cdot k=\boxed{83 KB (532 words) - 09:22, 11 July 2023
- ...of which are quadrilaterals. A space diagonal is a line segment connecting two non-adjacent vertices that do not belong to the same face. How many space d ...ratio was <math>\frac{300}{500} = \frac{3}{5}</math>. The largest possible two-day success ratio that Beta could achieve is <math> m/n, </math> where <mat9 KB (1,434 words) - 13:34, 29 December 2021
- Dividing the two equations yields ...\theta</math>, so <math>\angle B'EA = \pi-2\theta</math>. Then <math>\tan(\pi-2\theta)=\frac{15}{8}</math>, or9 KB (1,501 words) - 05:34, 30 October 2023
- ...to the smaller can be expressed in the form <math> \frac{a\pi+b\sqrt{c}}{d\pi-e\sqrt{f}}, </math> where <math> a, b, c, d, e, </math> and <math> f </math ...; the rest of the area of the circle is then equal to <math>\frac{2}{3}r^2\pi</math>.2 KB (329 words) - 23:20, 4 July 2013
- ...to the smaller can be expressed in the form <math> \frac{a\pi+b\sqrt{c}}{d\pi-e\sqrt{f}}, </math> where <math> a, b, c, d, e, </math> and <math> f </math ...es and 10 blue candies. Terry picks two candies at random, then Mary picks two of the remaining candies at random. Given that the probability that they ge9 KB (1,410 words) - 05:05, 20 February 2019
- ...llows the straight path that produces the earliest possible meeting of the two skaters, given their speeds. How many meters does Allie skate before meetin pair A=(0,0),B=(10,0),C=6*expi(pi/3);7 KB (1,045 words) - 20:47, 14 December 2023
- ...th>x^{}_{}</math> satisfy the equation <math>\frac{1}{5}\log_2 x = \sin (5\pi x)</math>? Two three-letter strings, <math>aaa^{}_{}</math> and <math>bbb^{}_{}</math>, ar7 KB (1,106 words) - 22:05, 7 June 2021
- ...is called ascending if, in its decimal representation, there are at least two digits and each digit is less than any digit to its right. How many ascendi In Pascal's Triangle, each entry is the sum of the two entries above it. The first few rows of the triangle are shown below.8 KB (1,117 words) - 05:32, 11 November 2023
- ...the player's hand. The game ends if the player ever holds three tiles, no two of which match; otherwise the drawing continues until the bag is empty. Th ...\,</math> determine the number of times the light beam will bounce off the two line segments. Include the first reflection at <math>C\,</math> in your co7 KB (1,141 words) - 07:37, 7 September 2018
