All Questions ⁺⁰237828 Questions

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Complex numbers

Find all the solutions to z^4 = -4 - 5z^2 in complex numbers.

Express all the solutions in the form a + bi, where a and b are real numbers.

Guest Dec 22, 2022

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205

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Inequality

(a) Prove that if a, b, c, d, e, f are nonnegative real numbers, then (a^2 + b^2)^2 (c^4 + d^4)(e^4 + f^4) >= 32abcdef.
(b) Prove that if a, b, c, d, e, f are nonnegative real numbers, then (a^2 + b^2)(c^2 + d^2)(e^2 + read more ..

Guest Dec 22, 2022

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counting

There is a group of five children, where two of the children are twins. How many ways can I distribute 10 identical pieces of candy to the children, if the twins must get an equal amount of candy?

Guest Dec 22, 2022

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triangle

In triangle PQR, let M be the midpoint of QR, let N be the midpoint of PR, and let O be the intersection of QN and RM, as shown. If QN perp PR, QN = 12, and PR = 14, then find the area of triangle PQR.

Guest Dec 22, 2022

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204

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Find the value of the variable in the parallelogram

Rz = 3x+9
Sw = 7x-9

Guest Dec 22, 2022

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math

Together, teammates Pedro and Ricky got
2673
base hits last season. Pedro had
279 read more ..

Guest Dec 22, 2022

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172

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Algebra

Find all real numbers x such that
(3^x - 27)^3 + (27x - 3)^3 = 3x + 27x - 30.

Guest Dec 22, 2022

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181

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graphing question

The graph of y = f(x) is shown below.

For each point (a,b) that is on the graph of y = f(x), the point ((a - 7)/2, (3b + 1)/4) is plotted, forming the graph of another function y = g(x). As an example, the point read more ..

Guest Dec 22, 2022

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185

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Probability

In the SuperLottery, three balls are drawn (at random, without replacement) from white balls numbered from 1 to 12, and one SuperBall is drawn (at random) from red balls numbered from 13 to 20. When you buy a ticket, you choose three numbers from 1 to 12, read more ..

Guest Dec 22, 2022

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help counting

In the array below, in how many different ways can we start with the letter A and move from letter to letter (horizontally, vertically, or diagonally), to spell the word "ARCH"?

A
RR read more ..

Guest Dec 22, 2022

+2

216

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+53

Geometry

The line AB has length 1. If ADB is a quarter circle, and CFB is a semicircle, with E being the midpoint, what is the area of the petal like shape of FB?(area, not length) read more ..

billy.zhang Dec 22, 2022

Dec 21, 2022

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236

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+349

derivatives

$$Find \ the \ derivative \ of \ \frac{log(\frac{3x^2}{sin(x)})}{ln(2x)} \ + \ 3$$

hipie Dec 21, 2022

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Help

We have a triangle $\triangle ABC$ and a point $K$ on segment $\overline{BC}$ such that $AK$ is an altitude to $\triangle ABC$. If $AK = 6,$ then what is the perimeter of the triangle?

Guest Dec 21, 2022

+22

278

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+1307

Prime numbers...

How many prime numbers less than 100 have a units digit of 3?

dolphinia Dec 21, 2022

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214

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How to demonstrate that 59|3^(n+3)+2^(n+5)*31^n ?

How to demonstrate that 59 | 3n+3 + 2n+5 * 31n ?

Thank you

Guest Dec 21, 2022

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204

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Function

The function f(n) satisfies
binom(2n)n - binom(2n + 1)(2n) = f(n) *binom(2n + 1)(n + 1)
for all positive integers n. Find f(n).

Guest Dec 21, 2022

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PLS HELP URGENT

Report Error
If a, b, c and d are replaced by four different digits from 1 to 9 , inclusive, then what's the largest possible value for a.bc + 0.d

Guest Dec 21, 2022

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