Precalculus Solutions | Expert Assistance for Problems & Examples

Show that $4 \cos \frac{π}{5} \cdot \sin \frac{π}{10} = 1$

Emery Boone 2022-05-28

Tried playing with the formula of Conditional probability and some variations of combinatorics, because i know for sure that the 6th toss was head (we stop on the 3rd time we get head, and it's given to us that we stopped after 6 tosses). I know the answer is 0.4, but I cant unserstand how to get this answer, any help?

Rocatiwb 2022-05-28

Solving $z = - i \ln (- c i + \sqrt{(1 + c) (1 - c)})$ for c
Given,
$z = - i \ln (- c i + \sqrt{(1 + c) (1 - c)})$
I would like to solve for c. First multiply through by i,
$i z = \ln (- c i + \sqrt{(1 + c) (1 - c)}) .$
Then take the exponential of both sides,
$e^{i z} = - c i + \sqrt{(1 + c) (1 - c)}$
Not sure where to go from here, can I say
$ℑ (e^{i z}) = ℑ (- c i + \sqrt{(1 + c) (1 - c)}) ⟹ \sin z = - c ?$

Hugo Brady 2022-05-28

There are three colors of counter, red, green and blue.
There are 5 red, 3 green and 2 blue counters already in the bag.
Another counter is added to the bag (completely randomly).
A counter is chosen from the bag.
Given that the counter chosen is green, what's the probability that the counter added to the bag was green?

Jaycee Mathis 2022-05-28

Now given the exponential generating function of the Hermite polynomial
$e^{u x - (1 / 2) u^{2}} = 1 + \sum_{n = 1}^{\infty} \frac{u^{n}}{n!} h_{n} (x),$

groupweird40 2022-05-28

How to write $f (x) = x^{n} + (1 - x)^{n}$ in terms of $r = x (1 - x)$

katkoota00ys 2022-05-28

What is the period of $f (x) = \sin^{4} (x) + \cos^{4} (x)$ ?

Hayley Sanders 2022-05-28

Proof of $\sin (\frac{3 π}{2} - A) = - \cos (A)$ geometrically

Elisha Kelly 2022-05-28

Evaluating $\int \cos (7 x) \cos (17 x) \cos (27 x) d x$

Despiniosnt 2022-05-27

Number of roots of $Σ_{r = 1}^{2009} \frac{r}{x - r}$

wanaopatays 2022-05-27

Decomposing $\sum_{i = 0}^{2 n} x^{i}$ as a simple sum of squares

Brice Colon 2022-05-27

Evaluate this integral:
$a_{n} = \frac{1}{π} \int_{- π}^{π} {(\frac{T}{2 π})}^{2} y^{2} \cos n y d y$

Rocatiwb 2022-05-27

Finding tanx from $24 \sin x \cos x - 5 = 14 \cos^{2} (x)$

velitshh 2022-05-27

Finding f(x) in $\cos^{2} (x) f (x) = x^{2} - 2 \int_{1}^{x} \sin (t) \cos (t) f (t) d t$
I can apply the FToC and I get:
$(2 \cos (x) - \sin (x) f (x)) + (\cos^{2} x f^{'} (x)) = 2 x \sin (x) \cos (x) f (x)$
Now I don't understand how to find f(x).

Kellen Perkins 2022-05-27

Prove that $(\binom{2 n}{n}) = \sum_{k = 0}^{n} {(\binom{n}{k})}^{2}$
So far I have tried writing the right hand side in different ways: expressing it in its factorial form and have tried to implement the identity
$(\binom{n}{k}) = (\binom{n - 1}{k - 1}) + (\binom{n - 1}{k})$
but have not gained any new ground. If any one has an algebraic proof, or even a simple combinatorics proof that is intuitive and used with an example that would be preferable.

rs450nigglix2 2022-05-27

Show that 1 is a root of the polynomial $n X^{n + 2} - (n + 2) X^{n + 1} + (n + 2) X - n$ . Determine its multiplicity.

Monfredo0n 2022-05-26

How does $π - \arctan (\frac{8}{x}) - \arctan (\frac{13}{20 - x}) = \arctan (\frac{x}{8}) + \arctan (\frac{20 - x}{13})$ ?

raulgallerjv 2022-05-26

Prove $\frac{\sec (x) - \csc (x)}{\tan (x) - \cot (x)}$

Antoine Hill 2022-05-26

If $a + b = c + d$ , and $a^{3} + b^{3} = c^{3} + d^{3}$ , then prove that:
$a^{2011} + b^{2011} = c^{2011} + d^{2011}$

Brooke Kramer 2022-05-26

Let
$σ (n) = \sum_{d ∣ n} d$
the sum of divisor function. I've deduced, but I don't know how prove directly
$σ (n) = \sum_{m = 1}^{n} \sum_{k = 1}^{m} (- 1)^{n k} \cos (\frac{π n (2 - m) k}{m}) .$

Precalculus problems and solutions are hard to find online even though this topic is quite popular among college students majoring in Engineering. Keeping this fact in mind, we decided to provide you with a list of questions and answers that will help you with various precalculus problems. Regardless if it is related to equations or any other problem, these precalculus problems and composite functions examples and solutions below will help you see the logic and compare solutions as you check your original task.

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