Precalculus Solutions | Expert Assistance for Problems & Examples

Two balls are chosen randomly from an urn containing 8 white, 4 black, and 2 orange balls. Suppose that we win 2 for each black ball selected and we lose 2 for each black ball selected and we lose 1 for each white ball selected. Let X denote our winnings. What are the possible values of X, and what are the probabilities associated with each value?

Use the Divergence theorem 2.the surface S that is the boundary of the solid between Z=0 and Z=X square 1.

If t is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is unique. Let A = and b = 1 -3 2 -6 0 1 -3 -7 2 -7 4 -2 Find a single vector x whose image under T is b x =

please solve this question as soon as possible

Cheexorgeny 2022-01-04

Find a vector a with representation given by the directed line segment AB. Draw AB and the equivalent representation starting at the origin.
$A (- 2, I)$ , $B (l, 2)$

b2sonicxh 2022-01-03

Can you please show me the process that determines $\int_{- 1}^{1} \frac{d x}{\sqrt{- x^{2} + 1}} = π$ ? Unfortunately I only know that the derivative of $\sin^{- 1} (x)$ is equal to the integrand of that, but I don't actually know what to do with it.

Bobbie Comstock 2022-01-03

Prove and compute the limit of this function.
$\lim_{x \to 0^{+}} \frac{\sin (6 x)}{\sqrt{\sin (2 x)}}$
Trying converting it into different functions like $\cos (\frac{π}{2} - 2 x)$ or multiplying by the inverse function and so on, but it keep getting back to $0 / 0$ .

Find the relative maximum / minimum / points of inflection of

the following functions:

y 6 7 3 2 y = x + x +

y y = 2x (1− 2x)

y y = ln(2x − 5)− ln x

y 15 300 150

Mabel Breault 2022-01-02

How could I approach
$lim_{n \to \infty} {(\frac{1 + \cos (\frac{1}{2^{n}})}{2})}^{n}$
I tried several things to evaluate it, namely looking at it as ${\cos (\frac{1}{2^{n + 1}})}^{2 n}$ instead or as $\exp (2 n \cdot \ln (\cos (\frac{1}{2^{n + 1}}))$ and then trying to show that the limit of $n \cdot \ln (\cos (\frac{1}{2^{n + 1}}))$ is 0 (for example using LHopitals rule), but I havent

Donald Johnson 2022-01-02

$\frac{1}{2} = \frac{\sin^{2} x}{\tan x}$
What would be my next step to get to $x = 45 °$ ?

elvishwitchxyp 2022-01-02

Find, in radians the general solution of $\cos 3 x = \sin 5 x$
I have said, $\sin 5 x = \cos (\frac{π}{2} - 5 x)$
so
$\cos 3 x = \sin 5 x \Rightarrow 3 x = 2 n π \pm (\frac{π}{2} - 5 x)$
When I add $(\frac{π}{2} - 5 x) to 2 n π$ I get the answer $x = \frac{π}{16} (4 n + 1)$ , which the book says is correct.
But when I subtract I get a different answer to the book. My working is as follows:
$3 x = 2 n π - \frac{π}{2} + 5 x$
$2 x = \frac{π}{2} - 2 n π$
$x = \frac{π}{4} - n π = \frac{π}{4} (1 - 4 n)$

PEEWSRIGWETRYqx 2022-01-01

To me the most common identity that comes to mind that results in 1 is the trigonometric sum of squared cosine and sine of an angle:
$\cos^{2} θ + \sin^{θ} = 1$ (1)
and maybe
$- e^{i π} = 1$ (2)
Are there other famous (as in commonly used) identities that yield 1 in particular?

Terrie Lang 2022-01-01

The general solution of $| \sin x | = \cos x$ is -
(A) $2 n π + \frac{π}{4}, n \in I$
(B) $2 n π \pm \frac{π}{4}, n \in I$
(C) $n π + \frac{π}{4}, n \in I$
(D) None of these
So what I did was - I made a case for when $\sin x$ is greater than 0 and equated it to $\cos x$ to get $\tan x = 1$ which implies $x = \frac{π}{4}$ . The other case was when $\cos x = - \sin x$ . Here, $x = \frac{3 π}{4}$ . I don't understand how to proceed from here.

lugreget9 2022-01-01

I was trying to find the least value of $| \sin x | + | \cos x |$ and applied the above inequality as :
$| \sin x + \cos x | \leq | \sin x | + | \cos x |$
$\Rightarrow \sqrt{2} \leq | \sin x | + | \cos x |$
But the range of the given function is $[1, \sqrt{2}]$ .

Mary Reyes 2022-01-01

How am I supposed to expand $\sin^{2} A + \sin^{4} A = 1$ into $1 + \sin^{2} A = \tan^{2} A$ ?

David Young 2021-12-31

What is general solution of $\frac{\cos 5 x \cos 3 x - \sin 3 x \sin x}{\cos 2 x} = 1$
1) $\frac{k π}{3}$
2) $\frac{k π}{2}$
3) $\frac{2 k π}{5}$
4) $\frac{2 k π}{3}$
The numerator of the fraction is $\cos (5 x + 3 x)$ . so I should find general solution of $\cos 8 x = \cos 2 x$ . I'm not sure how to do it, I can write $\cos 8 x$ in term of $\cos 2 x$ :
$\cos 8 x = 2 \cos^{2} 4 x - 1 = 2 {(2 \cos^{2} 2 x - 1)}^{2} - 1$
After substituting it in the equation and using $\cos 2 x = t$ we have degree four equation

crealolobk 2021-12-31

Find the sationary points of the curve and their nature for the equation $y = e^{x} \cos x$ for $0 \leq x \leq \frac{π}{2}$
I derived it and got $e^{x} (- \sin x + \cos x) = 0$
$e^{x}$ has no solution but I don't know how to find the x such that $- \sin x + \cos x = 0$

Kaspaueru2 2021-12-31

Basically, write $\cos 4 x$ as a polynomial in $\sin x$ .
I've tried the double angles theorem and $\cos 2 x = \cos^{2} x - \sin^{2} x$ . I'm still having trouble right now though.

Wanda Kane 2021-12-31

How to integrate hyperbolic function $\frac{1 - \sin (x)}{1 + \sin (x)}$

Kathleen Rausch 2021-12-31

Complex arithmetic with conjugates Show that the conjugate of the sum (product, or quotient) of two complex numbers, $z_{1}$ and $z_{2}$ , is the same as the sum (product, or quotient) of their conjugates.

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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