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High School

Identify each function as modeling either exponential growth or exponential decay . What percent of increase or decrease does the function model ? 2. y = 0.32 * (0.99) ^ x 3. y = 0.1 * (1.7) ^ x 4. y = 7.3 * (0.8) ^ x; y = 15 * (1.45) ^ x

Efrain Watkins 2022-04-07

For how many values of x in $0 \leq x < 2 π$ does $\frac{\sin (5 x)}{\sin (x)} - \frac{\cos (5 x)}{\cos (x)} = 2$
Using the sine and cosine addition rules, I tried to express $\sin (5 x)$ and $\cos (5 x)$ in terms of $\sin (x)$ and $\cos (x)$ . However, it took me quite a while, and I was wondering if there was a quicker way

Aedan Berry 2022-04-07

Fixing $γ, γ^{'}$ two reals numbers such that
$| γ^{'} | < \frac{1}{2} and 0 < γ < 1$ ,
and $α, β \in (0, π)$ , define
$x_{n} = \sin (2 π n γ + α + β) + \sin (2 π n γ^{'} + α - β)$
Could someone give me a simple statement equivalent to $x_{n} \geq 0$

Bryson Whitney 2022-04-07

First order diferential equation with two integrating factors can be solved by separation of variables
$M (x, y) d x + N (x, y) d y = 0$
if f(x) and g(y) are integrating factors then the diferential equation can be solved by separation of variables.

Leonard Montes 2022-04-07

Finding the vertex of $y = x^{2} - 6 x + 1$ . My solution doesn't match the book.

Kasey Castillo 2022-04-07

Finding the maximum and minimum values of
$f (x) = | x - 1 | + | x^{2} - 2 x |$ for $x \in [0, 2]$

Henry Winters 2022-04-07

Finding the limit of a sequence
$lim_{n \to \infty} \sqrt[3]{n^{2}} (\sqrt[3]{n + 1} - \sqrt[3]{n})$

Alan Zavala 2022-04-07

Finding the coefficient of $x^{n}$ in the expansion of ${{({\log_{e} (1 + x)})}^{2}}$
I've been trying to find the coefficient of xn in the expansion of ${({\log_{e} (1 + x)})}^{2}$ .I wrote out the expansion of ${{({\log_{e} (1 + x)})}^{2}}$ explicitly and tried to generalize the terms involving $x^{n}$ , but...so far no luck.
Is there any other alternative ?

Quinn Dean 2022-04-07

Finding $\frac{1}{1 + {\tan 70}^{\circ}} + \frac{1}{1 + {\tan 20}^{\circ}}$

Saul Cochran 2022-04-07

Finding $lim_{x \to \infty} (\sqrt{9 x^{2} + 3} - 3 x)$

Camila Glenn 2022-04-07

Finding $lim_{x \to 0} \frac{\sin (π \cos^{2} (\frac{x}{2}))}{\sin (\sin (x))}$
I have the following solution, only the first equality of which bothers me:
$lim_{x \to 0} \frac{\sin (π \cos^{2} (\frac{x}{2}))}{\sin (\sin (x))} = lim_{x \to 0} \frac{\sin (π \sin^{2} (\frac{x}{2}))}{\sin (\sin (x))} = lim_{x \to 0} π \frac{\sin (\frac{x}{2})}{2 \cos (\frac{x}{2})} . \frac{2 \sin (\frac{x}{2}) \cos (\frac{x}{2})}{\sin (2 \sin (\frac{x}{2}) \cos (\frac{x}{2}))} . \frac{\sin (π \sin^{2} (\frac{x}{2}))}{π \sin^{2} (\frac{x}{2})} = 0$
What is the justification for replacing $\cos^{2}$ with $\sin^{2}$ ?

Yaritza Estrada 2022-04-07

Finding non-zero function such that $f (2 x) = f^{'} (x) \cdot f^{″} (x)$ .
I am thankful if someone can help me or show me the clue. As honestly as possible, I got stuck on this problem.
I need some help in finding a $f (x) \neq 0$ such that
$f (2 x) = f^{'} (x) \cdot f^{″} (x),$
where f', f" are the first and second derivatives, respectively. It is not an ordinary differential equation.
My last try was to put $f (x) = k e^{a x}$ , and then
$k e^{2 a x} = k a e^{a x} \cdot k a^{2} e^{a x} .$
Now by canceling $e^{a x}$ , we have
$k = k^{2} a^{3} .$
This shows $k = 1, a = 1$ and finally $f (x) = e^{x}$ . But I want to solve the problem analytically.

fernandoval3sbr 2022-04-07

Finding Hamilton function which equations do I have to solve to find $v (θ, ϕ, \dot{θ}, ϕ)$ ?
$L (θ, ϕ, \dot{θ}, \dot{ϕ}) = \frac{m b^{2}}{2} ({\dot{θ}}^{2} + \sin^{2} (θ) {\dot{ϕ}}^{2}) + m b g \cos (θ)$

Ormezzani6cuu 2022-04-07

Finding a Quadratic Function Find a quadratic function f (with integer coefficients) that has the givenzeros. Assume that b is a positive integer and a is an integer not equal to zero.
(a) $\pm \sqrt[()]{b} i$
(b) $a \pm b i$

runddansm88e 2022-04-07

Finding a constant such that the following integral inequality holds:
Constant: $c > 0$ such that for all $C^{1}$ function in $(0, 1)$
$c u {(0)}^{2} \leq \int_{0}^{1} u^{' 2} + u^{2} d t$

George Michael 2022-04-07

Find:
$lim_{x \to 0} \frac{1 - \cos 4 x}{x \tan 6 x}$

Ramiro Grant 2022-04-07

Find zeros of a polynomial and apply them to an another equation
If a and b are the zeros of quadratic polynomial $x^{2} - 4 x - 5$ , find the value of $\frac{1}{a^{3}} + \frac{1}{b^{3}}$ .

Rosa Townsend 2022-04-07

Find value of
$\prod_{r = 1} \sin (\frac{(2 r - 1) π}{2 n})$
Where $n \in N$ and $n > 1$

Colt Rhodes 2022-04-07

Find the values of ${\sin 18}^{\circ}$

delitzo1d4 2022-04-07

Find the value of the following series.
$\tan θ + 2 \tan (2 θ) + 2^{2} \tan (2^{2} θ) + \dots + 2^{14} \tan (2^{14} θ) + 2^{15} \cot (2^{15} θ)$

1
…
1281
1282
1283
1284
1285
…
2358

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High School

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