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High School

The front 1.20 m of a 1 400-kg car is designed as a “crum- ple zone” that collapses to absorb the shock of a collision. If a car traveling 25.0 m/s stops uniformly in 1.20 m, (a) how long does the collision last, (b) what is the mag- nitude of the average force on the car, and (c) what is the acceleration of the car? Express the acceleration as a mul- tiple of the acceleration of gravity.

Jazmin Strong 2022-04-07

Identify for each of the following studies the scale of measurement.
1. Number of pages in Quantitative Technique II book.

Quinn Dean 2022-04-07

I've attempted to integrate the function:
$\frac{2 x + 7}{x^{2} + x + 1}$

Bryson Whitney 2022-04-07

I'm trying to prove the following problem:
$\frac{\sec^{2} (x)}{\cot (x)} - \tan^{3} (x) = \tan (x)$

Destinee Adams 2022-04-07

I'm trying find an exact value for
$\cos (\frac{1}{3} \arctan (\frac{- 10}{9 \sqrt{3}}))$

Devin Dougherty 2022-04-07

I'm stuck on this problem:
If ,
then find the value of:
$2^{n} \prod_{k = 0}^{n - 1} \cos (2^{k} θ)$

Angelina Kaufman 2022-04-07

I'm quite ashamed that I'm at a math-related course at the university and I'm stuck. I can't solve at all this equation:
$n = 8 \log_{2} (n) .$
I have tried applying the log property so it becomes $2^{n} = 2^{8 n}$
Besides that this didn't help me, I'm not even sure if I applied right the property that says $x = \log_{2} (y) \Rightarrow 2^{x} = y$
Thanks in advance! Best Regards,

Quinn Dean 2022-04-07

i'm having hard time with $lim_{x \to \infty} \frac{x (1 + e^{x^{2}}) \tan x - 2 \sin^{2} x}{x (\tan x - x)}$
i've tried to simplify it using $\cos 2 x$ identity ( $\cos 2 x = 1 - 2 \sin^{2} x \to \cos 2 x - 1 = - 2 \sin^{2} x$ ) ,or tried to break it into 2 different fractions, but i couldn't get it to a point where i could use mclaurin in order to solve the given limit.

fanairana7lu1 2022-04-07

I would like to know why $\frac{\sin (n)}{n^{2}} < \frac{1}{n^{2}}$ ? It becomes obvious when you look at a graph, but for instances where you can’t do that how do you tell if the comparison is true?

Willie Kelley 2022-04-07

I was trying to find two limits which are trivial using l'Hopital, but I can't seem to find a way to do it without it. For example :
$f (x) = \frac{e^{2 \sin (x)} - 1}{x}$
I tried to do it using the fact I know $lim \frac{e^{x} - 1}{x} = 1$ as $x \to 0$ . Then,as $2 \sin x$ tends to 0 as well as $x \to 0$ , I first tried to prove the limit of $f (x)$ would be 1, but I know it is 2 (using l'hôpital).

Leia Sullivan 2022-04-07

I would like to compute
$\int_{0}^{2 π} \frac{\sin^{4} (4 x)}{\sin^{2} (x)} d x$

Emmy Decker 2022-04-07

I was solving the trigonometric equation
$\tan^{2} x + \cot^{2} x = 2 - \cos^{2014} (2 x)$

Alan Zavala 2022-04-07

I wanted to use this
$\sin (\frac{π}{15}) \cdot \sin (2 \frac{π}{15}) \dots \sin (7 \frac{π}{15}) = \sqrt{15}$

Blaine Jimenez 2022-04-07

I want to show that $x = \cos \frac{π}{11}$ is a solution of equation :
$8 x^{2} - 4 x + \frac{1}{x} - 4 = 4 \sqrt{\frac{1 - x}{2}}$

Cash Duncan 2022-04-07

I want to show that
$\lim_{n \to \infty} \sqrt{n} (\sqrt[n]{n} - 1) = 0$

Aliyah Mendez 2022-04-07

I want to know if it's true.
$\sin (\frac{π}{2} + 2 π K) > \sin (3 (\frac{π}{2} + 2 π k))$

Izabelle Walsh 2022-04-07

I want to find this limit for complex variable z
$lim_{z \to - 1} (z + 1) \sin (\frac{1}{z + 1})$
In the real case I know sin(z) is bounded by -1,1, and the limit is 0. But in the complex case $\sin (z)$ is not bounded. How can I find the limit or prove that it doesn't exist?

Emilia Hoffman 2022-04-07

I want to evaluate
$\int \frac{\cos θ d θ}{\sqrt{2 - 9 \sin^{2} θ}}$

Jasiah Vincent 2022-04-07

I need two methods different conclusion.
$lim_{(x, y) \to (0, 0)} \frac{{(x^{3} - y^{2})}^{2}}{x^{4} + y^{4}}$

Lisa Cooper 2022-04-07

I need to write this functions in rectangular coordinates:
$f (r, θ) = r^{2 k + 5} \cos 5 θ$
$g (r, θ) = r^{2 k + 5} \cos 5 θ$

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High School

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