Sydney Bement

Saint Louis University
Teaching Assistant

Biography

I'm committed to nurturing the next generation of scientists, encouraging them to question, analyze, and contribute to the evolving landscape of physics.

Education

BS Mathematics
Saint Louis University

Educator Statistics

Numerade tutor for 4 years
192 Students Helped

Topics Covered

Integration
Mastering Integration Techniques for Optimal Results
Discovering Conic Sections: An Introduction
Stand Out with Differentiation Strategies | Boost Your Business

Sydney's Textbook Answer Videos

0:00
College Algebra

Find the solution set for each system by graphing both of the system's equations in the same rectangular
coordinate system and finding points of intersection. Check all
solutions in both equations.
$$
\left\{\begin{aligned}
(y-2)^{2} &=x+4 \\
y &=-\frac{1}{2} x
\end{aligned}\right.
$$

Chapter 7: Conic Sections
Section 3: The Parabola
Sydney Bement
0:00
Calculus: Early Transcendental Functions

A plane is located $x=40$ miles (horizontally) away from an airport at an altitude of $h$ miles. Radar at the airport detects that the distance $s(t)$ between the plane and airport is changing at the rate of $s^{\prime}(t)=-240 \mathrm{mph} .$
(a) If the plane flies toward the airport at the constant altitude $h=4,$ what is the speed $\left|x^{\prime}(t)\right|$ of the airplane?
(b) Repeat with a height of 6 miles. Based on your answers, how important is it to know the actual height of the airplane?

Chapter 3: Applications of Differentiation
Section 8: Related Rates
Sydney Bement
0:00
Calculus: Early Transcendentals, Metric Edition

Graphs of the position functions of two particles are shown, where $t$ is measured in seconds. When is the velocity of each particle positive? When is it negative? When is each particle speeding up? When is it slowing down? Explain.

Chapter 3: Differentiation Rules
Section 7: Rates of Change in the Natural and Social Sciences
Sydney Bement
0:00
Calculus: Early Transcendentals, Metric Edition

For the particle described in Exercise 7 , sketch a graph of the acceleration function. When is the particle speeding up? When is it slowing down? When is it traveling at a constant speed?

Chapter 3: Differentiation Rules
Section 7: Rates of Change in the Natural and Social Sciences
Sydney Bement
0:00
Calculus: Early Transcendentals, Metric Edition

The height (in meters) of a projectile shot vertically upward from a point $2 \mathrm{~m}$ above ground level with an initial velocity of $24.5 \mathrm{~m} / \mathrm{s}$ is $h=2+24.5 t-4.9 t^{2}$ after $t$ seconds.
(a) Find the velocity after $2 \mathrm{~s}$ and after $4 \mathrm{~s}$.
(b) When does the projectile reach its maximum height?
(c) What is the maximum height?
(d) When does it hit the ground?
(e) With what velocity does it hit the ground?

Chapter 3: Differentiation Rules
Section 7: Rates of Change in the Natural and Social Sciences
Sydney Bement
1 2 3

Sydney's Quick Ask Videos

04:08
Calculus 1 / AB

A cannonball is shot into the air such that its height h, in meters, after time t, in seconds, can be modeled by the function h(t) = -9.8t^2 + 78.4t + 1.5.

3a. Determine the average rate of change in height of the ball on the interval [1,3].
Estimate the instantaneous rate of change in height of the ball at 2 seconds.
Find the following limit: lim(x→4) (x - 4) / √(-2).
Find the equation of the tangent line at point (-2,-3) on the curve f(x) = x^2 + 3x - 1.

Sydney Bement
05:27
Precalculus

In Exercises 35 through 42, the slope f'(x) at each point (x, y) on a curve y = f(x) is given along with a particular point (a, b) on the curve. Use this information to find f(x).
35. f'(x) = 4x + 1; (1, 2)
36. f'(x) = 3 - 2x; (0, -1)
37. f'(x) = -x(x + 1); (-1, 5)
38. f'(x) = 3x^2 + 6x - 2; (0, 6)
39. f'(x) = x^3 - 2/x^2 + 2; (1, 3)
40. f'(x) = x^-1/2 + x; (1, 2)
41. f'(x) = e^-x + x^2; (0, 4)
42. f'(x) = 3/x - 4; (1, 0)

Sydney Bement
09:24
Prealgebra

13. Consider the permutations ̑ = (1 5 3 2)(4 6) and ̑ = (2 4 6 5)(1 3) of {1, 2, 3, 4, 5, 6} expressed in cycle notation. Which one of the following is a correct expression for a permutation ̑ with the property ̑ = ̑⁻¹̑̑ where we compose from left to right? (a) ̑ = (1 4 5 2)(3 6) (b) ̑ = (1 2 4 5)(3 6) (c) ̑ = (1 4 6 2 3) (d) ̑ = (1 6 3 4)(2 5) (e) ̑ = (1 4 3 5 6) 14. Consider the permutations ̑ = (5 2 1 4 3), ̑ = (1 3)(2 4 6), ̑ = (1 2 4)(3 5 6) of {1, 2, 3, 4, 5, 6} expressed in cycle notation. Which one of the following is correct? (a) ̑ and ̑ are odd, and ̑ is even. (b) ̑ and ̑ are even, and ̑ is odd. (c) ̑ and ̑ are even, and ̑ is odd. (d) ̑ and ̑ are odd, and ̑ is even. (e) ̑ and ̑ are even, and ̑ is odd.

Sydney Bement
02:38
Calculus 1 / AB

Use the figures below to evaluate the indicated derivative, or state that it does not exist. If the derivative does not exist, enter dne in the answer blank. The graph to the left (in black) gives f(x), while the graph to the right gives g(x) (which is constant for values of x greater than 10).

d/dx f(g(x))|_{x=5} =
(If the derivative does not exist, enter dne.)

Sydney Bement
06:41
Prealgebra

Consider the function f(x) = ∑x and the point (4,2) on the graph of f. Find the equation of the secant line passing through (4,2) and (5, f(5)).

Complete the table and use the result to estimate the limit: lim(x→3) (x - 3) / (x" - 16x + 39)

x | 2.9 | 2.99 | 2.999 | 3.001 | 3.01 | 3.1
f(x) | | | | | |

Sydney Bement
01:17
Calculus 1 / AB

Given a function f. If f'(3) = 0 and f''(3) = -8, then which of the following must be true?
a) There is a local maximum at x = 3
b) There is a local minimum at x = 3
c) There is an inflection point at x = 3
d) There is an x-intercept at x = 3

Sydney Bement
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