Josie Rutledge

Numerade Educator

Biography

Passionate STEM educator dedicated to making science and math accessible and enjoyable for students at all levels. Let's embark on a journey of discovery and problem-solving together.

Education

Josie has not yet added their education credentials.

Educator Statistics

Numerade tutor for 4 years
146 Students Helped

Topics Covered

The Power of Algebraic Language: Unlocking Mathematical Potential
Mastering Equations and Inequalities: Your Guide to Mathematical Success
Understanding Complex Numbers: A Comprehensive Guide
Mastering Polynomials: Essential Tips and Tricks | [Brand Name]
Rational Functions: Understanding Their Properties and Applications
Functions
Discover the Basics of Trigonometry: Your Introduction to Triangles
Applications of Trigonometric Functions
Graphing Trigonometry Functions
Write Linear Equations
Master Trigonometry with Our Comprehensive Guide

Josie's Textbook Answer Videos

0:00
Algebra and Trigonometry

In physics, it is established that the acceleration due to gravity, $g$ (in meters/sec'), at a height $h$ meters above sea level is given by
$$
g(h)=\frac{3.99 \times 10^{14}}{\left(6.374 \times 10^{6}+h\right)^{2}}
$$
where $6.374 \times 10^{6}$ is the radius of Earth in meters.
(a) What is the acceleration due to gravity at sea level?
(b) The Willis Tower in Chicago, Illinois, is 443 meters tall. What is the acceleration due to gravity at the top of the Willis Tower?
(c) The peak of Mount Everest is 8848 meters above sea level. What is the acceleration due to gravity on the peak of Mount Everest?
(d) Find the horizontal asymptote of $g(h)$
(e) Solve $g(h)=0 .$ How do you interpret your answer?

Chapter 5: Polynomial and Rational Functions
Section 2: Properties of Rational Functions
Josie Rutledge
0:00
Algebra and Trigonometry

The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.
Determine whether the graph of the equation $2 x^{3}-x y^{2}=4$ is symmetric with respect to the $x$ -axis, the $y$ -axis, the origin, or none of these.

Chapter 5: Polynomial and Rational Functions
Section 2: Properties of Rational Functions
Josie Rutledge
0:00
Algebra and Trigonometry

Mollweide's Formula For any triangle, Mollweide's Formula (named after Karl Mollweide, $1774-1825$ ) states that
$$
\frac{a+b}{c}=\frac{\cos \left[\frac{1}{2}(A-B)\right]}{\sin \left(\frac{1}{2} C\right)}
$$

Chapter 9: Applications of Trigonometric Functions
Section 2: The Law of Sines
Josie Rutledge
0:00
Trigonometry

Explain how to use identities from this section to find the exact value of $\sin 7.5^{\circ} .$

Chapter 5: Trigonometric Identities
Section 6: Half-Angle Identities
Josie Rutledge
0:00
Trigonometry

The half-angle identity
$$\tan \frac{A}{2}=\pm \sqrt{\frac{1-\cos A}{1+\cos A}}$$
can be used to find $\tan 22.5^{\circ}=\sqrt{3-2 \sqrt{2}},$ and the half-angle identity
$$\tan \frac{A}{2}=\frac{\sin A}{1+\cos A}$$
can be used to find $\tan 22.5^{\circ}=\sqrt{2}-1 .$ Show that these answers are the same, without using a calculator. (Hint: If $a>0$ and $b>0$ and $a^{2}=b^{2},$ then $a=b$.)

Chapter 5: Trigonometric Identities
Section 6: Half-Angle Identities
Josie Rutledge
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Josie's Quick Ask Videos

02:34
Algebra

In formal writing and communication, the common size of
bond paper are the following:
Foolscap ---- 216 mm by
343 mm
A4 ------------- 210 mm by 297 mm
B4 ------------ 250 mm by
353 mm

A3 ----------- 297 mm by
420 mm
Which paper type is nearest to the Golden Ratio in terms of
width to length ratio?

Josie Rutledge
07:27
Prealgebra

Draw a Venn diagram to represent the relationships among the
categories and answer the questions.
The staff at Tiny Little Cherubs (abbreviated TLC) day-care
center observed the eating habits of their 64 students during
several lunches. They observed that 59 children ate green beans, 56
ate cauliflower, 60 ate broccoli, 55 ate green beans and
cauliflower, 54 ate cauliflower and broccoli, 56 ate green beans
and broccoli, and 53 ate all three. How many children did not eat
any of these three types of vegetables? How many children ate green
beans but not cauliflower? How many children did not eat broccoli?
How many children ate only cauliflower? How many children ate
exactly two of these three vegetables?

Josie Rutledge
03:43
Algebra

A company produces custom greeting cards. The cost C (in dollars) of producing n greeting cards per month can be modeled by the function C = 400 + 1.75n. Find the inverse of the model. What does n=?
Use the inverse to determine the number of greeting cards produced when the company's cost to produce the cards was $1450.00.

Assume that the function f is one-to-one. If f^(-1)(-4) = -8, find f(-8).

Find an equation of the inverse of the following one-to-one function.
f(x) = 2x + 9
f^(-1)(x) =

Find f^(-1)(x) for the function.
f(x) = 8 - x
f^(-1)(x) =

Josie Rutledge
06:11
Precalculus

A hot bowl of soup is served at a dinner party. It starts to cool according to Newton's Law of Cooling so that its temperature at time t is given by
T(t) = 58 + 125e^(-0.25t)
where t is measured in minutes and T is measured in °F.
(a) What is the initial temperature of the soup?
(b) What is the temperature after 10 min?
(c) After how long will the temperature be 100°F?
(d) Sketch the graph of the temperature versus time for 0 ≤ t ≤ 20 minutes.

Josie Rutledge
05:48
Algebra

The profit P, in thousands of dollars, that a manufacturer makes is a function of the number N of items produced in a year, and the formula is as follows: P = -0.2N^2 + 3.6N - 9.

(a) Express using functional notation the profit at a production level of 3 items per year. P(3) Calculate that value.
______ thousand dollars

(b) Determine the two break-even points for this manufacturer—that is, the two production levels at which the profit is zero.
N = ___ (smaller value)
N = ___ (larger value)

(c) Determine the maximum profit if the manufacturer can produce at most 16 in a year. ____ thousand dollars

Josie Rutledge
03:04
Geometry

Here is point A on the line, and point B that is not on it.

Use these straightedge and compass moves to create a line parallel to the given line that goes through point B:

1. Create a line through point A and B, extending in both directions. Label this line AB.
2. Create a circle centered at point A with a radius of AB. This circle intersects with the line in two places. Label the intersection point to the right of A as C.
3. Create a circle centered at point B with a radius of BA. This circle intersects with the line at point A and another point. Label the new intersection point as D.
4. Create a circle centered at point C with a radius of BC. This circle intersects with the circle centered at point B in two places. Label the intersection point to the right of B as E.
5. Using a different colored pencil, create a line through points D and E, extending in both directions.

Josie Rutledge
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