TutorMe homepage

SIGN IN

Start Free Trial

Etan M.

Student at Purdue University

Tutor Satisfaction Guarantee

Pre-Calculus

TutorMe

Question:

A specific function has the following equation: $$ \frac{x+3}{x^2 - 16} $$ Of which, $$ x $$-values does the function output no solution?

Etan M.

Answer:

An equation outputs no solution whenever there is a zero (0) in the denominator. So, in order to find out which $$ x $$-values show no solution, we must find out when the denominator equals zero (0). This can be displayed as: $$x^2$$- 16 = 0 Now, simplify the expression: $$x^2$$ = 16 To isolate $$x$$, we must take the square root of both sides: $$x$$ = 4 But since $$(-4)^2$$ also equals 16, $$x$$ also equals -4, so: The function outputs no solution when $$x$$ = 4 and $$x$$ = -4.

Trigonometry

TutorMe

Question:

One of the smaller sides of a right triangle has a measurement of 5 feet, and the angle that it creates with the longest side is 30 degrees. What is the length of the longest side?

Etan M.

Answer:

We can solve this problem using the basic trigonometric identities. But instead of using any random identity, we must find out which one to use. The sine (sin) of an angle is equal to the side that doesn't touch the angle (opposite) divided by the longest side of the triangle (hypotenuse). We are dealing with the side that DOES touch the angle, so this trigonometric identity won't be useful. The tangent (tan) of an angle is equal to the side that doesn't touch the angle (opposite) divided by the side that touches the angle (adjacent). Since we are trying to solve for the longest side, this trigonometric identity isn't useful either. The cosine (cos) of an angle is equal to the side that touches the angle (adjacent) divided by the longest side of the triangle (hypotenuse). Because we are given the adjacent side length and the angle, we can find the length of the longest side (hypotenuse). The equation for that is represented as: cos(angle) = adjacent / hypotenuse The angle we are given is 30 degrees, and the length of the side touching it (adjacent) is 5 feet. Plug those numbers into the equation: cos(30) = 5 / hypotenuse Now simplify the equation: cos(30) = 5 / hypotenuse cos(30) * hypotenuse = 5 hypotenuse = 5 / cos(30) When using a calculator, make sure the mode is in degrees, or else your number will be completely different. hypotenuse = 5 / cos(30) hypotenuse = 5 / 0.866 hypotenuse ≈ 5.774 The length of the longest side is around 5.774 feet.

Algebra

TutorMe

Question:

For Thanksgiving, Emily, Joseph, and Sofia all receive different amounts of money based on their age. Joseph was given $4 less than one-half of what Sofia got, and Emily received $6 more than twice of what Joseph got. If Joseph was given $20, how much did Emily and Sofia receive?

Etan M.

Answer:

We already know that Joseph has $20, so we must find the relationship between Joseph and the rest of the kids. First, give each of the kids a specific variable. Emily will be represented by E, Joseph by J, and Sofia by S. We know that Joseph was given $4 less than one-half of what Sofia got. Using our variables, we can say that: J = (1/2)S - 4 or 20 = (1/2)S - 4 <-- Because we know that Joseph was given $20, we substituted J with 20 To solve for S or the amount of money Sofia received, we must isolate S from the rest of the equation: 20 = (1/2)S - 4 24 = (1/2)S 48 = S Sofia was given $48. We also know that Emily received $6 more than twice of what Joseph got. Using our variables, we can say that: E = (2)J + 6 or E = (2)(20) + 6 <-- Because we know that Joseph was given $20, we substituted J with 20 To solve for E or the amount of money Emily received, all you need to do is multiply and add the numbers together: E = (2)(20) + 6 E = 40 + 6 E = 46 Emily was given $46.

Send a message explaining your

needs and Etan will reply soon.

needs and Etan will reply soon.

Contact Etan

Ready now? Request a lesson.

Start Session

FAQs

What is a lesson?

A lesson is virtual lesson space on our platform where you and a tutor can communicate.
You'll have the option to communicate using video/audio as well as text chat.
You can also upload documents, edit papers in real time and use our cutting-edge virtual whiteboard.

How do I begin a lesson?

If the tutor is currently online, you can click the "Start Session" button above.
If they are offline, you can always send them a message to schedule a lesson.

Who are TutorMe tutors?

Many of our tutors are current college students or recent graduates of top-tier universities
like MIT, Harvard and USC.
TutorMe has thousands of top-quality tutors available to work with you.

Made in California

© 2019 TutorMe.com, Inc.