Enable contrast version

Tutor profile: David C.

Inactive
David C.
college and secondary instructor and tutor for decades
Tutor Satisfaction Guarantee

Questions

Subject: Pre-Calculus

TutorMe
Question:

Use the Fundamental Theorem of Algebra to find how many roots are in \[f(x)=x^3-1\] and find the roots.

Inactive
David C.
Answer:

The highest power on the variable, x, is 3, so there are a total of 3 roots, though some may not be real roots. Find the roots by factoring \[x^3-1=0\] This is the difference of two cubes formula, \[a^3-b^3= (a-b)(a^2+ab+b^2)\] where a=x and b=1. Substituting yields \[x^3-1=(x-1)(x^2+x+1)\] So, solve \[(x-1)(x^2+x+1)=0\] The first factor gives \[x-1=0\], or x=1 The second is not factorable over the Real numbers, so use the quadratic formula. For ax^2+bx+c=0 x=(-b\pm \sqrt{}(b^2-4ac)/2a Substituting a=1, b=1, c=1 x=(-1\pm \sqrt{}(1^2-4(1)(1))/2(1) Thus, the two complex roots are (-1+\sqrt{3}i)/2 and (-1-\sqrt{3}i)/2

Subject: Pre-Algebra

TutorMe
Question:

There are 8 classrooms of students in a school, and each class has the same number of students. The Principal assigns a smartphone to every student. Write an expression for the number of smartphones distributed.

Inactive
David C.
Answer:

Lets use "x" as the number of students in each class, since it will be the same in every class. To get the number of smartphones in total, we multiply 8 by the number of students in each class. If the number of students per class were 10, then the number of smartphones in total would be 8 (10). If the number of students per class were instead 12, the number of smartphones would be 8 (12). But, the number of students per class is "x", so the number of smartphones in total is 8x.

Subject: Algebra

TutorMe
Question:

Travis bought 2 gallons of raw milk and 3 pounds of grassed butter, totaling $48.00. If the butter costs $8 per pound, how much does the milk cost?

Inactive
David C.
Answer:

If we let m=the number of gallons of milk, then the cost of all the milk would be the number of gallons bought times the price per gallon, or 2m. If we let b=number of pounds of butter purchased, then the cost of all the butter would be the number of pounds purchased times the cost per pound, or 3b. To find the total cost of the entire purchase, add the total cost of all the milk to the total cost of all the butter, or 2m + 3b. We know this will be $48.00. Therefore, we can make an equation for this problem: 2m + 3b = 48, where m is the cost of the milk per gallon and b is the cost of the butter per pound. Since we know the price of the butter is $8 per pound, substitute the 8 for the "b", giving 2m + 3(8) = 48. Simplifying yields 2m + 24 = 48, which is a one variable equation we can easily solve. Subtract 24 from both sides, yielding 2m + 24 - 24 = 48 - 24. Simplifying both sides, we get 2m = 24. Dividing both sides by 2 yields 2m/2 = 24/2, simplifying to m = 12. So, the cost of the milk per gallon is $12.

Contact tutor

Send a message explaining your
needs and David will reply soon.
Contact David

Request lesson

Ready now? Request a lesson.
Start Lesson

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 Lesson" 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.