Math Help

Archive for March, 2008

Question: Math Homework Help!Ratios and Proportions!?

Im just kinda confused on a few.My class is doing a review for a big test and shes grading this

“Mr.Lowery has 8 3/4 pounds of ground beef that he will use to make hamburgers for a picnic. What is the maximum number of quarter-pound hamburgers he can make?”
1)9
2)17
3)35
4)36

“Huey is reading a book that is 697 pages long. He tells a friend that he is about 3/4 of the way done.
About how many more pages must Huey read before he finishes the book?”
1)150 pages
2)160 pages
3)175 pages
4)250 pages

“What is the ratio of the circumference of a circle to its diameter?”

“The Massachusetts Department of Employment and the Training predicts that
*374,000 new jobs will be created in Massachusetts between 1994 and 2005,and
*about 2 out of 5 of those jobs will require a college education
Based on the information given above, ABOUT how many of the new jobs will require a college education”
1)37,400
2)187,000
3)72,800
4)149,600

please help!10 points!

Answer: 8 3/4 pounds

she wants quarter pounds so that’s 1/4 pound

in one pound fits 4 x 1/4
so in 8 pound fits 8x 4 x 1/4 = 32x 1/4
in 3/4 fits 3x 1/4

32 x 1/4
3 x 1/4
————– +
35 x 1/4
so 35 quarterpounders

697 pages is the entire book; 100% or 4/4
if hes on 3/4 of the book that means you can calculate how far he is by dividing the entire book by 4 and multiply it by 3

so 697/4×3=522.75

so he has read 522.75 out of 697 pages;
697-522.75=174.25 which is approximately 175

the ratio of the circumference of a circle to its diameter

the circumference of a circle is pi x d
so the ratio is pi which is approximately 3.1415

jobs
374000 jobs. 2/5 requires college education.
374000 / 5 x 2 = 149600 jobs that require a college education

Using Ratio and Proportion 1

Question: I Need Math Help!!!!!!!!!!!!!!!!! Radius, Logarithms, Direct Distance, Factoring, Point Of Discontinuity?

I need help with a few questions:

1. Find the radius of the circle x^2 + y^2 + 16x – 24y – 17 = 0.

2. Solve for x to the nearest hundreth: 19^x = 420

3. Find the direct distance from the point (3,4) to the line 10x + 24y – 9 = 0.

4. Which of the following is a factor of the polynomial x^3 – 2x^2 – 13x – 10 ?
(x + 1), (x – 1), (x + 2)

5. The function f(x) = (x^2 – 5x – 14) / (2x^3 + 4x^2) has a point of discontinuity at x = ?

Any explanation would be great.

Answer: 1.
Rewrite as
(x+8)^2+(y-12)^2=15^2
Hence radius is 15.

2.
19^x = 420
x=log(420)/log(19)=2.05 (2dp)

3.
Distance is |10*3+24*4-9|/sqrt(10^2+24^2)=117/26=4.5

4.
x^3-2x^2-13x-10 =
(x+1)(x^2-3x-10) =
(x+1)(x-5)(x+2)
Hence (x+1) and (x+2) are both factors.

5.
f(x) = (x^2 – 5x – 14) / (2x^3 + 4x^2)
= [(x-7)(x+2)]/[2x^2(x+2)]
Point of discontinuity is at x=-2.

Volume of a Cone – YourTeacher.com – Math Help

This section of Math Help online covers Rolle’s Theorem. 

What is Rolle’s Theorem?

Rolle’s Theorem is the elementary result in mathematical analysis from which the Mean Value Theorem follows that if a real function is continuous at and between and differentiable between, two points for which it has the same value, there is some intermediate point at which its derivative is zero. 

Rolle’s theorem is named after the French math analyst, algebraist, and geometer, Michael Rolle (1652-1719). 

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Rolle’s Theorem

Let the function f  be 

• defined and continuous on the closed interval [a,b] and

differentiable in the open interval (a,b).

Also, let 

• f (a) = f (b) = 0.

Then there is at least one number c between a and b where f ‘ (x) = 0. In another word, 

f ‘ (c) = 0