# Math

Math

The letters R, Q, N, and Z refers to a set of numbers such that: R = real numbers includes all real number [-inf, inf] Q= rational numbers ( numbers written as ratio) N = Natural numbers (all...

Latest answer posted September 7, 2010, 12:47 pm (UTC)

Math

A linear equation has the following form: y = mx + b where m is the slopeb is the y-intercept. You can also perform a vertical line test. If the line touches your graphed function in more than...

Latest answer posted October 7, 2013, 8:13 pm (UTC)

Math

We are traveling at a speed S = 60 m/h The distance we are traveling is D = 50 m We know that: Speed (S) = distance (D)/ Time (T) 60 = 50 / T ==> T = 50/60 = 5/6 hour ==> T = 5/6 * 60 minutes...

Latest answer posted August 3, 2010, 12:41 am (UTC)

Math

Raabe's test is the ratio test for convergence of a series. Consider the limit lim_(n->) |a_(n+1)/a_n| = L Raabe's test says that if L<1 then the series converges. If L>1 then the...

Latest answer posted November 27, 2012, 2:59 pm (UTC)

Math

They're already in increasing order, which is obvious. If you want to "prove" it (in quotes because the fact may be considered so basic as to not need proof), you can always write the numbers with...

Latest answer posted October 24, 2012, 5:48 am (UTC)

Math

We have to find the sum of 1+2+3+. . . +100. Here n=100 We have a formula to calculate the sum of n numbers as: Sum=(n(n+1))/2 So we have:  Sum=(100(100+1))/2=5050  Hence the sum is 5050.

Latest answer posted October 9, 2017, 12:54 am (UTC)

Math

f(x) = 2x g(x) = x + 3 First let us find (fog)(x) (fog)(x) = f(g(x) = f(x+3) = 2(x+3) = 2x + 6 ==> (fog)(x) = 2x + 6 Now let us find (gof)(x): (gof)(x)...

Latest answer posted August 17, 2010, 8:49 am (UTC)

Math

What you have to remember here is the formulas for area and circumference of a circle. The area of a circle is equal to the square of its radius times pi. The circumference of a circle is equal to...

Latest answer posted April 24, 2010, 5:49 am (UTC)

Math

You can make use of equations. For instance, let the number of years you need to grow to become 100 years old be x. Then 4 + x = 100 x = 100 - 4 = 96 When you are 4 years old, your sister is half...

Latest answer posted November 21, 2017, 11:03 am (UTC)

Math

The product of n natural numbers can only be found by multiplying the n numbers. There is no formula for that. If you have tables for the factorials of numbers you could find the value of the...

Latest answer posted April 13, 2011, 3:37 pm (UTC)

Math

log20 = log(2*(10)) I assume you are using the base 10 in your log. According to logarithm laws, we know, log(ab) = loga + logb Therefore, log20 = log2+log10 From table, log20 = 0.3010 +...

Latest answer posted May 16, 2012, 9:38 am (UTC)

Math

A = 1/2h(b1+b2) Multiply both sides by 2 2A = h(b1+b2) Multiply both sides by 1/h 2A/h = b1+b2 Add -b1 to both sides 2A/h + -b1 = b2 Answer: b2 = 2A/h - b1

Latest answer posted November 14, 2011, 5:49 am (UTC)

Math

An exam has a weightage of 30%. The student's score before the exam is 82%. If the student scores 40% in the exam, the score of the student is 0.82*0.7 + 0.4*0.3 = 0.694. Similarly, if the student...

Latest answer posted June 29, 2012, 5:18 pm (UTC)

Math

int x/(x-1)^2 dx  u= x-1 ==gt x= u+1 du = dx ==gt int x/(x-1)^2 dx = int (u+1)/u^2 du = int u/u^2 du+ int 1/u^2 du  = int 1/u du + int 1/u^2 du  = ln u - 1/u + C = ln (x-1) - 1/(x-1) + C...

Latest answer posted March 14, 2012, 8:10 am (UTC)

Math

The roll has 6 sides, the probability of rolling a six when the die is rolled once is 1/6 When rolled 4 times, each time has a probability of 1/6. Then the probability is: 1/6 * 1/6 *1/6 *1/6...

Latest answer posted June 25, 2010, 10:03 pm (UTC)

Math

To write sin x in terms of cos x use the relation sin^2x + cos^2x=1 => sin^2x = 1 - cos^2x Taking the square root of both the sides gives two values of sin x sin x = sqrt(1 - cos^2x) and...

Latest answer posted May 15, 2012, 7:13 am (UTC)

Math

The answer to this is 47/8. You can simplify that to 5 7/8. Here is how to get to this answer. First, you can convert 11 3/4 to a simple fraction. You do this by multiplying 11 by 4 and adding...

Latest answer posted May 10, 2010, 11:45 pm (UTC)

Math

1 year consists of 365 days. 1 day has 24 hours, each hour has 60 minutes and each minute has 60 seconds. This gives the number of seconds in an hour as 60*60 = 3600 and the number of seconds in a...

Latest answer posted February 26, 2012, 10:04 pm (UTC)

Math

We have a^2 - b^2 = 8 and ab = 2 Now (a - b)^2 = a^2 + b^2 + 2ab => (a^2 - b^2)^2 = a^4 + b^4 - 2*a^2*b^2 a^4 + b^4 => (a^2 - b^2)^2 + 2*a^2*b^2 => 8^2 + 2* (ab)^2 => 64 + 2*2^2 =>...

Latest answer posted January 11, 2011, 12:09 pm (UTC)

Math

The product of the two positive numbers is 16. Let one of the numbers be X, the other number is 16/X . The sum of the two numbers is S = X + 16/X . The value of S is minimized for X such that...

Latest answer posted March 9, 2013, 4:10 am (UTC)

Math

The answer depends on the margin of how badly you failed your final exam. Here is the equation to calculate your final average, if x=exam grade: .15x + 86 (.85) = Final overall average. So if...

Latest answer posted May 28, 2012, 6:30 pm (UTC)

Math

f(x)=x^3+2 To find the inverse function f(x)^-1 , we will assume" y=x^3+2 y-2= x^3 ==> x= (y-2)^1/3 ==> f(x)-1= (x-2)^1/3

Latest answer posted May 29, 2010, 12:54 am (UTC)

Math

Here are some ways to write the number 100 using only +- or 2 digit numbers.: 1 + 2 + 3 - 4 + 5 + 6 + 78 + 9 = 100 12 + 3 - 4 + 5+ 67 + 8 + 9 = 100 1 +2 + 3 - 4+ 5 + 6 + 78 + 9 = 100

Latest answer posted September 19, 2011, 10:10 pm (UTC)

Math

We have to prove that log_a b = 1/(log_b a) Use the property for changing the base of logarithms: log_a b = (log_c b)/(log_c a) Change the base of log_a b to b log_a b = (log_b b)/(log_b...

Latest answer posted January 6, 2012, 3:37 pm (UTC)

Math

The domain and range of the function f(x) = |x - 2| has to be determined. The domain of a function is all values of x for which the value of f(x) is defined. The range of the function is all values...

Latest answer posted August 26, 2014, 2:26 pm (UTC)

Math

We will find how many numbers contain no ones: There are 9 choices of numbers for the first digit: 0,2,3,4,5,6,7,8,9 Simarly there are 9 choices for the second, third, fourth, fifth,and sixth...

Latest answer posted July 20, 2012, 5:01 am (UTC)

Math

1/3 of 240 = 80 apples 1/4 of 240 = 60 oranges 1/5 of 240 = 48 bananas 80+60+48 = 188 mixed fruits/240 total fruits 240-188 = 52 mangoes/ 240 as a reduced fraction = divide both the numerator...

Latest answer posted May 8, 2009, 8:58 pm (UTC)

Math

The reciprocal of a number is the number's multiplicative inverse: in other words the number that when you multiply by that number you get 1. The reciprocal of -2 is -1/2 since (-2)(-1/2)=1 **...

Latest answer posted March 19, 2012, 10:05 am (UTC)

Math

The answer is a): a > 0 and b > 0 A logarithm is positive when the base is greater than 1 and the argument is greater than 1, and it is also positive when the base is less than 1 and the...

Latest answer posted July 4, 2013, 6:09 pm (UTC)

Math

The perimeter of a rectangle can be written as P=2l+2w where w is the width and l the length. Here P=2l+2w or 20=2l+2w The area of a rectangle is A=lw. We can express the width of the rectangle in...

Latest answer posted March 26, 2015, 7:59 pm (UTC)

Math

According to logarithm; log_ab = (log_kb)/(log_ka) If we consider k = 10 which is log in base 10 then; log_ab = (logb)/(loga) Similarly we can write;...

Latest answer posted July 10, 2013, 11:11 am (UTC)

Math

First, I think we should go over what integers mean. A clear definition of integers will lead to a discussion about opposites, which should reveal how the two are related. Integer is another word...

Latest answer posted September 20, 2020, 5:37 pm (UTC)

Math

The numebers chosen are from 1 to 10. Then possible outcomes are: 1,2,3,4,5,6,7,8,9,10 The probability of chosen a 5 OR and even number = probability of chosen a 5 + probability of chosen an even...

Latest answer posted November 8, 2010, 12:12 pm (UTC)

Math

y = f(x)+5 is just the same shape as y=f(x) except shifted up 5 units since 5 has been added to every y value. So if the first graph has the point (-1, -3), the second graph will have the...

Latest answer posted January 18, 2012, 8:10 am (UTC)

Math

If a line has no y-intercept, that means it never intersects the y-axis, so it must be parallel to the y-axis. This means it is a vertical line, such as x=3 . This slope of this line is...

Latest answer posted September 26, 2012, 12:10 am (UTC)

Math

We have to convert 0.99999..... into a proper fraction. Let 0.99999... = f 10f = 9.9999... 10f - f = 9.99999... - 0.99999 => 9f = 9 => f = 9/9 => f = 1/1 The representation of .9999... as...

Latest answer posted June 2, 2011, 9:30 pm (UTC)

Math

Show that G={1,w,w^2} where w is a cube root of unity is a cyclic group. It suffices to show that the only subgroup H of G that contains w is G itself. Let H<=G,winH . Now the...

Latest answer posted August 3, 2012, 6:58 pm (UTC)

Math

The circumference of a triangle is given by 2*pi*r where r is the radius and the area is pi*r^2. Here circumference = 12*pi = 2*pi*r => r = 6 The area = pi*r^2 = 36*pi The area of the circle is...

Latest answer posted April 13, 2011, 11:02 am (UTC)

Math

Given the logarithm expression : log2 (32) We need to find the value. We will assume that the value of log2 (32) = x Now we will rewrite the equation using the exponent form. ==> log2 (32) = x...

Latest answer posted January 9, 2011, 6:29 am (UTC)

Math

y= 16(0.25)^x The exponential equation represents an exponential decay because the rate of decay is 0.25 which is less than 1. The general form equation is: y(x)= a(1-r)^x such that r is the decay...

Latest answer posted May 23, 2012, 2:05 am (UTC)

Math

The commission of the real estate agent is 6% on the selling price of the house. The commission received is 8880. Let the selling price be S. We have 6% of S equal to 8880 => .06* S = 8880 =>...

Latest answer posted January 11, 2011, 11:13 am (UTC)

Math

See the attached image with the steps. The child pulls the sled at an angle 36 degrees above horizontal. Vertical component F_V = 30sin36 = 17.6N Horizontal component F_H = 30cos36 = 24.3N

Latest answer posted September 30, 2013, 5:07 am (UTC)

Math

Hello! Denote the unknown number as x. Factor the given numbers into primes: 36 = 2^2*3^2, 60 = 2^2*3*5, 6 = 2*3, 900 = 2^2*3^2*5^2. The GCF(36,60)=2^2*3=12, not 6. Therefore to...

Latest answer posted May 31, 2016, 7:44 pm (UTC)

Math

The sum of three consecutive even number is 84. Let the number be 2*n , 2*n + 2 and 2*n + 4. We have 2n + 2n + 2 + 2n + 4 = 84 => 6n + 6 = 84 => 6n = 84 - 6 => 6n = 78 => 2n = 78/3...

Latest answer posted March 24, 2011, 11:51 am (UTC)

Math

The value of a trigonometric function is undefined when the ratio for the function involves division by zero. The function thus has an asymptote at such a point. The trigonometric function y =...

Latest answer posted September 20, 2020, 2:18 pm (UTC)

Math

Find the probability of drawing 3 clubs from a shuffled, standard deck of cards: The probability is the number of possible ways to draw 3 clubs divided by the total number of 3 card draws....

Latest answer posted December 9, 2012, 6:34 pm (UTC)

Math

In statistics, if we have a set of observations expressed in numbers (for example, lengths of trees in meters, weights of animals in kilograms and so on), then the difference between maximum and...

Latest answer posted March 18, 2016, 7:26 pm (UTC)

Math

We have to find the value of 11 3/4 divided by 2. First convert 11 3/4 to an improper fraction 11 3/4 = (11*4 + 3)/4 = 47/4 Divide 47/4 by 2 => 47/8 This can be converted to a mixed number form...

Latest answer posted August 2, 2011, 1:32 am (UTC)

Math

Hello! The formula for an average speed is a distance travelled divided by a time spent, V=d/t. In our problem the average speed V and the distance d are given, and we are looking for the...

Latest answer posted February 25, 2016, 6:48 pm (UTC)

You need to solve for y the inner integral, considering x as constant, such that: int_(x-1)^(x+1) e^(x+y) dy = e^(x+y)|_(x-1)^(x+1) int_(x-1)^(x+1) e^(x+y) dy = e^(x+x+1) - e^(x+x-1)`...