
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...

Math
The easiest way I have for knowing the difference between linear and nonlinear is the exponent value on the variable x. It is important to understand the root word in linear. It is LINE. A...

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)...

Math
Primary and secondary data fall within the scope of statistics and can be used as part of a research method. The collected data may assist a company in measuring, assessing and discussing the...

Math
When you were 4 years old, your sister was half your age. Half of 4 is 2, your sister was 2 years old when you were 4 years old or she is 2 years younger to you. Your present age is 100, as your...

Math
Let x and y be the two numbersWe want xy = 8 and xy=P as small as possibleAs you wrote, x=8+yOnce you have that, you can substitute into the other equation, and getP=(y+8)y = y^2 + 8yJust as you...

Math
A square and a rectangle each have 4 sides and 4 angles. The only difference between them is that a square is a rectangle with equal sides. Both have 4 90 degree (right) angles. A triangle has 3...

Math
A linear function is one that has the form f(x) = ax + b. Here for each value of x there is only one corresponding value of f(x) and every value of f(x) is due to only one particular value of x. In...

Math
Without people who can do math, we would not have many of the things we take for granted. We wouldn't have cars, highways, or plane travelmath is required to design and build such things. Tall...

Math
We have to find the chain rule to find the derivative of f(x) = e^3x. The chain rule for the function f(x) = g(h(x)) gives f'(x) = g'(h(x))*h'(x). Here f(x) = e^3x f'(x) = e^3x * (3x)' => e^3x *...

Math
Use a linear function to approximate `125.1^(1/3)` : (1) Let `f(x)=x^(1/3)` (2) We will find a linear approximation to f(x) at x=125. (3) `f(125)=5` (4) `f'(x)=(1/3)x^((2)/3)` . This is the...

Math
There are two different ways to graph that equation. 1. You can use the slope and yintercept of the line to graph it. The slope is the number that is in front of x (in your example 5 would be the...

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...

Math
Reallife limits are used any time you have some type of realworld application approach a steadystate solution. As an example, we could have a chemical reaction in a beaker start with two...

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...

Math
A very simple example of combinations would be in the number of pizzas one could create given a certain number of criteria. In other word, given that a pizza place has: 3 types of crust thin,...

Math
1. Construction of angle 105 degree using compass:(Refer attached image) Steps: Draw a line AB and mark point O on it where angle is to be drawn. With O as center draw an arc (semicircle) which...

Math
An alternate approach to proving this identity involves using the "unit circle" (radius = 1). Since the radius is also the hypotenuse of the right triangle formed by the angle...

Math
In arithmetic the least common multiple (LCM) of two numbers a and b is the smallest positive integer that is a multiple of both a and b. So, the multiples of 3 are : 3, 6, 9, 12, ...The multiples...

Math
This question is a little vague. It's difficult to simply "verify" a given linear approximation without some parameters. Let's assume that it means that at `x = 0`, the logarithm and the...

Math
TThe ratio of boys to girls is 12 to 16, 12:16 or 12/16 (all different ways this can be written). The fraction form 12/16 can be reduced by dividing by the greatest common factor. Both 12 and 16...

Math
A fraction is really a division problem. Onethird means ONE divided into THREE parts. So, to find the decimal equivalent, do the division. 1 divided by 3 = 0.33333333 etc. In a case like this,...

Math
How do you find the vertex of the graph of a quadratic function written in intercept form? Intercept form is also known as factored form: y=(xp)(xq) where p,q are the xintercepts. One way to...

Math
First we need to calculate the area of the floor Since it is a rectangulal floor, then the area to be covered is L*I= 9*3=27 m ^2 =270,000 cm^2 Now we need to cover the area with (n)...

Math
Let the length be "L" and the width "W" We know that the ration is 5:3 Then, L/W = 5/3 Cross multiply: ==> 3L = 5W ==> L = (5/3)*W .......(1) Also, it is given that the perimeter P is 32:...

Math
`sqrt(3)sinx+cosx=1` `sqrt(3)sinx=1cosx` `3sin^2x=12cosx+cos^2x`  square both sides `3(1cos^2x)=12cosx+cos^2x`  Pythagorean relationship `4cos^2x2cosx2=0`  clear parantheses and...

Math
`int "tan"^n x dx =` `int ("tan" ^(n2) x) ("tan" ^2 x) dx =` `int ("tan" ^(n2) x) ("sec"^2 x  1)dx = ` `int ("tan" ^(n2) x ) "sec"^2 x dx  int "tan" ^(n2) x dx=` To do the first integral, use...

Math
We are given the equation x^25xy+3y^2=7 and we have to find dy/dx. Differentiating each term of x^2  5xy + 3y^2 = 7 with respect to x, we get 2x  5x(dy/dx) 5y + 6y(dy/dx) = 0 taking the terms...

Math
Let, EQ.1 y = cos x EQ.2 y = sin x Solve the intersection points between the two equations. `y = y` `sin x = cos x`...

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...

Math
Since the line is perpendicular to the xaxis, then, the line is vertical. And if the line passes throught the point (2,1), hence the equation is x = 2. Answer: Equation of the line is x=2 .

Math
If a line has no yintercept, that means it never intersects the yaxis, so it must be parallel to the yaxis. This means it is a vertical line, such as `x=3` . This slope of this line is...

Math
We know that the area of the circle is given as the following function: A = (r^2)*pi where r is the radius. But we know that: C = 2r ( c is the circumference) ==> r = C/2 Now substitute...

Math
The volume of a sphere is linked to its radius by the formula: `V=4/3pir^3` where V is the volume of the sphere and r is the radius. The rate of change of one value with respect to another is found...

Math
Given that the number of boys and girls in a class is as follows: Number of boys = 11 Number of girls = 9 Then we conclude that the total number of students in the class= 20 students. Then, the...

Math
The circle should pass through the three points (7,4),(4,5) and (0,3) Call the center of the circle P. Then PA=PB=PC since all radii of a circle are congruent. PA=PB implies that P lies on the...

Math
You need to expand the binomial using the formula `(ab)^2 = a^2  2ab + b^2` . Hence, substituting x for a and 2 for b yields: `(x  2)^2 = x^2  4x + 4` You may also use distributive...

Math
Evaluate `int (lnx)/x dx` : We ` `` `let `u=lnx` . Then `du=1/xdx` and we have: `intudu=1/2u^2+C` . Substituting for `u` we get `1/2(lnx)^2+C` . Thus the integral evaluates as `1/2(ln(x))^2+C`

Math
Given `125.8<=mu<=152.6` : The confidence interval for the mean is of the form: `bar(x)"error"<=mu<=bar(x)+"error"` where `bar(x)` is the point estimate for the mean. Here we have...

Math
Given `f(x)=1/3 x^3+1/2x^2+10` `f'(x)=x^2+x` Newtons method begins with a "guess", `x_1` , then proceeds towards the actual value using `x_n=x_(n1)(f(x_n))/(f'(x_n))` `x_1=3`...

Math
To round a number to the nearest digit we must look at the digit to the right of the number we are rounding to. In this case, since we are rounding to the nearest ones place, or units, we will look...

Math
This equation is in the slopeintercept form y=mx+b where m is the slope and b is the y intercept. In the linear equation y=5x1, the slope is 5 and the y intercept is 1. Here is the graph:

Math
The square root of 169 is 13. This is so because 13 times 13 gives 169  the definition of a square root of a number k is the number such that when you multiply it by itself you get k. Note that...

Math
The equivalent resistance of two resistances connected in parallel is given by `1/R = 1/R1 + 1/R2` `R = (R1*R2)/(R1 + R2)` `(dR)/(dt) = ((R1*(dR2)/dt + R2*(dR1)/dt)(R1 + R2)  (R1*R2*((dR1)/dt +...

Math
Translate the written/verbal expression "twice a number x" into mathematical/symbolic notation: Twice a quantity usually indicates to take two of the things in question; usually this indicates to...

Math
Given the equation: x^3+ x^2 + x +1 = 0 We need to find x values that satisfies the equation. First we will simplify by factoring. We will factor x^2 from the first two terms. ==> x^2 ( x+1) +...

Math
First, rewrite each equation in slopeintercept form. 2x + y  3 = 0 y = 2x + 3 x  y  6 = 0 y = x  6 2x + y  5 = 0 y = 2x + 5 Now graph the three equations...

Math
Another way to answer this question is that you know any linear function can always be written y = mx + b, where m is the slope. Find m first, (4  3)/(2  1)=1/3. Then plug in one point to...

Math
If 3/5 is 15, then 1/5 must be 5 (15/3). So 5/5 of that number would be 5 x 5 = 25. So 25 is your answer.

Math
You need to remember that the vertices of the square lie on the circumference of circle and the center of circle is also the midpoint of diagonals of the square. Notice that diagonals of the...