
Math
We are asked to find the area of the region bounded by `f(x)=x^2+4x` and `y=0` . We can factor the quadratic to y=x(x4); the xintercepts are 0 and 4. The equivalent question then is to find the...

Math
An annuity is very different than a mutual fund; although, there is an intersection between the two. A mutual fund, to define that first, is an investment pool in which multiple individuals,...

Math
To answer your question in short: yes and yes. To answer your question in long . . . Philosophers have been arguing for literally millennia about whether or not mathematics (and by extension number...

Math
For this first problem, for the first part, you would take the derivative of the given equation s = 7t + 4t^2, because v = ds/dt. So, this would give you. . .v = 7+8tSo, after 3 seconds, the...

Math
Problem #1. Find the points on the curve `y = 2x^3+3x^212x+5` where the tangent line is horizontal. Solution: Take the derivative of the function. `y'=6x^2+6x12` A horizontal line has a slope of...

Math
There are a number of problems here; some solutions, not in order, are as follows: (5),(9) You are asked to find the derivative using the definition. Typically that means using the limit...

Math
Inscribed angles are angles inside circles where the vertex is "on the circle", as in the attachment, the angle in red. The green angle is called a central angle.As for solving them, that would...

Math
Hello! 1. Let us start from the first question, as it is the most straightforward. (a) As we see, when x approaches positive infinity, f(x) approaches 2. (b) As x approaches negative...

Math
The ton is a unit of measurement for weights. According to the Encyclopedia Britannica the word “ton” originates from the word “tun” which refers to big wine casks. Initially, the word...

Math
When simplifying a square root, we need to try to write the number as a product of a perfect square (e.g. 4, 9, 16, 25, 36 etc.) and some other number. In this case, `27` can be written as `9cdot3`...

Math
An angle is a geometric figure constructed of two rays with the same endpoint.An easy way to think of it would be the sun, and how the sun has "sunrays." All of those sunrays, if you were to draw...

Math
Hello! I suppose that the variable of integration is `x.` Because the limits of integration are not given, I suppose we are speaking about the indefinite integral, which is also called the...

Math
Hello! Unfortunately, your question contains an unknown function `f,` and it is present only at the left part of the equation with the value 4/5 as an argument. We can find this number `f(4/5),`...

Math
I assume you mean d/dx.With this being a quotient, we would use the quotient rule. With that, the top is always the hardest.In general, if we are given f(x)/g(x), the quotient rule states:d/dx of...

Math
What is a polygon? A lost parrot. Seriously, there is not an agreed definition of a polygon, the primary difference being whether the interior is included or not. Polygon translates as many...

Math
Pi is a letter of the Greek alphabet: `pi` . In mathematics, it universally denotes a number which is defined as the ratio of the circumference of a circle to its diameter. This number is the same...

Math
Different people will find different topics "interesting," but here are some ideas: (1) Biographies: There are a large number of interesting people who have contributed to mathematics. There are...

Math
Hello! To factor a polynomial it is useful to find its roots. If a polynomial `P(x)` has a root `a,` then it may be expressed as `P(x) = (x  a)Q(x),` where `Q(x)` is a polynomial of the degree one...

Math
A fraction is made up of two parts, the numerator and the denominator. The numerator is the upper number of the fraction, while the denominator is its lower part. For example, in `\frac{2}{5}` ` `...

Math
In research there are several methods used for data collection, which fall into two categories: primary data and secondary data. The difference between both are explained below: Primary data:...

Math
The sequence you've posted seems to be following a pattern based on ones and threes in sets of two. With each new set, the amount of times the number is increased by one increases, while the amount...

Math
Hello! Consider the pairwise differences between the terms of this sequence. They are 16  15 = 1, 19  16 = 3, 20  19 =1, 23  20 = 3. So we can suppose that the next difference will be 1, then...

Math
By using the fact that a circle also has 360 degrees. You can measure the angles around the center. Each one will be approximately 51.43 degrees.

Math
Let us say the coordinates of the point closest to (0,3) are (a,b). The distance (L) between these two points can be given as; `L = sqrt((0a)^2+(3b)^2)` By getting `L^2` `L^2 = a^2+(3+b)^2`...

Math
Hello! Probably you mean "tangent of (x plus `pi / 2`)", not "(tangent of x) plus `pi / 2`", i.e. `tan(x + pi / 2) =  cot (pi / 2).` It is correct. The simplest way to verify it is to recall that...

Math
We have to expand the formula ` ev=log_2(\frac{f^2}{t})` using properties of logarithms. We know that, ` log(\frac{a}{b})=log(a)log(b) ` and, `log(a^2)=2log(a) ` Using the above we can write, `...

Math
We are given a rectangular yard with area of 24 square meters, and we are asked to find the possible perimeters. Since the yard is a rectangle (a parallelogram with right angles), we can describe...

Math
Hello! We know the formula `sin(u + v) = sin(u)cos(v) + cos(u)sin(v),` but it is not enough because we a given only `sin(u)` and `cos(v),` but neither `cos(u)` nor `sin(v).` But we can find them...

Math
We are asked to find `lim_(x>infty) ((3x)/(e^(2x)+7x^2))^(1/x)` : First, use the fact that the limit of a product is the product of limits to get: `=lim_(x>infty)3^(1/x) *...

Math
Hello! It is a relatively simple task. The only formula we need to solve this is the formula of cosine of a sum of two angles: `cos( u + v ) = cos( u ) * cos( v )  sin( u )*sin( v ).` This formula...

Math
How to solve 3xy=6: To solve an equation is to find all of the values for the variables that make the equality a true statement. A linear equation in one variable will have either no solutions,...

Math
Table 4 in this study presents the results of an ANOVA analysis looking at only females. This table compares the differences in victimization scores and negative outcomes (including poor academic...

Math
Hello! Denote the elevation angle as `alpha(t)` (in radians, `t` is in hours). Denote the known speed as `V` and the (unknown) horizontal distance between the airplane and the kangaroo that...

Math
The definition of derivative of a function `f(x) ` is `f'(x) = lim_(h >0) (f(x+h)  f(x))/h` (the limit of the quotient of the difference between f(x + h) and f(x) and h, as h approaches...

Math
`2x4(3x+6)=6(2x+1)4` Remove bracket by multiplying; `2x4xx3x24 = 6xx2x64` `2x12x24 = 12x64` `10x24 = 12x10` Take all x parts to one side, and put the numbers on the other side....

Math
This is not a very clear question, but it seems that you need to show that the complex solutions of the equation of the form `x^3 + a^3 = 0` or `x^3  a^3 = 0` will contain a radical of 3...

Math
We are asked to find the derivative of cot(log(x)): (1) Assuming that log(x) is the common logarithm (logarithm base 10) of x: Note that the derivative of cot(u) (where u is a differentiable...

Math
We are asked to find an antiderivative of `(2x+5)^6 ` : This is essentially equivalent to evaluating the indefinite integral `int (2x+5)^6 ` Now `int u^n du=1/(n+1) u^(n+1) ` with u a...

Math
Given that a funnel is in the shape of a cone with radius = r= 5 inch height = h= 20 inch We know that the volume of the cone is given by the formula: `Volume=V=\frac{1}{3}\pi r^2 h` i.e....

Math
Hello! We can find the rate at which sand is leaking in volume per time. It is natural to measure time in minutes and volume in cubical inches for this problem. Denote the radius of the cone (and...

Math
There is a story behind this problem. It is said that a famous mathematician by the name of Carl Gauss was punished for poor behavior in class, so he was told to stay after school. As punishment,...

Math
Some of the early computers that used decimal system (either exclusively or in combination with binary) include ENIAC, UNIVAC I and II, and several IBM computers. Some processors today use binary...

Math
The question is a little vague. Ten huskies are to be selected to pull a dogsled. The number of ways in which this can be done is dependent on the total number of huskies from which these ten are...

Math
Hello! The most straightforward way is to use Cramer's Rule. The main determinant of this system is `D = [a,b],[b,a] = a^2b^2 = (ab)(a+b).` If it is nonzero, the system has the only solution....

Math
Hello! I suppose the equation is `1.25+5.25*k` . It may also be `1.25*k+5.25.` a. Then we see that the number `1.25` (the free term) is in dollars (or other currency) and it represents the fixed...

Math
The bell curve essentially "sums up" all the possibilities that can occur given a particular experiment. Especially, in many cases, as the number of times the experiment is repeated, and all...

Math
a) Denote the number of hours it takes Ashlee to repair a DVD by h. Then, the amount of money M Ashlee would charge to repair a DVD, in dollars would be M = 25 + 20h ($25 to inspect and $20 per...

Math
(a) We have to solve the initial value problem given by: `x'=10y` `y'=10x` with initial conditions: `x(0)=3` `y(0)=4` Now we can write the above problem in matrix form as shown:...

Math
According to the variations of parameters method, the formula for the particular solution of the equation of the form `y''+q(x)y' + r(x) y = g(x)` is `Y_P = y_1 int y_2(x)g(x)/(W(y_1, y_2))...

Math
The divergence theorem states that `int_S (F*hatn) dS = int_V (grad*F) dV,` where `S` is a closed surface, `V` is the volume inside it and `F` is a good enough vector field defined inside `S` and...