
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...

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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...

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Your sister is 2 years younger than you as when you are 4 she is 2(half your age); therefore when you are 100 your sister is 98 years old.

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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)...

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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...

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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...

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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...

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Another method is knowing to take the derivative of f(x) = sin^2(x) + cos^2(x) f '(x) = 2 sin(x) cos(x) + 2 cos(x) (sin(x)) = 2 sin(x) cos(x)  2 cos(x) sin(x) = 0 Since the derivative is zero...

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Hey Shelly, All of these answers are great, but unless you get a better conceptual understanding of the basic parts of a slope intercept equation you will continue to struggle with these equations...

Math
Math is necessary for even the most basic of life functions. Whether you're buying groceries, determining a budget for yourself, calculating interest on investments, or carrying out a whole myriad...

Math
e^2x3e^x +2 =0 Let us assume that e^x =y. Now substitute: ==> y^2 3y +2 =0 Factorize:\ (y2)(y1)=0 y1= 2 ==> y1=e^x1= 2 ==> x1=ln2 y2=1 ==> y2=e^x2= 1 ==> x2=0 The solution for...

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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...

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The average of the four numbers is 8. This gives the sum of all the four numbers as 8*4 = 32. As the sum of three of the numbers is 22, the fourth number is 32  22 = 10. The correct answer is...

Math
Give the formula for the following sequence: 4, 12, 36, ... Since 4 x 3 = 12, and 12 x 3 = 36, you can determine that this is a geometric sequence in which the common ratio is 3. Geometric...

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Empirical probability of an event is estimated by observing results of actual experiments. For example, if you wanted to know the probability of the number 6 turning up when a fair die is rolled...

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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
tan75: method (1): tan75 = sin75/cos75 = sin(45+30)/cos(45+30) = (sin45cos30+sin30cos45)/(cos45cos30  sin45sin30) = [sqrt2/2*sqrt3/2 +...

Math
f(x) = 1/(x^2  4) First wewill implify using partial fractions: ==> 1/(x^2 4) = 1/(x2)(x+2) ==> A(x2) + B(x+2) = 1/(x2)(x+2) ==> A(x+2) + B(x2) = 1 ==> Ax + 2A + Bx  2B = 1...

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This should be soled as integrals by parts. In Integrals by parts it says if U and V are fuctions then, `intUdv = UVintVdu` So let us take U= x and V=e^(2x) Then by differentiation with respect to...

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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:...

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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...

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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`...

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The equation that is written as y = mx + c represents a straight line graph. At any place on the horizontal (or "x") axis the line passes through a particular place on the other (vertical, or "y")...

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We need to prove that: sec^2 x +csec^2 x = (sec^2 x)(csec^2 x) Let us start with the left side: We know that secx= 1/cosx and csec x = 1/sinx ==> sec^2 x+ cosec^2 x= 1/cos^2 x + 1/sin^2 x =...

Math
2cosx + 1 = 0 First we will move 1 to the right side by subtracting 1 from both sides: ==> 2cosx + 1  1 = 01 ==> 2cosx = 1 ==> now we will divide by 2: ==> cosx = 1/2 Now we know...

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...

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we need to show that `inttan^n(x)dx=(tan^(n1)(x))/(n1)inttan^(n2)(x)dx` We know that `tan^2(x)=sec^2(x)1` hence we can rewrite our integral in the following manner:...

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
Melody has two coins that equal 15 cents. What are the two coins if one of them is not a nickel? This really is a word problem. That is to say, it is a trick problem. One of the coins is not a...

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
To find 10% of a number, just move the decimal one place to the left. 10% of 123 is 12.3 or, multiply the number by the decimal equivalent. 10% is also written as .10 500 x .10 = 50. 20% is also...

Math
dy/dx = x  yUse substitution:v = x  yDifferentiate with respect to xdv/dx = 1  dy/dxdy/dx = 1  dv/dxNow we use above substitutions in differential equationsdy/dx = x  y1  dv/dx = vdv/dx = 1 ...

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...

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You should use factorial formula for combinations such that: `C_n^k = (n!)/(k!(nk)!)` Reasoning by analogy yields: `C_4^2 = (4!)/(2!(42)!) => C_4^2 = (4!)/(2!2!)` You may write 4! such that:...

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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...

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Probability of head and 3 on a die is: P( head and 3 ) = p(head )* P(3) We multiply probabilities because we have 2 independent events. We know that p(head) = 1/2 Also p(3) = 1/6 Then P( head and...

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...

Math
Given f(x) = e^3x We need to find the first derivative f'(x) using the chain rule. We will assume that u= 3x ==> u' = 3 ==> f(x) = e^u ==> Now we will differentiate: ==> f(x) = (e^u)' =...

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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...

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f(x)=x^3+2 To find the inverse function f(x)^1 , we will assume" y=x^3+2 y2= x^3 ==> x= (y2)^1/3 ==> f(x)1= (x2)^1/3 https://www.youtube.com/watch?v=Ec5YYVxyq44

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x^3+2xx2=0 Substitute with 1: 1+212=0 Then 1 is one of the function's roots. Then (x1) is one of the factors. Now divide the function by (x1). x^3+2xx2=0 (x1)(x^2+3x+2)=0 Factorize:...

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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...

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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...

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Think about what you know. First, you are dealing with fractions, which means that each part has to be equal. Second, you know that if you add 3 of those equal parts together you get 15. The next...

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
The integral `int sin^6 x dx` has to be determined. `int sin^6 x dx` => `int (sin^2 x)^3 dx` => `int (1  cos^2x)^3 dx` => `int cos^6 x + 3*cos^4x  3*cos^2 x + 1 dx` Now use the...

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The volume of a cube with sides of length L is given by L^3. We have the volume of the cube as 343. L^3 = 343 => L^3 = 7^3 => L = 7 The surface area of a cube of length L is 6*L^2. As L = 7,...

Math
The first 4 terms of the series are 1, 3, 9 and 27. It is seen that `(3/1)= (9/3) = (27/9) = 3` . The ratio between consecutive terms is the same and equal to 3. This is the characteristic of a...

Math
I think the previous posts discuss very well the idea of basic arithmetic in daily life. I would also suggest that one of the critical uses of math on a daily basis is that it gives us a way to...

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This is a minimization problem hence, you need to find a function that models the distance between a point `A(x,y)` that lies on the given curve and the fixed point `(3,0).` You need to use the...