
Math
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.

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
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
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...

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
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
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
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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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...

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
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
A "mixed number," in math terms, is a whole number with a fraction attached to it. What you have posted in your question is essentially an "improper fraction," a situation that occurs when the top...

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
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)' =...

Math
`y=1+sec(x),y=3` Refer the image. From the graph, the curves intersects at x=pi/3 and x=pi/3. Using washer method, A cross section is a washer of cross sectional area A(x) with, Inner...

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
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
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
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...

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
We are given that the mean is 80 and the standard deviation is 6. We want to determine the score that is the cut score at 95%. To find the `z` score that has 5% above and 95% below, we consult the...

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...

Math
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
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. 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
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 curve y=(x1)/(x+1). At any point on the curve, the slope of the tangent to the curve is equal to the value of y' at that point. As equations of the tangents have to be determined that are...

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
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
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...

Math
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...

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...

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
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
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 `a(t)` and `b(t)` be functions denoting length and width of the rectangle at time `t.` Since area of rectangle is product of length and width we have `A(t)=a(t)b(t)` To get the the rate of...

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
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...

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
A ball is thrown into the air with an initial velocity of 40 ft/s vertically upwards. t seconds after it has been thrown up, the height of the ball is given by the function `f(t) = 40t  16t^2` ....

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
Let f(x) be the cubic function. Then, we will write the function into the standard format: f(x) = ax^3 + bx^2 + cx + d Now to dteremine a,b,c,and d values, we will subsitute the points given. The...

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
We will use one of the formulas for arc length: `int_a^b sqrt(1+(dx/dy)^2) dy` `x=(1/8)y^4+(1/4)y^(2)` `dx/dy = (1/2)y^3(1/2)y^(3)` `(dx/dy)^2 = (1/4)y^6  (1/2) + (1/4)y^(6)` `1+(dx/dy)^2...

Math
I suggest you to transform the difference of like trigonometric functions into a product such that: sin alpha  sin beta = 2 cos ((alpha+beta)/2)*(sin(alphabeta)/2) sin 4x  sin2x = 2 cos...

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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`int e^(3x) dx ` `==gt u= 3x ==gt du = 3 dx ` `==gt int e^(3x) dx = int e^u (du)/3 ` `==gt int e^(3x) dx = (1/3) int e^u du = (1/3) e^u + C ` `==gt int e^(3x) dx = (1/3) e^(3x) + C` ``

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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...