
Math
The term is also spelled "inclinometers" and it is used to measure angels on slant (elevation and depression). They are commonly used in forestry. There are different models of inclinometers...

Math
The man can go straight across a river in 5 minutes when the water flows at 10 m/s. To do this he would have to travel at an angle such that the component of his velocity in the direction opposite...

Math
`2sin(2x)=4cos(x)sin(x)+1` We can write `sin(2x)` as `sin(2x) =2sin(x)cos(x)` `4sin(x)cos(x)4cos(x)+sin(x)1=0` `4cos(x)(sin(x)1)+1(sin(x)1)=0` `(4cos(x)+1)(sin(x)1) = 0` This gives us two...

Math
`y = te^(t^2+1)` Differentiating wrt t. `y' = 1(e^(t^2+1))+t(2t)(e^(t^2+1))` `y' = (12t^2)e^(t^2+1)` For extreme points (maxima, minima and inflection points), `y' = 0` `(12t^2) = 0` `t...

Math
The function `f(t) = te^(t^2) + 1` f'(t) = `(1  2t^2)*e^(t^2)` f'(t) = 0 => `(1  2t^2)*e^(t^2) = 0` `1  2t^2 = 0` => `2*t^2 = 1` => `t^2 = 1/2` =>` t = sqrt (1/2)` and `t =...

Math
The function `y = ln(3x  1)  2*ln x` Using the property of logarithms y = `ln(3x  1)  ln x^2` => `ln((3x  1)/(x^2))` The derivative of y is y' = `(2  3x)/(3x^2  x) ` y' = 0 => `(2...

Math
The container is an upside down cone. The height, `H = 45 cm` The area of the top of cone, `A = pi(15)^2 = 225pi` If the water height at time t is h and diameter is 2r``. The water volume filled...

Math
There are two ways to compute the abundancy number for an integer n; it is the sum of the divisors of n divided by n, or the sum of the reciprocals of the divisors. For example:...

Math
`lim_(xgt+oo)sqrt(x2)/(x^2+5)` If you try to evaluate the limit straight away, you would get `oo/oo` answer which indeterminate. We can avoid this by dividing both numerator and denominator by...

Math
I may need some clarity on the equation you are asking about, so you may correct me if it does not look like this: `xiy=sqrt(aib)/(cid)` . Also, I am not sure what you wish to solve for....

Math
Find a way for students to incorporate something they are interested in. When I was in high school, if a math teacher had let me work in something about baseball statistics I would have been a lot...

Math
hey bro just turn off 2,3,4,5 they are the only things that would affect your whole composition. Even though there are other possibilities just turning off those i mensioned before will end up in...

Math
The problem is being solved for a total of N hand shakes. This can be used to determine the number of people at the reunion for any value of N. Let the total number of people equal X. Any person...

Math
First you need to be careful with the word equivalence. Equivalent sets have the same members, loosely speaking, so the integers and the positive integers are not equivalent. However, the "size" of...

Math
You're correct. You're looking for the characteristic matrix of the transformation. Thankfully, your transformation makes the process somewhat simple. Let's take care of it in vector form: `vecx =...

Math
There are 7 letters in the word ARRANGE. Of these there are two instances of A. two instances of R and one instance each of N, G and E. The number of ways in which these letters can be rearranged...

Math
Johann Bernoulli's postulate is simple: it says that a value does not change if an infinitesimally small value is added to it or subtracted from it. An infinitesimally small value essentially takes...

Math
There are 11 male and 15 female candidates for the 4 member debate team. There is no restriction mentioned for the number of male and female members that can form the team. This gives the number of...

Math
Factoring applies to real life so much,there are a lot of ways, however there is one way i would use factoring in real life. If i am making a party, and i invited 12 of my close friends and i have...

Math
You put the points in L1 they should be arranged counter clockwise. If you put them in clockwise you will get 1*Area. I tested it a couple of times, and it works. Press PRGM goto New and enter...

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...

Math
I think there is an error in your problem the LHS should be +1 not 1 ***RHS=`(csc^2x)(secx1)=1/(sin^2x)(1/(cosx)1)=` `1/(sin^2x)((1cosx)/cosx)=1/(1cos^2x)((1cosx)/cosx)=`...

Math
`(x4)^21=8=>(x4)^2=9=>x4=+3=>` `x4=3=>x=7` or `x4=3=>x=1` `h=50t2t^2` When t=5, we get `h=50*52(5)^2=>` `h=25050=200` Hence the height os 200 meters.

Math
In the triangle CAT, the angle T which is denoted by`/_T` is adjacent to the sides a and c As the side c is opposite to the `/_C` ,we can draw a perpendicular to the side c from `/_C` Then we can...

Math
The math is somewhat different in precalculus. In addition to algebra, it includes a lot of trigonometry. Believe it or not, I don’t think I really understood algebra until I took calculus. So...

Math
a) If you need to solve `(1  cos theta)/(tan theta + sec theta) = 0` , then, you need to substitute `sin theta/cos theta` for `tan theta` and `1/cos theta ` for `sec theta ` such that: `(1  cos...

Math
a) You need to solve the equation `cos^2 2 theta + cos 2 theta = 0` You need to factor out `cos 2 theta` such that: `cos 2theta(cos 2 theta + 1) = 0` `cos 2 theta= 0` => 2 `theta = pi/2` or 2...

Math
a) `cos 2 theta = 0 =gt 2 theta = cos^(1) 0 ` 2 theta = pi/2 or 2 theta = 3pi/2 `theta = pi/4or theta = 3pi/4` `b) tan theta = 1` `theta = tan^(1)(1) + n*pi` `theta = pi/4 + n*pi` Hence, the...

Math
The characteristic equation of a circle is given by, `(xa)^2+(yb)^2=r^2` Where (a,b) is the center and r is the radius. The given equation is, `x^2 + y^2  4x  4y  6 = 0` Let us convert this...

Math
From the given, we notice that the smallest value n can take is 2. So when n=2, we have `11/(2^2)=11/4=3/4` and `(2+1)/[2*2]=3/4` Hence the statement is true for n=2. Now suppose that the...

Math
***Being clear is really important when writing this type of question. I'm unsure if the problem is (5x6)/(4+3)>12, 5x(6/4)+3>12, or (5x6)/4 + 3>12. ***The above solution is correct if...

Math
An important rule while working in Algebra, we do not like decimal approximation in the begining of the problem. It can lead to a large margin of error. Fraction lowest term is what you need to...

Math
Notice that the integrating factor is the coefficient of y such that: `mu` (x) `= e^(int (2/x)dx) = e^(2ln x)` `mu (x) = e^(ln (x^(2)))` `mu (x) = x^(2) =gt mu (x) = 1/x^2` You need to solve...

Math
` `` ``E[S^2] = E[1/n sum_1^n (X_i bar(X))^2]` `= E[1/n{sum_1^n(X_i^2  2X_ibar(X) + bar(X)^2)}]` `= E[1/n sum_1^n X_i^2  2bar(X) sum_1^n(X_i/n) + (nbar(X)^2)/n]` `= E[1/n sum_1^n X_i^2 ...

Math
If you have 24 matches and you want to see how many different triangles you can make with them, you can think of each match as one unit and determine how many triangles can possibly have a...

Math
The distance around a track field (circumference). The distance around a car tire, which shows how far one roll is. The surface area on a pizza.

Math
Let A be the tea that sells 240 pesos per kilo and Let B be the tea which sells 200 pesos per kilo. The amount taken from A is x and amount taken from B is y. Then, Total amount = `150 = x+y`...

Math
Let the amount of the first tea to be mixed is x and the second be y. ==> The cost for the first tea is 240x ==> The cost for the second tea is 200y. The cost for the mixture is 240x+200y =...

Math
Let x be amount invested at 5.5%, and y the total amount invested. y=4,000+x Let's construct the following table Amount 4,000 Pesos x pesos y pesosinvested Interest...

Math
To find the inverse function we set it equal to y and solve for x. `y=2/[x+1]=>x+1=2/y=>x=2/y1=>x=[2y]/y` Hence the inverse function is `h^(1)(x)=[2x]/x` Domain: The new function is...

Math
Given the quadratic equation : kx^2 + kx  3x 3 = 0 ==> kx^2 + (k3) x  3 = 0 Given that the roots are equal. ==> x1= x2= x. We know that: x1+x2= b/a ==> 2x = (3k)/k ==> 2x = 3/k ...

Math
This question is wrong. It should be an equilateral triangle. I will prove this for an equilateral triangle. In an equilateral triangle `A=B=C` and `A+B+C = pi` Therefore, `A=B=C= pi/3`...

Math
To add polunomials, I suggest the vertical method, that means set the two polynomial on top of each other, like we do in regular addtition. The catch: you have to make sure that same degree...

Math
Statement: If a triangle has an obtuse angle, then it is an obtuse triangle. Contrapositive: If a triangle is not an obtuse triangle, then it has no obtuse angle.

Math
`x^2=8y=>y=1/8x^2` Vertex: x=b/2a=>x=0, plug it in the original function, y=0. Hence vertex (0,0) Focus:To find the p, we set 4p=coefecient of the unsquare part (use the given equation...

Math
I am assuming you have indicated` sec(theta) = 2` Therefore, `1/cos(theta) = 2` and `cos(theta) = 1/2` The primary solution for this is, `theta = pi pi/3 = (2pi)/3` To find the solutions in...

Math
`cosec(theta) = 2` we know, `cosec(theta) = 1/sin(theta)` , then, `1/sin(theta) =2` This gives, `sin(theta) = 1/2` `theta = sin^(1)(1/2)` `theta = pi/6` This is the primary solution, to...

Math
1) `10x^2+4x+2 = 0` First try to simplify this by dividing by 2. This would get, `5x^2+2x+1 = 0` To solve this problem you can use the general formula. For a quadratic equation of `ax^2+bx+c = 0`...

Math
The given equation is `a(v) = 12v6` and initial conditions are v=6 at t=0 and s = 0 when t = 0. `a = 12v 6` We can write acceleration as, `a = (dv)/(dt)` Therefore, `(dv)/(dt) = 12v6`...

Math
This can be solved by using derivatives and integration. We know acceleration is the rate of velocity change and velocity is rate of change of displacement or distance. So in general notation, if...