
Math
The shade is made of a piece of material that has a length of 1.5 m and a width of 2 m. It is placed at an angle of 60 degrees to the ground when the shade is created. At 12 noon, when the sun is...

Math
The tension in the rope used by which the box is being moved is equal to 350 N. The rope makes an angle of 50 degrees with the horizontal. The box is on a ramp inclined at 20 degrees. It is pulled...

Math
There are originally 4 red balls and 7 blue balls in the box. When the first ball is drawn, the probability of drawing a blue ball is 7/11. If the 1st ball is blue it is kept outside, there are now...

Math
The first airplane is flying at 400km/h and going towards the west. The second airplane is traveling at 500 km/h and flying towards the south. They both pass each other at 11:00 a.m. At 1:00 pm, 2...

Math
We have to express (x3) raise to the power of two / 5 + (y+3) raise to the power of two / 6 = 1 in the general form The given statement can be used to construct the following matrix: ((x  3)^2)/5...

Math
We use the symbol "^" to refer to the power or the exponent. In some math platforms, the system does not support some mathematical symbols. For example: 2^2 = 2 (square) = 4 3^2 = 9 4^2 = 16 We use...

Math
We have to solve the system of equations 3x  4y = 25 2x + y = 10 3x  4y = 25 => 3x = 25 + 4y => x = ( 25 + 4y)/3 substitute in 2x + y = 10 => 2 ( ( 25 + 4y)/3) + y = 10 => ( 25...

Math
We have to solve sqrt ( 3x  2)^2 < 5 => (3x  2)^2 < 25 Now (3x  2)^2 can be less than 25 if 3x  2 is less than sqrt 5 or if 3x  2 is greater than  sqrt 5 This gives two inequalities...

Math
We have to solve the equation 2x + 5 = 2x  5 Now 2x + 5 = 2x + 5 or 2x  5 So we get 2x + 5 = 2x  5 => 4x = 10 => x= 5/2 and 2x  5 = 2x  5, which does not yield a solution The...

Math
(3 + 2i)^2  3(3i)(2+2i) We need to write into the standard form z= a+ bi Let us open the brackets. ==> (3+2i)^2 = (3)^2 +2*3*2i + 4i^2 But i^2 = 1 ==> (3+2i)^2 = 9  12i  4 = 5...

Math
We have log (7) a + log (a) 7 = 2 We use the relation for logarithms that log a + log b = log (a*b) and log (a) b = 1 / log(b) a. log (7) a + log (a) 7 = 2 => log (7) a + 1/ log (7) a = 2 =>...

Math
We have log(3) [3^(b+1)  18] = 2 log(3) [3^(b+1)  18] = 2 taking the antilog of both the sides 3^(b+1)  18 = 3^2 => 3^( b + 1)  18 = 9 => 3^( b+ 1) = 27 => 3^( b + 1) = 3^3 As the...

Math
We have ln (ln (x)) = 4 ln x has a base of e. Taking the antilog of both the sides => ln (x ) = e^ 4 Taking the antilog of both the sides again => x = e^ ( e^4) The required value of x is...

Math
The line 2x = 8 or x = 4 is one that is parallel to the yaxis. The slope of the line is infinity. 3y = 15 or y = 5 is parallel to the x axis. This line has a slope equal to 0. As the xaxis and...

Math
Given the points ( 2,3) and (4, 6) passes through a line. We know that the equation of the line is given by : yy1= m(xx1) where (x1,y1) is any point on the line and m is the slope. Let us...

Math
Given the points ( 4, 5) and the point ( 3, 7) passes through line L. We need to find the slope of any perpendicular line to L. First we will determine the slope of L. We know that: m =...

Math
For the inequation x^2  5x + 6 > 0 we first write the quadratic expression as factors x^2  5x + 6 > 0 => x^2  3x  2x + 6 > 0 => x( x  3)  2(x  3) > 0 => (x  3)(x  2)...

Math
The answer to this problem can be found using a simple algebraic expression. We know that the height of the replica is 22 inches, and we know that this is 1/3 of the height of the original. Let's...

Math
Given the function: y= x^2 When adding 2 units up, then the y value will increase 2 unites. Then , y will be y+2 ==> y= x^2 +2 Now, when moving 3 units to the left, then x values will decrease...

Math
Given the quadratic equation: 3x^2  7x = 3 ==> 3x^2  7x 3 = 0 We need to determine the type of roots. Then, we will use the discriminant to find out. We know that: delta = b^2  4ac If delta...

Math
Let the age of Sheila be S, Nicole's age be N and Steve's age be T. Sheila's age is 2 more than Nicole's age. S = 2 + 2*N The sum of Sheila and Nicole's age is the same as that of Steve T = S + N...

Math
hyperbola: The standard form: (xx1)/a^2 + (yy1)^2/b^2 = 1 Examples: (x+1)^2/5+(y2)^2/25 =1 (x+2)^2/25(y1)^2/9=1 Circle: The standard form: (xx1)^2 + (yy1)^2 = r^2 (x1,y1) is the center...

Math
We have to integrate e^x / (x – 2) We use integration by parts here: The general formula is Int [ u dv] = u*v – Int [ v du] let u = (x – 2) , du = dx dv = e^x , v = e^x => Int [ (x – 2)...

Math
We have to prove that 1 [(cos x)^2 /( 1 + sin x)] = sin x 1 [(cos x)^2 /( 1 + sin x)] => [1 + sin x – (cos x)^2] / ( 1 + sin x) use 1 = (cos x)^2 + (sin x)^2 => [(sin x)^2 + (cos x)^2 +...

Math
We have f(x) = x + 4 and g(x) = 2x  5. fog(x) = f(g(x)) = f( 2x  5) = 2x  5 + 4 = 2x  1 To find the inverse function of fog(x), let y = fog(x) = 2x  1 => y = 2x  1 => y + 1 = 2x =>...

Math
It is given that u^2 = v^2 + (m/n)((uv)^2) and we have to prove that : v/u = (mn)/(m+n) u^2 = v^2 + (m/n)((uv)^2) => u^2  v^2 = (m/n)((uv)^2) => (u^2  v^2)/ (uv)^2 = (m/n) => (u ...

Math
For the given equations: For a quadratic equation ax^2 + bx + c = 0, the roots are [b+ sqrt (b^2  4ac)]/2a and [b  sqrt (b^2  4ac)]/2a. The sum of the two roots is 2b / 2a = b/a We have the...

Math
We have to prove that if y= a*sin nx + b*cos nx , y’’+ n^2*y= 0 y = a* sin nx + b*cos nx We know the derivative of sin nx = n* cos nx and the derivative of cos nx = n*sin nx y’ = na * cos nx...

Math
We have to solve x^3 + x^2 – 5x – 2 = 0 => x^3  2x^2 + 3x^2 – 6x + x – 2 = 0 => x^2( x – 2) + 3x ( x – 2) + 1(x – 2) = 0 => (x^2 + 3x + 1) (x – 2) = 0 => (x^2 + 3x +...

Math
Let the number consist of the digits x and y, or it is represented by xy. It is given that adding 27 to the number causes the digits to get interchanged:(xy + 27) = yx We can write this as (10*x +...

Math
A dice has 6 sides with the numbers 1,2,3,4,5 and 6. Of these 3 are even. When the dice is rolled the first time the chance of getting an even number is 3/6 = 1/2. On the second roll, the chance of...

Math
The general equation of a line expressed in terms of its intercepts is x/a + y/b = 1, where a is the xintercept and b is the yintercept. Substituting the values given: x/ 6 + y/ 14 = 1 => 14 x...

Math
The surface area and volume of solids like prisms, pyramids, cones, cylinders, and spheres can be determined by using the following formulae. Only the required values for the variables in the...

Math
The curve we have is : x^m/a^m+y^m/b^m=1 If we differentiate the two sides we get: (1/a^m)(m*x^(m1)) + (1/b^m)(m*y^(m1))dy/dx = 0 => dy/dx = [(1/a^m)(m*x^(m1))]/[(1/b^m)(m*y^(m1))] The...

Math
We have the following simultaneous equations to solve: 3x + 4y + z = 7 …(1) 2y + z = 3 …(2) 5x + 3y + 8z = 31 …(3) From (2), we get 2y + z = 3 => z = 3 – 2y substitute in (1) => 3x...

Math
I assume the earlier answer did not match your solution as you had not specified the exact direction of the wind. It is blowing from 25 degrees, but 25 degrees to what. Also, you had specified the...

Math
The bumper is initially hung vertically and it has a weight of 150 N. The sailor grabs the rope holding the bumper and pulls it horizontally so that the rope makes an angle of 40 degrees with the...

Math
L(t) = 1208 ( 1.265)^t The environmentalists needs t years in order to solve the problem. Since they have enough rainbow for only 10,000 leprechauns, then they have time until the population reach...

Math
Given that: v1= 226 where D= 6 in ==> The radius (r1)= 6/2 = 3 ==> v1 = r^2 * pi * h1 ==> 226 = 9 * pi * h1...........(1) We need to find the value of the volume (v2) when the height is...

Math
To cover a certain area the builder needs x numbers of 4in tiles and y numbers of 16in tiles. If he will only use the 4in tiles he will need to replace y numbers of 16in tiles with the 4in...

Math
In the problem we are given the length of two of the sides of the triangle and we have two of the angles. The sum of the three angles of a triangle is equal to 180 degrees. Using this, the third...

Math
The general form of a circle with a center (a, b) and radius r is (x  a)^2 + (y  b)^2 = r^2 We have the center as (2 , 3) and the radius is 8 Substituting these values we get : (x + 2)^2 + ( y...

Math
We have to find the units digit of 3^4027. 3^1 = 3, 3^2 = 9, 3^3 = 27, 3^4 = 81, 3^5 = 243... We see that the units digit follows the series 3, 9, 7, 1 and it repeats after 4 powers. 3^4027 =...

Math
If the given integration is correct the derivative of (u/8)*(2u^2  a^2)sqrt( a^2  u^2) + (a^4/8)arc sin (u/a) + C should be u^2*sqrt ( a^2  u^2) [(u/8)*(2u^2  a^2)sqrt( a^2  u^2) + (a^4/8)arc...

Math
We have to find the tangent to the circle x^2 + y^2 + 10x  6y  2 = 0 parallel to y = 2x without using calculus. The given circle is x^2+y^2+10x6y2=0 => x^2+ 10x + 25 + y^2  6y + 9 = + 25 +...

Math
The line x + 8y = 9 can be rewritten in the form y = x / 8 + 9/8 where 1/8 is the slope. The angle that is formed by the line with the positive x – axis is arc tan (1/8). We need to find the...

Math
The slope of the tangent to a curve at any point is the value of the first derivative at that point. Here, we have the curve y = sqrt ( 2x^2 +1) y' = 4x * (1/2) (2x^2 + 1)^(1/2) => y' = 2x/...

Math
The area of a triangle is given by the formula (1/2)* base * height. To enclose a triangle with the largest area within a rectangle its base would have to be one of the sides of the rectangle and...

Math
Imagine 4inch tiles laid out on top of a 16inch square tile. There would be 4 rows of 4inch squares, with 4 tiles in each row. Each 4inch square tile has an area of 16 square inches (4 x 4),...

Math
I think by x you mean one of the angles of the triangle. If we look at the relation y = sin x , the independent variable is x and the dependent variable is y. The value of sin x for an angle x is...