
Math
x+2y+6z=4..............(1) 3x+2yz=4............(2) 4x+ 2z=16..............(3) To solve the system we will use the elimination method. First we will subtract (2) from (1). ==> 4x +7z = 8...

Math
The sheet of metal we have has sides equal to a. Let the sides of the squares that are cut from all the corners be x. Now we have a length equal to a – 2x, to fold on all the sides and create the...

Math
We have to solve log(15) [1/(3^x + x  5)] = x * (log(15) 5  1). log(15) [1/(3^x + x  5)] = x * (log(15) 5  1) => log(15) [1/(3^x + x  5)] = x*log(15) 5  x => log(15) [1/(3^x + x  5)] =...

Math
I don't feel as if this is going to be especially helpful to you, but here it goes. I copied the image to a word document, and rotated it, looked at it from multiple angles, and etc. The best guess...

Math
The street is 40 meters long. We will count the trees from the beginning of the street to the end. There are two trees on the beginning of the street==> 2 trees After 10 meters, there are two...

Math
We have to find the value of lim x,y>0 [(x^3y^3)/(x^2+y^2)] We cannot substitute x and y with 0 in the expression as that would yield 0/0 which is indeterminate. We see that the expression is...

Math
Let one of the sides be x. Given that the other side is 5 cm less than 2 times x. Then the other side is (2x5). Now given that the perimeter is 38. But, we know that the perimeter is given by: P...

Math
If I'm reading your description of the problem correctly, then the key to this problem is first finding the total surface area of the box, then subtracting the surface area of the two doors. The...

Math
We have the equation 9x^2 + 4y^2 + 36x – 8y + 4 = 0 9x^2 + 4y^2 + 36x – 8y + 4 = 0 collect the x and y terms together => 9(x^2 + 4x) + 4(y^2 – 2y) = 4 complete the squares of the terms...

Math
Here we use the identity cos (x – y) = cos x * cos y + sin x * sin y substituting x with theta and y with pi/3, we get r* cos ( theta – pi/3) = 3 => r*( cos theta * cos (pi/3) + sin theta *...

Math
The possibilities are for the committee are: ( 5 men and 0 women) OR ( 4 men and 1 woman) OR ( 3 men and 2 women) Now we will determine in how many ways we could arrange each possibility. ( 5 men...

Math
We have to solve the equation u^2 + 6u = 27. First bring all the terms to one side => u^2 + 6u  27 = 0 One method of finding the roots which works when the roots are integers or fractions is to...

Math
We have to find (3/5)^3. Let's open the brackets, we get (3/5)^3 = (3)^3 / 5^3 => 3^3 / 5^3 => 27 / 125 => 0.216 This gives (3/5)^3 = 0.216

Math
John starts along the highway at 50 mph at 11:00, Jimmy starts 15 minutes later or at 11:15 with a speed of 65 mph. I assume they move at a constant speed once they have started. For Jimmy to catch...

Math
Since the problem is incosistent (there are not given the locations of the points E and H), you may solve only the magnitude of the vector BD. The vector BD denotes the diagonal of the square. You...

Math
The missile is fired at 840 m/s at an angle x to the horizontal. We can divide its velocity into a horizontal component equal to 840* cos x and a vertical component equal to 840* sin x. The...

Math
For instance, the first interval is finite on the left side and infinite to the right side. Why? Because, the left end of the interval is a real number, since the right end is a symbol, and not a...

Math
Given that A(4,2) and B(1,3) Let us calculate the length of AB. ==> AB = sqrt(4+1)^2 +(23)^2 = sqrt10 ==> Then, the length of GH is also sqrt10. But, GH is in oppsite direction of AB....

Math
Given that A(4,2) and B(1,3) Then the vector AB is written as follows. => AB = ( 1+4)i + (32)j = 3i + j Now given that F( 3,2). We will assume that E (x. y). ==> EF = (3x)i + (2y)j =...

Math
Given that A(4,2) and B(1,3) Then we will write the vector AB as follows. ==> AB = (1+4)i + (32)j ==> AB = 3i + j Also, given that C (6, 0), we need to find D such that: AB = CD Let us...

Math
We have to find the point on the graph where the tangent is horizontal. When a line is horizontal its slope is zero. The slope of the tangent to a graph at any point can be found by finding the...

Math
The demand slope is given by D(p) = 20 / sqrt (p  1) The slope of the curve is the value of the first derivative at the required point. D(p) = 20 / sqrt (p  1) => 20* ( p  1)^(1/2) D'(p) =...

Math
We have to find f(x), lim x> 4 The function f(x) has the value: f(x) = 1 at x not equal to 4 and f(x) = 1 at x = 4 We see that approaching x=4 from x = + inf, f(x) = 1 Approaching x = 4 from...

Math
By the Pythagorean Theorem, we know that the sum of the squares of the legs equals the square of the hypotenuse. So we square all of the terms that you have given. We get x^2 + 4x^2 = 400 5x^2 =...

Math
The sign of a ratio is determined by the signs of both numerator and denominator. If both have the same sign, then the ration is positive. If they have different signs, then the ration is...

Math
We have 10100101, which is a binary number, so there are only two digits 1 and 0. 10100101 = 1*2^0 + 0*2^1 + 1*2^2 + 0*2^3 + 0*2^4 + 1*2^5 + 0*2^6 + 1*2^7 => 1 + 4 + 32 + 128 => 165 Binary...

Math
When the farmer sells wheat at $120, he pays a tax of 120*0.1 = $12. In the next stage the trucker adds a margin of 10% and sells the wheat to the cookie company. The taxes he pays are...

Math
The square root of the given complex number can be expressed as a complex number x + iy. We have x + yi = sqrt (8 + 6i) take the square of both the sides => (x + yi) ^2 = 8 + 6i => x^2 +...

Math
The minute hand of a clock completes 1 circle in a minute. As the length of the minute hand is 1.12 m, the tip moves in a circle with a circumference of 2*pi*1.12 = 2.24*pi m. This distance is...

Math
The sides of the rectangle are 18r and 8r. The area of the rectangle therefore is 18r*8r = 144*r^2 There are 6 semicircles of radius 3r in total on two sides and 2 semicircles of radius 4r on the...

Math
The dimensions of the rectangle are 170 cm by 90 cm. From this the maximum number of circular disks of diameter 8 cm are cut. Looking at the length and width of the sheet we find that 21*11 disks...

Math
We have a parallelogram ABCD, with the point F dividing AD in two equal parts. Let us take the distance between the sides BC and AD as d. Now, BC*d = AD*d = 80 cm^2. We have AF = AD/2 The area of...

Math
The cost to produce x unit of lipstick is given as c(x) = 60x + 10000 and the revenue is r(x) = 85x If the break even is at N c(N) = r(N) => 60*N + 10000 = 85*N => 25N = 10000 => N =...

Math
We have g(x) = 2 log (x  3) + 1 Let y = g(x) = 2 log (x  3) + 1 => y  1 = 2 log (x  3) => (y  1)/2 = log (x  3) taking the base of the log as 10 => 10^[(y  1)/2] = x  3 => x =...

Math
We have a:b = 5:6 and b:c = 3: 7 We have to find (3c + 2a):a Now a:b = 5:6 => a/b = 5/6 b:c = 3:7 => b/c = 3/7 (a/b)*(b/c) = (5/6)*(3/7) => a/c = 5/14 => c/a = 14/5 (3c + 2a):a =>...

Math
We have to solve sin x + x = 0 sin x + x = 0 subtract x from both the sides => sin x = x Now the only solution for this can be x = 0 as 0 = 0 and sin 0 = 0. For no other value of x is sin x =...

Math
We have to find the value of 1*1! + 2*2! + 3!*3! + ............ n*n! Now we know that n! = 1*2*3*4…*n 1*1! + 2*2! + 3!*3! + ............ n*n! can be written as (2 – 1)*1! + (3 – 1)*2! + (4...

Math
The largest circle that fit into a square has a diameter equal to the side of the square. Let the side of the square be S. The radius of the circle is S/2. The area of a circle of radius S/2 is...

Math
The price of the stock on Monday when they were bought is $4. It crashes by 15% on Tuesday to reach $4*(1 – 15%) = $4*0.85. The price recovers by 5% over the rest of the week. For three days the...

Math
In a quadratic equation that has complex roots, the roots are conjugates of each other. So, if one of the roots of the quadratic equation is x + iy, the other root is x – yi. Here we have one of...

Math
We need to determine x given that 40 + x is 12 times 40 – x 40 + x = 12*(40 – x) => 40 + x = 12*40 – 12x => x + 12x = 480 – 40 => 13x = 440 => x = 440/13

Math
We have to solve 4  sqrt (x  1) = sqrt (x + 7) 4  sqrt (x  1) = sqrt (x + 7) square both the sides => 16 + (x  1)  8*(x  1) = (x + 7) => 16 + (x  1) x  7 = 8*(x  1) => 8 = 8*(x...

Math
A complex number z = x + yi, can be expressed as a line with a length equal to z or sqrt (x^2+ y^2). The line makes an angle A with the positive xaxis that is known as its argument and equal to...

Math
We have to find the absolute value of (1 + i) (6 + 2i)/ (4 + i) (9 + 3i). First we convert it to a form x+iy and then use the formula sqrt(x^2 + y^2) to determine the absolute value. (1 + i)(6 +...

Math
Mathematics texts have been found that are quite ancient. Babylonian texts from 1800 B.C. and Egyptian texts from 20001800 B.C. have been found. These texts have information about the Pythagorean...

Math
We have to solve the inequation: (3x)^2  (1+x)^2 >1/2 open the brackets => 9 + x^2  6x  1  x^2  2x > 1/2 => 8  8x > 1/2 => (1  x) > 1/16 => x  1< (1/16) => x...

Math
We have to solve (2^x  1) / (2^x  1) = 0 { Note: It is not possible to solve (2^x  1) / (2^x  1), so I have equated it to 0} (2^x  1) / (2^x  1) = 0 => [(1/2^x)  1]/(2^x  1) = 0 let...

Math
If f(x)= ax^2 + bx + c and x1 and x2 are the roots. ==> x1+x2 = b/a ==> x1*x2 = c/a In all 4 cases we have a= 1 ==> x1*x2 = b ==> x1*x2= c Let us test the roots we have. Given that...

Math
Given the curves: xy =16 Then we will rewrite as a function of x. ==> y= 16/x ...........(1) And the curve : y= x...............(2) We need to find the intersections points . ==> y= y ==>...

Math
Given the set of pairs : R= { (2,3) , (a,4) , (1,9) , (0,7) We need to find the values of x so the set presents a function. The definition of the function is that for each value of y, we have only...