• Math
You need to remember that the tangent line to the curve, at a point, is given by the derivative of the function at that point. You also need to remember that f'(x_0) = m , where m represents the...

• Math
You need to know that the product cancels if one of its factors cancels. Hence, cancelling the first factor yields: sin 2x =0 =gt 2x = sin^-1(0) + n*pi =gt 2x = 0 + n*pi =gt x = npi/2 Cancelling...

• Math
We have to find the value of tan (pi/2 - arc tan(1/2)) use the relation tan (pi/2 - x) = cot x tan (pi/2 - arc tan(1/2)) => cot (arc tan (1/2)) => 1/tan ( arc tan (1/2)) => 1/(1/2) =>...

• Math
We have to find x that lies in the range 0 < x < 360 such that sin 2x = (-1/2)*sqrt 3 sin 2x = (-1/2)*sqrt 3 => 2x = arc sin ( -sqrt 3/2) => 2x = -60 => x = -60/2 => x = -30 In...

• Math
Each of the figures of which the area has to be determined can be divided into rectangles and triangles. The area of a rectangle with sides of length a and b is A = a*b. And the area of a triangle...

• Math
Let the point of intersection of x + 3y + 8 = 0 and x - 7y + 9 = 0 be (X, Y). This gives us the following set of simultaneous equations to solve for X and Y: X + 3Y + 8 = 0 ...(1) X - 7Y + 9 = 0...

• Math
We have to find the points of intersection of x^2 + 2y^2 + y - 1 = 0 with the line x + 2y = 0. x + 2y = 0 => x = -2y => x= -2y Substitute this in the other equation x^2 + 2y^2 + y - 1 = 0...

• Math
The point of intersection of the lines 3x + 2 = 18 and x - y = 7 has to be determined. 3x + 2 = 18 => 3x = 16 Substitute x = 16/3 in x - y = 7 => y = 16/3 - 7 => y = -5/3 The point of...

• Math
Let the point be (x,y). Now the slope of the tangent to a point on any curve is the first derivative of the curve. Here y = 1 + 1/x => y' = -1/x^2 Now, the slope of a line between (x1, y1) and...

• Math
For the curve y^2 + 4x^2 = 8, the slope of the tangent to the curve at x = c is given by dy/dx at x = c. Using explicit differentiation, 2y*(dy/dx) + 8x = 0 => dy/dx = (-8x)/(2y) =...

• Math
The point on the curve 3x^2 + 2y = 8 is required where the tangent makes an angle of 45 degrees with the x-axis. The slope of the tangent is tan 45 = 1. The slope is also the value of dy/dx at...

• Math
The matrix A = [[-2,1],[-1,4]] In the elementary matrix E_1 the first row if A is multiplied by 1/6 . E_1 = [[-1/3,1/6],[-1,4]] E_1^-1 = 1/(-4/3 + 1/6)*[[4, -1/6],[1, -1/3]] =...

• Math
The center of mass of the rectangle (1,-3) (4,-3) (4,5) (1,5) has to be determined. The diagram of the rectangle is: The coordinates of the center of mass of the rectangle is given by: M_x =...

• Math
You need to notice that the function will have two vertical asymptotes at x = +-1 , since the function is not defined at x = +-1. You need to check if the function has maximum and minimum...

• Math
You need to evaluate the function (fog)(x) using the property of composition of two functions, such that: (fog)(x) = f(g(x)) Replacing g(x) for x in equation of the function f(x) yields:...

• Math
Let the time taken for B to pass A be t. Then when B passes A, has travelled 1000 m more than A. Therefore, Distance travelled by B = Distance travelled by A +1000 To find distance travelled by B,...

• Math
lim_(x->5) arctan((x^2-25)/(5x^2-25x)) We can simplify the rational expression by factoring (x^2-25)/(5x^2-25x) = ((x-5)(x+5))/(5x(x-5))=(x+5)/(5x) as long as x!=5 So lim_(x->5)...

• Math
The plane through the points A(2, –4, 0), B(–4, 0, –4), C(–1, 4, 1) has to be determined. vec (AB) = [(–4) – 2]i + [0 – (–4)]j + [(–4) – 0]k = -6i + 4j - 4k vec(AC) = [(–1) – 2]i + [4 – (–4)]j...

• Math
Cedric has 4 pencils, a blue pen, and a black pen on his desk. He draws 2 of them from the desk without replacement. The total number of ways of picking 2 items is C(6,2) = 15. The number of ways...

• Math
To get the phase shift and vertical shift, you must get the equation in the following form: f(x) = acos(b(x-phi))+ c Where a denotes the amplitude, b denotes the factor by which we divide 2pi...

• Math
The question does not give all the information needed to answer it, but I will try and shed some light on this topic. A segment that has a slope of eight over zero is going to be vertical. The...

• Math
The period of the function f(x) = sin x is 2*pi . For the function y = 2*sin(3*A) the period is 2*pi/3 The period of the function y = 2*sin (3*A) is (2*pi)/3

• Math
You should remember that the period of tangent function is pi . Your tangent function is tan (x/2) , therefore you should divide the period pi by x/2 . Use the notation p for period. p =...

• Math
The period of a function f(x) = sin x is 2*pi For sin(x/4) the period is 2*pi*4 = 8*pi The period of the function y = sin (x/4) is 8*pi

• Math
The period of the function tan(2*x + 7) has to be determined. For f(x) = tan x, the period is pi . If the period of the function is A, 2*(x + A) + 7 = 2*x + 7 + pi => 2*x + 2*A + 7 = 2*x +...

• Math
We have the graph y = 2sinx(2pix) + 1 a) the period is 1 - this is the length of one complete phase b) the amplitude is 2 - this is the height of the peaks from the centre of the wave c)...

• Math
We have to prove [(tan x)^2 + 1]/[1 - (sin x)^2] = (sec x)^4 Start from the left hand side [(tan x)^2 + 1]/[1 - (sin x)^2] tan x = sin x / cos x => [(sin x/cos x)^2 + 1]/[1 - (sin x)^2] =>...

• Math
Given the right angle triangle with two sides 3 and 4 To find the perimeter first we will need to determine the length of the third side which is the hypotenuse. We will use the formula to find the...

• Math
Let the vertices of the triangle be : A(-1,1) B( 2,0) and C ( 4,-2) First we will calculate the length of the sides: AB = sqrt( 2+1)^2+ ( 0-1)^2 = sqrt(3^2 + 1) = sqrt( 10) ==> AB...

• Math
sin^2 (pi/6) - 2sin (pi/6) cos (pi/6) + cos^2 (-pi/6)  First, we know that: cos(-x) = cos(x)  ==gt cos^2 (-pi/6) = cos^2 (pi/6) Also, we know that: 2sinxcosx = sin2x ==> 2sin (pi/6) cos...

• Math
It is possible to write cos(pi/2 - x) = sin (x) as the two trigonometric functions are shifted along the x-axis by pi/2 cos (pi/2) = 0 cos(pi/2) - cos x = -cos x = cos x The right hand side...

• Math
When simple interest is being calculated, the interest I is given by the formula I = P*r*t where P is the principle amount, r is the rate of interest per period and t is the number of periods....

• Math
You should use the following logarithmic identity such that: log_a b = (log_c b)/(log_c a) log_4 x = (log_2 x)/(log_2 4) => log_4 x = (log_2 x)/2 Substituting (log_2 x)/2 for log_4 x...

• Math
Here we have log(x) 2 = 0.5, where the base of the log is x. log(x) 2 = 0.5 use the relation that log(a) b = c => b = a^c => 2 = x^(1/2) => 2^2 = x => x = 4 The solution is x = 4.

• Math
490 g as a percentage of 7 kg is equal to ((490/1000)/7)*100 = (0.49/7)*100 = 49/7 = 7 490 g is 7% of 7 kg.

• Math
The predicted yield of the reaction is 21 g but only 3.8 g is recovered. This gives the percentage yield as (3.8/21)*100 % ~~ 18.095 % The percentage yield is approximately 18.095%

• Math
The problem requires finding the integral of 16x * sin^3(2x^2 + 1)*cos (2x^2 + 1) with substituting 2x^2 + 1 with u Int [16x * (sin (2x^2 + 1))^3*cos (2x^2 + 1) dx] let u = 2x^2 + 1 du = 4x * dx...

• Math
The percentage of 760 that 950 is can be determined by evaluating (950/760)*100 = = 1.25 = 125 % 950 is 1.25 or 125% of 760

• Math
We have the present value and the future value in 3 years time so we can use the compound interest formula: F= P (1+i)^n where F is the future value (Rs 7290) P is the present value (Rs 5120) i...

• Math
It seems that math is a difficult class in which to address learning styles. My memory of math classes is that they build on each other. Most of these math classes seem very linear in structure...

• Math
We have to prove that (x+y)^5 - (5yx^2+5xy^2)(x^2+xy+y^2) = x^5 + y^5. (x + y)^5 = x^5 + 5*x^4*y + 10*x^3*y^2 + 10x^2*y^3 + 5*x*y^4 + y^5 (5yx^2+5xy^2)(x^2+xy+y^2) = 5yx^4 + 5y^2x^3 + 5y^3x^2 +...

• Math
sqrt(18)/ sqrt(2) rationalize the denominator (which will eliminate square root denominator) = sqrt(18)/ sqrt(2) times sqrt(2)/sqrt(2) = sqrt(36)/ 2 A square root can be positive or negative...

• Math
(a) -6x=-27+3x Subtract 3x from both sides of the equation -9x=-27 Divide both sides of the equation by -9 x=3 The solution is x=3: Check -6(3)=-18=-27+9=-27+3(3)...

• Math
One could get 4/3 from -4 by multiplying -4 by -1/3 : -4*-1/3 = 4/3 Likewise, one could get -4/9 from 4/3 by multiplying by -1/3 : 4/3 * -1/3 = -4/9 If we multiply this by -1/3 ,...

• Math
The partial fraction decomposition of  3/(x - 3)^2 has to be determined. Let 3/(x - 3)^2 = A/(x - 3) + B/(x - 3)^2 => 3/(x - 3)^2 = (A(x - 3))/(x - 3)^2 + B/(x - 3)^2 => 3 = Ax - 3A +...

• Math
You need to remember the form of the equation of the quadratic: f(x) = ax^2 + bx + c Hence, you need to calculate the parameters a,b,c. You should consider the given facts: f(-1)=4; f'(1)=4 ;...

• Math
The difference of two cubes is x^3-a^3=(x-a)(x^2+xa+a^2) So p^3-8=(p-2)(p^2+2p+4) Factoring p^2+2p+4 using the quadradic formula is...

• Math
We can solve for x and y using trigonometry. Here, tan 60 = y/x = √3 or, y = √3 x Similarly, tan 30 = y/(1000+x) = 1/√3 . or, √3 y = 1000 + x Substituting the value of y from previous equation, we...

Since we have 2^x, we will be using ln which stands for logarithm base e. If we apply ln to both sides of the given equation we get: ln(e^x)=ln(20) logarithm and exponential with the same base...
You need to remember the formula of sin 2a = 2sin a*cos a Hence, you need to prove that: 2 sin a* cos a = (2 tan a)/(1 + tan^2 a) I suggest you to form the tangent function to the left side...