
Math
You have the answer with you, it's the formula, you just need to substitute the numbers. I'll help you with that. Bob has invested $1000 in the bank CD, so P = $1000 The CD earns 3% interest...

Math
We have to simplify: (x^28x+16)/(x^2x12)÷(4xx^2)/(2x) Now, x^2  8x + 16 = (x  4)^2 x^2  x  12 = x^2  4x + 3x  12 => x(x  4) + 3(x  4) = (x + 3)(x  4) 4x  x^2 = x(4  x)...

Math
The replicas in Katy of the Forbidden Garden terracotta army are 1/3 scale. So a replica is 1/3 the dimensions of the original. The replica in Katy has a height of 22 inches. If the original has a...

Math
We have to solve the following set of simultaneous equations: x  2y = 6 ...(1) x + 2y = 8 ...(2) (2)  (1) => x + 2y  x + 2y = 8  6 => 4y = 2 => y = 2/4 => y = 1/2 substitute in (1)...

Math
We have to solve the following set of simultaneous equations: 2x + 4y = 1 ...(1) 4x + 9y = 2 ...(2) 2*(1)  (2) => 4x + 8y  4x  18y = 2  2 => 10y = 0 => y = 0 substitute in (2) 4x + 0...

Math
We have to solve the following set of simultaneous equations: 3x + 2y = 6 ...(1) 18x + y = 9 ...(2) 6*(1)  (2) => 18x + 12y  18x  y = 36  9 => 11y = 27 => y = 27/11 substitute in (2)...

Math
We have to prove that the functions f(x) = sqrt (x^2 + 5) and g(x) = (2*sqrt x – 1)^2 grow at the same rate as x >inf. Two functions grow at the same rate if [lim x> inf ( f(x) )] /...

Math
We have to find the derivative of f(x) = 5x * (x1)^4 We can use the product rule here: f(x) = 5x * (x1)^4 f'(x) = (5x)' * (x1)^4 + 5x * [(x1)^4]' => f'(x) = 5* ( x  1)^4 + 5x * 4*(x  1)^3...

Math
We know that the derivative of ln x = 1/x , but ln x is log(e) x. We have to find the derivative of log(10) (x^3 + 3x). First we convert it to log to the base e. y = log(10) (x^3 + 3x) => y =...

Math
We have to determine the value of Int [ (sin x)^3 dx] Int [ (sin x)^3 dx] => Int [ (sin x)^2* sin x dx] => Int [ (1 – (cos x)^2 )* sin x dx] let u = cos x => du = sin x dx => Int [...

Math
We have to find the integral of ln x. The easiest way to do this is by using integration by parts. The formula we have to substitute values in is Int [ u dv] = u*v – Int [ v du] …(1) Take u =...

Math
We have to solve (x+1)^2=2x^25x+11 for x. (x+1)^2=2x^25x+11 open the brackets => x^2 + 2x + 1 = 2x^2  5x + 11 => x^2  7x + 10 = 0 => x^2  5x  2x + 10 = 0 => x(x  5)  2(x  5) =...

Math
The model that Ariana and her father build has a scale of 0.08. Each foot in the real structure is represented as 0.08 foot in the model. The square footage of the model is 7.68 and one side is 3.2...

Math
To find the value of the given expression: 2048x^67 * 9850xy, multiply the numeric terms and the terms x and y. 2048*x^67 * 9850*x*y => 2048*9850 * x*67*x * y => 20172800 * x^(67 + 1) * y...

Math
The pilot is travelling at an airspeed of 100 km/h towards the East. The pilot has to steer the airplane to tackle the wind which is blowing. The wind is blowing at 100 km/h at an angle of 25...

Math
If the roots of the equation are equal, since the equation is a quadratic, its discriminant has to be zero. Discriminant = delta = b^2  4ac a,b,c, are the coefficients of the equation: delta =...

Math
Let the total number of camels be C. We have that (1/4) of the camels had been seen in the forest. Twice the square root of the total number had gone to the forest. The number that remains is equal...

Math
We have to determine (4* sqrt 2  2 sqrt 3) (4* sqrt 2 + 2* sqrt 3) (4* sqrt 2  2 sqrt 3) (4* sqrt 2 + 2* sqrt 3) => 16* 2 + 8*sqrt 3* sqrt 2  8*sqrt 2* sqrt 3  4*3 => 32  12 => 20 The...

Math
We have to determine (2* sqrt 5 + 3*sqrt 3)^2 (2* sqrt 5 + 3*sqrt 3)^2 => (2* sqrt 5)^2 + (3*sqrt 3)^2 + 2* 2* sqrt 5*3* sqrt 3 => 4*5 + 9*3 + 12* sqrt 15 => 20 + 27 + 12*sqrt 15 => 47...

Math
We have to simplify sqrt 98 + sqrt 32  sqrt 63 sqrt 98 + sqrt 32  sqrt 63 => sqrt 49*2 + sqrt 16*2  sqrt 9*7 => 7* sqrt 2 + 4* sqrt 2  3*sqrt 7 => 11* sqrt 2  3* sqrt 7 The required...

Math
Given that log 4 (x) = 12 We need to find the values of log2 (x/4) Let us use the logarithm properties to simplify. We know that log a/b = log a  log b ==> log2 (x/4) = log2 x  log2 4 But log2...

Math
Let the sides be x, y and the hypotenuse h. Given that h is 2 more than the longer sides. Let the longer side be x. ==> h = x+2...............(1) The shorter side (y) is 7 less than the longer...

Math
Let the numbers be x and y. Given that the sum is 20. ==> x + y= 20 ..............(1) Also, given that the larger number is 4 less than twice the smaller. ==> x = 2y 4 ..............(2) We...

Math
Given that the area of the rectangle is 15 cm^2. Also, given that the perimeter is 16 cm^2 We need to find the length of the sides. ==> Let the sides be L and w. ==> L*W = 15 ...........(1)...

Math
Let the side of the second square be s, the size of the first is 5 less than the second or s  5. The area of the larger square is s^2. This is four times the area of the smaller square which is (s...

Math
Let us assume that the numbers are x and y. Given that the sum of the numbers is 26. ==> x+ y= 26............(1) Also, given that the product is 165. ==> x*y = 165..........(2) We will use...

Math
Let the revenue be R, the profit be P, and the cost be C. Then, we know that: Profit = Revenue  cost ==> Given that R= x^2+100x Also, given that C = 240x+500 ==> P = x^2 +100x  240x 500...

Math
Let f(x) = (x+3)/(2x5) We will use the quotient rule to find the derivative. We will assume that f(x) = u/v such that: u= x+3 ==> u' = 1 v = 2x5 ==> v' = 2 ==> Then, we know that...

Math
The length of a rectangular garden is 2 feet longer than 3 times its width. The perimeter of the garden is 100 feet. We have to find the width and the length of the garden. The perimeter of a...

Math
The circumference of a circle with a radius equal to r is given by the expression 2*pi*r. Here, we are given the circumference and have to find the radius. Let the radius be r 2*pi*r = 72*pi =>...

Math
We can solve y=(2+4x^2)^3 in two ways. One is use the chain rule y=(2+4x^2)^3 y' = 3*8x*(2 + 4x^2)^2 => y' = 24x*( 4 + 16x^4 + 16x^2) => y' = 96x + 384x^5 + 384x^3 Else expand (2+4x^2)^3...

Math
We have to simplify (x^2y^2+2x+1)/[(x+y)^2+2(x+y)+1] (x^2y^2+2x+1)/[(x+y)^2+2(x+y)+1] => (x^2y^2+2x+1)/(x + y + 1)^2 => (x^2 +2x+1  y^2)/(x + y + 1)^2 => [(x + 1)^2  y^2]/(x + y +...

Math
The point (2 , 3) lies on the graph f(x) and g(x). So we have 3 = a*2 + b  9 and 3 = 2*b*2  a This gives us two equations to solve for a and b. 2a + b = 12...(1) 4b  a = 3 ...(2) 4b  a = 3...

Math
We have to determine the result of the difference of fractions. This can be done by equating the denominator in both the fractions and subtracting the terms in the numerator. If possible the final...

Math
We have to find the area of the triangle with sides 8, 15, 17 without using Heron’s formula. If we have a look at the sides, see that 8^2 = 64, 15^2 = 225 and 17^2 = 289. Now, 64 + 225 = 289...

Math
We have to find lim x> inf, [1/(x  sqrt(x^2 + 2x))]. [1/(x  sqrt(x^2 + 2x))] => (x + sqrt(x^2 + 2x)/ (x  sqrt(x^2 + 2x)* (x + sqrt(x^2 + 2x) => (x + sqrt(x^2 + 2x)/ x^2  x^2  2x...

Math
The expenditure on the project is the function E(x). We have E'(x) = 12x + 3 wher x denotes the number of days since the project started. For a project that takes 6 days, the expenditure is the...

Math
We have to prove that: tan [i*log (aib/a+ib)] = 2ab/(a^2  b^2) Start with denoting a + ib in the form r*( cos x + i sin x) Equate the real and complex components to get r*cos x = a and r*sin x =...

Math
The lines can be written in the slope intercept form y = mx + c x 3y  2 = 0 => 3y = x  2 => y = x/3  2/3 The slope is 1/3 2x + y  5 = 0 => y = 2x + 5 The slope is 2 As the slope of...

Math
For an arithmetic progression, the nth term is given by: a + (n  1)*d , where a is the first term and d is the common difference. Here the first term is given as 2 and we have the fifth term as...

Math
The electric bill is twice higher than the selling price. This makes the electric bill three times the selling price. If the electric bill is E and the selling price is S, E = 3*S The selling price...

Math
Let the length be L and the width be W Given that the length is 12 more than the width. ==> L = 12+ W.............(1) Also, given that the area is 4 times the perimeter. ==> A = 4*P ==>...

Math
We have to express the given expression 5/(x^25x+6) as partial fractions. 5/(x^25x+6) => 5 / ( x^2  3x  2x + 6) => 5/ ( x(x  3)  2( x  3)) => 5/ (x  2)(x  3) => A / (x  2) +...

Math
Given that : ln a = 2 ln b = 3 We need to find the values of ln a^2/b^3 We will use the logarithm properties to solve. We know that ln a/b = ln a  ln b Then we will simplify: ln a^2/b^3 = ln a^2 ...

Math
We have the sides of the triangle given as 3, 5 and 6. We find the area using Heron's formula as sqrt [ s*(sa)(sb)(sc)] s = (3 + 5 +6)/2 = 7 sqrt [ s*(sa)(sb)(sc)] => sqtr [...

Math
Given that g(x) = (x2)/(x^24) We need to find the integral of g(x). First we will simplify. g(x) = (x2)/(x2)(x+2) = 1/(x+2) ==> g(x) = (x+2)^1 Now we will integrate. ==> Intg g(x) dx =...

Math
2x+ 2y = 5...........(1) x  3y = 2 ..........(2) We will use the substitution method to solve. From (2) we will re write x= 3y2 Now we will substitute into (1). ==> 2x +2y = 5 ==> 2(3y2)...

Math
We have 2z  3 + i = (3i)/(2+4i). We have to find z and z. 2z  3 + i = (3i)/(2+4i) => 2z  3 + i = (3i)(2  4i)/(2+4i)(2  4i) => 2z  3 + i = (3i)(2  4i)/(4+16) => 2z  3 + i =...

Math
f'(x) = x^2 5x 3 We need to find f(x). We know that f(x) = integral of f'(x). ==> f(x) = Int ( x^2 5x 3) dx = Int (x^2) dx  Int (5x) dx  Int 3 dx = x^3/3 ...

Math
We have the line y= 3x+2 and the curve g(x) = 2x^2 3x2 We need to find the points of intersection between g(x) and the line y. Then, we know that the points of intersection must verify the...