
Math
The equation `0.45x+0.50.5x=0.10*(19)` has to be solved for x. `0.45x+0.50.5x=0.10*(19` ) add all the terms containing x in the left hand side =>` 0.05x + 0.5 = 1.9` => `0.05x = 2.4`...

Math
You need to fit the sphere inside the cube, hence, the diameter of sphere needs to be equal to the side of cube such that: `D = a` D represents the diameter of the sphere a represents the side of...

Math
You need to evaluate `A^2` to check if a pattern comes up and this could be used later on, such that: `A^2 = A*A` `A^2 = ((3,0),(0,3))*((3,0),(0,3))` `A^2 = ((3*3+0*0 , 3*0+0*3),(0*3+3*0 , 0*0 +...

Math
The function o and * are defined as: xoy=xy3x3y+12 and x*y=x+y3 1o(2*3) 1o(2 + 3  3) = 1o2 =1x2  3x1  3x2 + 12 = 2  3  3 + 12 =14  6 = 8...(1) (1o2)*(1o3) (1x2  3x1  3x2 + 12)*(1x3 ...

Math
You need to check the inequality and not to solve it, since computing the definite integral yields a value that does not depend on x. Hence, you need to verify if `int_1^2 e^x*f_0(x)dx =lt e(e1)`...

Math
You should notice that `3 + 2sqrt2 ` is expansion of squared binomial `(1+sqrt2)^2` such that: `(1+sqrt2)^2 = 1 + 2sqrt2 + 2` `(1+sqrt2)^2 = 3 + 2sqrt2` Hence, `sqrt(3 + 2sqrt2) = sqrt((1+sqrt2)^2...

Math
There's no getting around the fact that you will have to work with trig in order to be successful with it. However, there are some tricks you can remember in order to make it easier. (1) Always...

Math
Remember, all sides are = on a cube.Surface area is the area of each side of a figure, added together. As a cube has 6 sides, take the total surface area and divide by 6 to find the area of one...

Math
Most likely this question was asked by your instructor with the intention of you researching local interest rates and account types available. Interest rates and account types vary by state,...

Math
It is certainly possible to find mathematical connections in almost every area. In the fine arts, you might look for equations or a statistical analysis of how a particular artist paints. For...

Math
I'm going to assume the vector is 3dimensional, but you can do this in any dimension. Say `vecK=<x,y,z>` Then `vecK=sqrt(x^2+y^2+z^2)` (this is the "magnitude" of K) The vector...

Math
Breakeven value is when the cost of production equals the revenue earned. No profit is earned. Therefore, you need to set the production cost = revenue earned. Defining the variable, x=products...

Math
The equation `log_9 (x5) + log_9 (x+3)=1` has to be solved. Use the property of logarithms log a + lob = log(a*b) `log_9 (x5) + log_9 (x+3)=1` => `log_9(x  5)(x + 3) = 1` => (x  5)(x +...

Math
The function `f(x)= 3x+5` and `h(x)= 3x^2 +3x + 2` . A function g(x) has to be determined such that `f@g(x) = h(x)` => `f(g(x)) = 3x^2 +3x + 2` => `3*g(x) + 5 = 3x^2 +3x + 2` One function...

Math
The function `f(x)=3x^24x+1` . `lim_(h>0) (f(1+h)f(1))/h ` => `lim_(h>0)(3*(1+h)^24*(1+h)+1  3*(1)^2+4*(1)1)/h` => `lim_(h>0)(3*(1+h  1)(1 + h + 1) + 4  4h + 1  4...

Math
For `f(t)=4t^2+3t+1` `lim_(h>0)(f(t+h)f(t))/h` => `lim_(h>0)(4(t+h)^2+3(t+h)+1  4t^23t1)/h` => `lim_(h>0)(4(t+ht)(t+h+t) + 3(t + h  t) + 1  1)/h` =>...

Math
The function `f(x) = (x^2 1)/(x^2 +1)` `y = f(x) = (x^2 1)/(x^2 +1)` => `yx^2 + y = x^2  1` => `yx^2  x^2 = 1  y` => `x^2 = (1  y)/(y  1)` => `x = sqrt((1 +y)/(1  y))` and...

Math
g(x) = 2x + 10 for `x<=2` x^2 for `2<x < 2` and 4 for `x > 2` At x = 2 `g(2) = 6` `lim_(x> 2) g(x) = 4` As the two are not equal the function is discontinuous at x...

Math
To answer this question, you would need to provide additional information. Is there a federal tax rate such as 33%, etc.? Most likely, in your assignment, there is a tax chart by which you can...

Math
The future value, F is given by, `F= P(((1+i)^n 1)/i)` P is the periodic installment, i is the interest rate for the period and n is the number of periods. `F= 5000(((1+0.04)^30 1)/0.04)` `F=...

Math
The future value of periodic investments is given by, `F = P (((1+i)^n1)/i)` Where, F  Future value P  Periodic investment i  Interest rate for the period n Number of periods In this case,...

Math
The number of employees in 2004 `= 68` The number of employees in 2014 `= 170` The increase in employees `= 17068 = 102` The percent increase wrt 2004 `= 102/68 xx 100 %`...

Math
The sum of the digits of a 2digit number is 14. If 29 is subtracted from the number, the digits of the resulting number are the same. If the number is represented by xy, x + y = 14 => x = 14 ...

Math
It is given that 1 USD = 0.64662 GBP and 1GBP = 1.23534 Euro. The number of Euros equivalent to 1 USD has to be determined. 1 USD = 0.64662 GBP, substitute 1 GBP = 1.23534 Euro in the first...

Math
The equation of the line perpendicular to 3x + 2y = 8 and passing through (6, 1) has to be determined. Use the property that the product of the slope of two perpendicular lines is equal to 1. 3x...

Math
The roots of 4x^2 + 7x + 3 = 0 have to be determined using factorization. 4x^2 + 7x + 3 = 0 => 4x^2 + 4x + 3x + 3 = 0 => 4x(x + 1) + 3(x + 1) = 0 => (4x + 3)(x + 1) = 0 (4x + 3) = 0 =>...

Math
You need to remember that the form of equation of vertical asymptote is x = a and f(a) does not exist. Hence, since the equation of the function is a fraction, then the function does not exist for...

Math
The identity `cos (x/2)=sqrt ((1/2)(1 + cosx))` has to be proved. `cos (x/2)=sqrt ((1/2)(1 + cosx))` let `x/2= y` , this gives the identity to be proved as `cos y = sqrt((1 + cos 2y)/2)` `sqrt((1...

Math
Supposing that the problem provides the measure of angle in degrees, hence `cos (1/4)^o = 0.999.` You need to evaluate the inverse of trigonometric function tangent such that: `tan^(1)(cos(1/4)^o)...

Math
Let the point of intersection of CP and AQ be R. If you draw a diagram you would see that, Consider APR and CQR traingles `Ahat(P)R = Chat(Q)R` (Given) `Chat(R)Q = Ahat(R)P` This gives,...

Math
`A = 2y^2+by` `2y^2+by = A` Divide both side by 2. `y^2+b/2y = A/2` I am going to make this a complete quadratic equation. `y^2+b/2y+(b/4)^2 = A/2+(b/4)^2` This gives, `(y+b/4)^2 = A/2+b^2/16`...

Math
Write the levels of the two factors as indicator variables. Choose a baseline level combination eg`` "a" for the first combined with "1" for the second variable. Then you will have vector indicator...

Math
First just draw a cylinder with radius a through the center of the cone without taking the materials out. Now there would be a location at which the cone's radius (Not the base radius, but let's...

Math
The graph of the function `y=(1/2)*cos((3/4)*x)` is: The maximum value of the function is (1/2). The minimum value is (1/2). The xintercepts can be determined by solving `cos((3/4)*x) = 0`...

Math
Note: `f@g(x) = f(g(x))` This means, where you used to see an "x" in the equation for f(x), now plug in "g(x)" To find `f^(1)(x)` First start with your equation, then switch the x and the y, then...

Math
The equation `(x^2+x^2)/(x+1)^2=3` has to be solved for x. `(x^2+x^2)/(x+1)^2=3` => `(x^2+x^2) = 3*(x+1)^2` => `2x^2 = 3x^2 + 6x + 3` => `x^2 + 6x + 3 = 0` `x1 = (6 + sqrt(36  12))/2 =...

Math
The function `f(x) = y= 3x + 4` . Isolate x and express it in terms of y. `y= 3x + 4` => `3x = y  4` => `x = (4  y)/3` => `f^1(x) = (4  x)/3` The domain and range of `f^1(x)` is...

Math
The radius is `(1)/(2)` the diameter.The diameter is 2.5, so the radius is 1.25The volume of a cylinder is`V=pi r^2 h`where r is the radius, h is the height, and V is the volumeSo for us,`V= pi...

Math
`f@g(x)=f(g(x))` `f(g(x))=1(g(x))^2` `=1(7x6)^2` `=1(49x^284x+36)` `=49x^2+84x35` `g@f(x)=g(f(x))` `g(f(x))=7f(x)6` `=7(1x^2)6` `=77x^26` `=17x^2` `f(x)=3x+5` Think of this...

Math
I think you have indicated C, the circumference. The circumference of a circle is given by following equations. `C = 2pir` Since `d = 2r` `C = pid` Therefore, `C/d = (pid)/d = pi` The answer...

Math
The identity tan A + 2*tan 2A + 4*tan 4A + 8*cot 8A = cot A has to be proved. If tan A + 2*tan 2A + 4*tan 4A + 8*cot 8A = cot A => tan A + 2*tan 2A + 4*tan 4A + 8*cot 8A  cot A = 0 Using the...

Math
The problem suggests that the triangle has no equal sides or angles, hence, the triangle ABC is scalene. Since the angle A is opposed to the side BC, you may use the law of cosines to evaluate its...

Math
Are you familiar with FOILing two binomials? F=first termsO=outside termsI=inside termsl=last terms FOIL the expression (a+b)(ab). F=(a)*(a)=a^2O=(a)*(b)=(ab)I=(b)*(a)= (ab)L=(b)*(b)=b^2 You...

Math
The annual income of A and B are in the ratio 3 : 4. If the income of A is 3x, the income of B is 4x. Their annual expenditure is in the ratio 5:7, if A's expenditure is 5y, B's expenditure is 7y....

Math
`int_oo^oo x e^(x^2) dx` Let's ignore the endpoints for a moment and just find an antiderivative for: `x e^(x^2)` This is a usubstitution problem:`u=x^2` `du=2xdx` `(1)/(2) du = xdx` And...

Math
`y = int(ln(x)+2)^2/xdx` Let `u = ln(x)` , then, `du = 1/x dx` Then the integral changes into, `y = int(u+2)^2du` This gives, `y = (u+2)^3/3 +c ` Where c is an arbitrary constant. Replacing u,...

Math
`(d^2y)/(dx^2)  3(dy)/(dx) + 2 = x^2` To find the general equation, we can find the characteristic equation first. `lambda^23lambda+2 = 0` `(lambda1)(lambda2) = 0` This gives `lambda = 1 or...

Math
I think part of problem 1 got cut off. `"cos" (x+y) = "cos"x "cos" y  "sin" x "sin" y` `"cos" (xy) = "cos"x "cos" y + "sin" x "sin" y` So:`"cos" (x+y) "cos" (xy) = ("cos"x "cos" y  "sin" x...

Math
`f(x)=x^210x` is a parabola opening down. Graphically: The range is the possible yvalues that can be obtained. For an upsidedown parabola, you can't get reach any yvalue taller than...

Math
`f(x)=(x+"sin" x)/("cos" x)=(x)/("cos" x) + "tan" x` To differentiate `(x)/("cos" x)` , you can use the quotient rule: `d/dx((x)/("cos" x)) = ((x)'("cos" x)(x)("cos" x)')/(("cos" x)^2)`...