# Math Homework Help

### Showing All Questions Answered Popular Recommended Unanswered Editor's Choice in Math

• Math
Since the problem provides the coordinates of the vertices, hence, you should evaluate the area of triangle using the following formula: `A = (1/2)*|[[x_A,y_A,1],[x_B,y_B,1],[x_C,y_C,1]]|` `A =...

Asked by lightjazz on via web

• Math
You should find the equation of the line that is perpendicular to the segment that connects the point `(2,2)` to the point on the line `y=-4` . You need to find first the equation of the segment...

Asked by bubbletrea on via web

• Math
You need to determine the internal dimensions of the tank, converting to cm the given thickness of 0.02 m such that: height = `100 - 2 = 98 cm` wide = `75 - 2*2 = 71 cm` deep = `50 - 2*2 = 46 cm`...

Asked by cherlinlee on via web

• Math
The average rate of change of a variable X over a given duration of time t is the difference between the initial value of the variable `X_0` and the final value of the variable `X_t` divided by t....

Asked by zala96 on via web

• Math
Let the distance to Las Vegas is X km. In the return trip the jet took 12 hours at an average speed of 309km/h. Distance = speed * time X = 309km/h*12h = 3708km So for the going trip if the...

Asked by insanity15 on via web

• Math
f(x)= (tan^4(4x)+sin(7x^3-4x+1)) Here we need to know the following. `(d(tanf(x)))/dx = sec^2f(x)*f'(x)` `(d(sinf(x)))/dx = cosf(x)*f'(x)` f’(x) `=...

Asked by miker124 on via web

• Math
`9cos^2(x)-2cos(x)-3=0` Let cosx = t Then; `9t^2-2t-3 = 0` `t = [-(-2)+-sqrt((-2)^2-4*9*(-3))]/(2*9)` So t = 0.699 OR t = -0.476 If t = 0.699; cosx = 0.699 `cosx = cos 0.253pi` General solution for...

Asked by lukassa on via web

• Math
The function f(x) is such that f'(x) = x^3 and the line x + y = 0 is a tangent to the graph of the function. f(x) = `int f'(x) dx` => `int x^3 dx` => `x^4/4 + C` As the line x + y = 0,...

Asked by chocobob on via web

• Math
For a function f(x) the tangent at any point is given by f’(x). F’’(x) = 6x F’(x) = `int f’’(x) dx` = `int 6x dx` = `3x^2+C` where C is a constant F(x) = `int f’(x)` dx = `int...

Asked by bobbyjimbo on via web

• Math
The function f(x) has to be determined such that f''(x) = -5x and f(x) has a relative maximum at (2, 3) f''(x) = -5x f'(x) = `int f''(x) dx` => `int -5x dx` => `(-5*x^2)/2 + C` As...

Asked by goldbergfan on via web

• Math
`G(x)=2sin^(-1) (sqrtx/2)` `F(x)=sin^(-1)((x-2)/2)` To determine the derivative of the two functions, use the formula `d/(du)sin u = 1/sqrt(1-u^2)*u'` . So G'(x) is: `G'(x) =...

Asked by bogshow24 on via web

• Math
`G(x)=2sin^(-1)(sqrtx/2)` (1) To determine G'(x), use the formula `d/(du) sin^(-1)u= 1/sqrt(1-u^2)*u'` . `G'(x)= 2*1/sqrt(1-(sqrtx/2)^2)*(sqrtx/2)'` `G'(x)=2/sqrt(1-x/4)*1/2*1/(2sqrtx)`...

Asked by bllybony on via web

• Math
1) You need to differentiate the given function with respect to x, using the chain rule, such that: `F'(x) = (1/(sqrt(1 - (x-2)^2/4)))*((x-2)/2)'` `F'(x) = 2/(2sqrt(4 - (x-2)^2)) => F'(x) =...

Asked by masterpiece56 on via web

• Math
`y =x^2+4` The first derivative of a function will give the gradient of the tangent line to the function at the point considered. So let us say the tangent line is y = mx+c It is given that...

Asked by swimmers on via web

• Math
The function f(x) = `x + sqrt x` . The slope of the line tangent to f(x) at the point where x = a is given by f'(a). f'(x) = `1 + 1/(2*sqrt x)` At x = 25, f'(x) = `1 + 1/10` The slope of the...

Asked by soccerfan55 on via web

• Math
(a) d/dx ((e^(x^3))+(log base 3 of pi)) Let y = ((e^(x^3))+(log base 3 of pi)) We know ; `(d(e^f(x)))/dx = e^f(x)*f'(x)` d(a)/dx = 0 where a is a constant. `dy/dx = e^(x^3)*3x^2+0 =...

Asked by rugby4life on via web

• Math
`f(x)=2ln(secx+tanx)` To start, take the first derivative of f(x). Use the formula `d/(du) lnu =1/u*u'` . `f'(x) = 2*1/(secx+tanx)*(secx+tanx)'` `f'(x)=2/(secx+tanx)*(secx+tanx)'` Then, take the...

Asked by hockeyfan54 on via web

• Math
`f(x) = (2sqrtx) lnx` To solve for f'(x), let's use the product formula of derivatives which is `(u*v)' = uv' + u'v ` . So let, `u=2sqrtx` and v`=lnx`...

Asked by master451 on via web

• Math
`f(x) = 3cos(x)*sin^(-1)(x)` To determine f'(x), use the product formula of derivatives which is `(uv)' = uv'+u'v` . So let, `u=3cos(x) ` and `v=sin^(-1) (x)` To...

Asked by mrbest55 on via web

• Math
`f(x)= sec^(-1) (7^x)` To take the derivative of f(x) use the formula `d/(du)sec^(-1)u= 1/(usqrt(u^2-1))*u'` . `f'(x) = 1/(7^xsqrt((7^x)^2-1))*(7^x)'` `f'(x)= 1/[7^xsqrt(7^(2x)-1)]*(7^x)'` To take...

Asked by veteran25 on via web

• Math
`y= tan^-1sqrt((4x^2)-1)` `tany = sqrt((4x^2)-1)` Derivate both sides with respect to x; `Sec^2y*(dy)/dx = 1/{2*[ sqrt((4x^2)-1)]}*8x` `dy/dx = 4x/[ sqrt((4x^2)-1)*sec^2y]` `Sec^2y` `= 1+tan^2y`...

Asked by masterpiece11 on via web

• Math
The function `f(x)=e^(3x)+7cos x*sin x`. The derivative of f(x) is: f'(x) = `3*e^(3x) + 7*(cos^2x - sin^2x)` => 3*e^(3x) + 7*cos 2x f''(x) = `9*e^(3x) - 14*sin 2x` The second derivative of...

Asked by sportsmaniac on via web

• Math
Here we need to know the following; If f(x) and g(x) are two function of x then; `(d((f(x)*g(x))))/dx = g(x)*(d f(x))/dx+ f(x)*(d g(x))/dx` `(d(f(x)/g(x)))/dx =...

Asked by blasto63 on via web

• Math
`f(x) = 8x^5sqrtx+ 4/(x^2sqrtx)` To simplify f(x), express the radicals as exponents. Note that `sqrtx=x^(1/2)`. `f(x) = 8x^5*x^(1/2) + 4/(x^2*x^(1/2))` Then, use the rule of exponents for...

Asked by bobby9901 on via web

• Math
`tan^2 x=3tanx` To start, subtract both sides by 3tanx. `tan^2x-3tanx=0` Factor left side. `tanx(tanx-3) = 0` Set each factor to zero and solve for x. >> `tan x = 0` `x=...

Asked by obennett12 on via web

• Math
Solving an inequality is similar to solving an equation except when multiplying or dividing by a negative changes the inequalities. `6(-2x-5)<-16-5x` distribute on the left side...

Asked by kittyremis on via web

• Math
A function `h(x)` is even if `h(-x)=h(x)` , or odd if `h(-x)=-h(x)` . Substitute `-x` into the function and we get: `h(-x)` `=-{(-x)^3}/{6(-x)^2-5}` `=-{-x^3}/{6x^2-5}` `=-h(x)` The function is...

Asked by mcelwee5 on via web

• Math
Graph `g(x)=4^(x-1)+5` The base function is `y=4^x` The exponent `x-1` shifts the base function 1 unit to the right. (Horizontal translation) The term +5 shifts the graph up 5 units. (vertical...

Asked by wideopen2424 on via web

• Math
Given the function: `f(x)= 4x^2 - x - 3` We need to find the domain of the function f(x). The rule of the domain of polynomial is clear. If the function is a polynimial, then, the domain is all...

Asked by stargsd5 on via web

• Math
The average rate of change is the difference in y-values divided by the difference in x-values. This means that `{Delta y}/{Delta x}={f(x)-f(1)}/{x-1}` `={x^3-x-(1^3-1)}/{x-1}` `={x^3-x}/{x-1}`...

Asked by stargsd5 on via web

• Math
When reflecting the function in the x-axis, we replace x by -x, to shift down by 7 we subtract 7 from the function and to shift left by 8, we replace x by x+8. This means that the function `y=2^x`...

Asked by stargsd5 on via web

• Math
For the function `f(x)=5(x+1)^2+1` , we can identify each transformation from the function `g(x)=x^2` . The 5 is a vertical stretch by a factor of 5, the 1 inside the brackets is a shift of 1 to...

Asked by stargsd5 on via web

• Math
The transformations are applied to the base graph `f(x)=|x|` . The -4 is a vertical reflection and vertical stretch of a factor of 4. The +2 is a vertical shift up by 2. The transformations can...

Asked by stargsd5 on via web

• Math
The graph of the function `y = -tan(x/2) + 2` for `-2*pi<=x<=3*pi` is required. The graph of y = tan x is: y = -tan x has a graph: y = -tan(x/2) has the following graph: And...

Asked by foxwit on via web

• Math
The two lines given are 2x - 3y = 18 and 6x - 9y = 18 2x - 3y = 18 => y = (2/3)x - 6 6x - 9y = 18 => y = (6/9)x - 2 = (2/3)x - 2 The slope of the lines is the same, therefore they are...

Asked by pizza35 on via web

• Math
The equation of the line passing through the points (-2, 3) and (3, 4) has to be determined. The equation of a line passing through (a1, b1) and (a2, b2) is given by `(y - b2)/(x - a2) = (b1 -...

Asked by burger45 on via web

• Math
The graph of the relation x^3 + y^2 + 6 = 0 is required. x^3 + y^2 + 6 = 0 => y^2 = -x^3 - 6 => `y = sqrt(-x^3 - 6)` and `y = -sqrt(-x^3 - 6)` The graph of these functions is:

Asked by lxsptter on via web

• Math
The roots of the cubic equation x^3+3x^2-46x+72 = 0 have to be determined. x^3+3x^2-46x+72 = 0 => x^3 + 9x^2 - 6x^2 - 54x + 8x + 72 = 0 => x^2(x + 9) - 6x(x + 9) + 8(x + 9) = 0 => (x^2 -...

Asked by lxsptter on via web

• Math
The equation x^4 - 13x^2 + 36 = 0 has to be solved. This is a bi-quadratic equation with 4 roots. x^4 - 13x^2 + 36 = 0 => x^4 - 9x^2 - 4x^2 + 36 = 0 => x^2(x^2 - 9) - 4(x^2 - 9) = 0 =>...

Asked by lxsptter on via web

• Math
Let the trapezoid be named ABCD with `bar(AB)||bar(CD)` . (1) Since the trapezoid is convex, in order for a circle to be inscribable in the trapezoid we must have `AB+CD=AD+BC` (2) The midline...

Asked by nishantmcg on via web

• Math
Notice that the given angle `hatA` is an included angle, hence, you may use the law of cosines to find the missing length such that: `(BC)^2 = (AB)^2 + (AC)^2 - 2AB*AC*cos 60^o` You need to...

Asked by mccee on via web

• Math
You should regroup the factors such that: `(((sin(pi/16)*cos(pi/16))*cos(pi/8))*cos(pi/4))` Notice that if you multiply `sin(pi/16)*cos(pi/16)` by `2` yields: `2sin(pi/16)*cos(pi/16) =...

Asked by mouhham on via web

• Math
You should notice that `x o y = xy - 3x - 3y + 12` , hence, you need to substitute `x*x - 3x - 3x + 12` for `x o x` in equation `x o x = x` such that: `x*x - 3x - 3x + 12 = x => x^2 - 6x + 12...

Asked by gaston55 on via web

• Math
You need to evaluate the limit of definite integral such that: `lim_(x->oo) (1/x^2)* int_0^x f(t) dt` Since the problem provides the equation of the function, then you need to substitute `(cos t...

Asked by chimpagi on via web

• Math
You need to prove the given reccurence relation `I_n +I_(n-1) = (a^n)/n` . Supposing that `I_n = int_0^a (t^n)/(t+1) dt` , hence, `I_(n-1) = int_0^a (t^(n-1))/(t+1) dt` You need to add the...

Asked by pakkati on via web

• Math
You should remember how you may find the coordinates of the centroid of a triangle ABC such that: `x_G = (x_A + x_B + x_C)/3` `y_G = (y_A + y_B + y_C)/3` You may find the coordinates of vertices A...

Asked by cane25 on via web

• Math
You need to express the general terms of this summation as `n(n+2)` , hence, opening the brackets yields: `n(n+2) = n^2 + 2n` `sum_(n=1)^10000 (n^2 + 2n) = sum_(n=1)^10000 n^2 + sum_(n=1)^10000...

Asked by happyhelper77 on via web

• Math
You should change the bases of logarithms using the logarithmic identity `log_a b = 1/(log_b a)` such that: `log_x 2 = 1/(log_2 x)` `log_(sqrt x) 2 = 1/(log_2 sqrt x) => log_(sqrt x) 2 =...

Asked by joinmcblue on via web

• Math
Let, A - # of people in Room A B - # of people in Room B The total number of people in A and B is 1200. So we have, `A+B=1200` (EQ.1) > Then, let's consider the number of...

Asked by yogz13 on via web