I need help in my math homework (Quadratic Functions)~~!?
A = 40x - x² a. when you are using the fencing to bound all four sides, you will obtain maximum area by designing a square (so width is 20). This only works for fencing on all four sides. to prove that in algebra, you would graph your function A = 40x - x², which looks like an upside down parabola, vertex (highest point) at x = 20. You could also do a table of values or use the derivative (calculus). b. maximum area is 400 ft².
Can you help me on my math homework? It's on quadratic functions.?
There's only 5 questions that I don't get on my homework. Can you show your work step by step? I really appreciate it. 1) Ling is cutting carpet for a rectangular room. The area of the room is 324ft^2. The length of the room is 3 feet longer than twice the width. What should the dimensions of the carpet be? Answer this with numerical dimensions. 2)If the sides of a square are lengthened by 5 meters, the area becomes 121m^2. Find the length of the original square. Answer this with numerical dimensions. 3) A number subtracted from its square is 110. Find the number. Solve by setting up your equation, setting equal to 0, and factoring. 4) A rectangular pool measures 4yd by 5yd. A concrete deck of uniform width is constructed around the pool. The deck and pool together cover an area of 90yd^2. How wide is the deck? Answer this with numerical dimensions. 5) A rectangular window pane has an area of 15x^2 - 19x + 6. The width of the window pane is 3x-2. What is the length of the window pane in polynomial form?
Math homework help! quadratic functions!?
Represent cost C(x) by : C(x) = ax² + bx + c We will arrive at three equations in a,b,c which we can solve. (1) When x = 2 , C(2) = a(2²) + b(2) + c = 45 (2) When x = 4, C(4) = a(4²) + b(4) + c = 81 (3) When x = 10, C(10) = a(10²) + b(10) + c = 285 So, 4a + 2b + c = 45 16a + 4b + c = 81 100a + 10b + c = 285 Subtracting 1st equation from 3rd 100a - 4a + 10b - 2b + c - c = 285 - 45 giving 96a + 8b = 240 Now subtract 1st equation from 2nd 16a - 4a + 4b - 2b = 81 - 45 giving 12a + 2b = 36 We have two equations in a and b 96a + 8b = 240 12a + 2b = 36 Simplifying 12a + b = 30 6a + b = 18 Subtracting 2nd from 1st 12a - 6a + b - b = 30 - 18 6a = 12 a = 2 We can now substitute this to find b and obtain b = 6 Similarly substitute a,b in one of the original equations to find c = 25 The quadratic is : C(x) = 2x² + 6x + 25 When x = 6, C(6) = 2(6²) + 6(6) + 25 = 72 + 36 + 25 = 133 To make 10 calculators it costs $133.
Quadratic functions; homework help?
Let x = the amount they increase their charges by Therefore the amount they charge this year = $20 + x The number of customers they have this year = 70 - x Therefore as their income = the charge multiplied by the number of customers, Total income = (20 + x)*(70 - x) Expand the brackets Total Income = 1400 - 20x + 70x - x^2 Simplify -x^2 +50x + 1400 The maximum amount is where x = -b/2a where b = 50 and is the coefficient of "x" and a = -1 and is the coefficient of "x^2" Therefore max is where x = -50/-2 x = 25 a) Therefore the club should charge $20 + x = $20 + $25 = $45 b) With the price set at $45, the number of customers = 70 - 25 = 45 Maximum income = $45 * 45 = $2025
Quadratic functions math help?
I am so confused by my math homework, can somebody help me please? 1.Find a function whose graph is a parabola with vertex (4, 6) and that passes through the point (3, −9). 2. A quadratic function is given. g(x) = 2x2 + 8x + 13 (a) Express the quadratic function in standard form. (it wants you to complete the square) 3.A soft-drink vendor at a popular beach analyzes his sales records and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by P(x) = −0.001x2 + 5x − 1875. What is his maximum profit per day? How many cans can he sell for max profit? Thanks
Math help!!! quadratic function =[?
x² - 16x + 56 = 0 So we first complete the square x² - 16x = -56 Take half of the middle term, square it, and add to both sides x² - 16x + 64 = -56 + 64 (x - 8)² = 8 And so: y = (x-8)² - 8 This is now in the form y = a(x-h)² + k where (h,k) is the vertex. So the vertex is: (8, -8) Have a good day!
Please help with my math homework. Quadratic functions and equations?
Erica has 20ft of chain link to make a rectangular cage for her pet rabbit. She will use all of the chain link, so the perimeter of the cage will be the same as the entire length. Let w represent the width of the cage in feet use w to write an expression for the length of the cage(Hint: Use the perimeter formula P=2l+2w and solve for length). Use your answer to question 2 to write a quadratic function for the cage's area, A, as a function of width, w.
Math Homework, Transforming Quadratic Functions.?
The position function for a free-falling object is given by h(t) = - 16t² + v0t + h0 where h = height in ft., t = time in secs., v0 = initial velocity in ft./sec. and h0 = initial height in ft.. Position Function for Drop 1: v0 = 0 ft./sec. h0 = 400 ft. h(t) = - 16t² + 400 Time to Impact: h(t) = 0: - 16t² + 400 = 0 16t² = 400 t² = 400 / 16 t² = 25 t = √25 t = 5 Time to Impact for Drop 1 = 5 secs. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ Position Function for Drop 2: h(t) = - 16t² + 1600 Time to Impact: 16t² = 1600 t² = 1600 / 16 t² = 100 t = √100 t = 10 Time to Impact for Drop 2 = 10 secs. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Math Quadratic Function Question?
The points of intersection are found by solving -3x^2 + 2x + 8 = x^2 - 4 -4x^2 + 2x + 12 = 0 2x^2 - x - 6 = 0 x = [1 +/- √( 1 - 4(2)(-6) ) ] / 2(2) x = [ 1 +/- √( 49) ] / 4 x = -3/2 and x = 2 f(-3/2) = g(-3/2) = 9/4 - 4 = (9 - 16)/4 = -7/4 f(2) = g(2) = 4 - 4 = 0 The two points are (-3/2,-7/4) and (2,0) Using the slope-intercept form and the point (2,0), you have y = mx + b 0 = 2m + b Using the slope-intercept form and the point (-3/2,-7/4) you have -7/4 = -3m/2 + b -7 = -6m + 4b The system is 2m + b = 0 -6m +4b = -7 The solution is m = 1/2 and b = -1 So the equation is y = (1/2)x - 1 Now check with a graphing calculator...
A quadratic function [math]3x^2 + px + q[/math] has the roots of -4 and 2, what is the value of p and q?
The quadratic function 3x^2+px+q has the roots of -4 and 2. What is the value of p and q?3x^2+px+q can be written as x^2+(p/3)x+(q/3) = 0(q/3) is the product of the roots and (p/3) is the sum or difference of the roots.So q/3 = (4)(-2) = -8, or q = -24p/3 = 4-2 = 2, or p = 6.Check: 3x^2+6x-24=03x^2+12x-6x-24 = 03x(x+4) -6(x+4) = 0(3x-6)(x+4) = 0x= 2 or -4. Correct.p = 6, q = -24.Another approach:3x^2+px+q = 0, has the roots of -4 and 2.Put x=-4 to get48–4p+q = 0 or-4p+q = -48…(1)Put x = 2 to get12+2p+q = 0, or2p+q = -12 …(2).Subtract (1) from (2) to get6p = 36 or p = 6.From (2), q = -12–2p = -12–12 = -24.So, p = 6, q = -24.