Let x = length, which is also the shared side. The width will be (200-3x)/4. Area = (l x w) A = x(200-3x/4) A = 50x - 3x2/4 take the first derivative, set = zero and solve for x 50-3x/2 = 0 x = 100/3

what dimensions should be used to make the gardens, and what will the largest area possible be? (answer)

Let x = length, which is also the shared side. The width will be (200-3x)/4. Area = (l x w) A = x(200-3x/4) A = 50x - 3x2/4 take the first derivative, set = zero and solve for x 50-3x/2 = 0 x = 100/3

A = (pi)r2 = (3.14)(9)2 = 254.34 km2

430/3 = 143.33sq ft of carpeteting Area square = side2 so 143.33 = x2 x= 11.97

0 < x < 17.3

19/4x+1 = 9x+1/5x-1 (answer)

Use cross multiplication: 19(5x-1) = (4x+1)(9x+1) 95x - 19 = 36x2 + 13x + 1 36x2 - 82x + 20 = 0 18x2 - 41x + 10 = 0 solve with the quadratic formula [41 +/- √(412 - 4(18)(10))]/(2(18) (41...

Let x = width, then 3x = length, Area = l x w so, (3x)(x) = 75 3x2 = 75 x = 5 = width, length = 15 Perimeter = 2l +2w = 10 + 30 = 40

Let x = the length of the square cut out of each corner. Then the length/width of our box is 18-2x. To find volume we use LxWxH or: (18-x)(18-x)(x) = x3 -36x2 + 324x Take the first derivative and set it equal to zero to mind the critical values: 3x2...

40p + 55 = 695 (answer)

To solve an equation, you need to isolate the variable on one side: 40p + 55 = 695 First subtract 55 from each side 40p = 640 now diveide both sides by 40 p = 16

Find the cost of the marble tabletop (answer)

The table is 8 ft in diameter, or has a 4 ft radius = 4/3 yards Area = Pi(r2) = 3.14(4/3)2 = 5.58 sq yds x $81 = $452.16

how do you graph a parabola (answer)

y = x2 - 2x - 3 Complete the square and put into vertex format y = (x2 -2x +1) -3 -1 y = (x-1)2 -4 The vertex is at (1, -4) the y intercept is (0, -3) and the x intercepts are at (-1,0) AND (3,0)

f(g(x)) = [√(x+4)]2 +5 = (x + 4) + 5 = x + 9

Let x = distance traveled by the prop plane after the jet takes off, then 400 + x is the distance the jet flies (x plus the distance the prop plan travels in 2 hrs. Since they will arrive at the same point at some time (t), and t=d/r then we set d/r for each pane equal to each other and...

Tom is going to carpet his 12 by 10 foot room how many square feet of carpeting does tom need (answer)

12 x 10 -120 sq ft of carpeting

The force of the firecracker will act equally on both hockey pucks. Since the mass of both is the same, then their velocities will be equal as well, just in opposite directions.

0.105x + 0.07(18,000 − x) = 1,505 (answer)

0.105x + 1260 - .07x = 1505 .175x = 245 x = 1400

n=4 f(1)=-234 zeros 3 and 4i (answer)

N=4 means a 4th degree polynomial that would have 4 roots. Since 4i is a given root then -4i must also be a root. Let the fourth root = a. We can set up the polynomial by multiplying the 4 corresponding factors: f(x) = (x-3)(x-a)(x+4i)(x-4i) and simplify...

Shift right 10 and reflect over the x axis

Right 4 units and stretch vertically (f, l)

Math question (answer)

1 hr = 60 minutes = 3600 seconds So in 1 hr: 4,200,000 x 3600 = 15,120,000,000 1 year = 365 days x 24 = 8760 hours so in 1 year: 15,120,000,000 x 8760 = 132,451,200,000,000

Sine is always positive in the 1st and second quadrants, so to find a angle in the 2nd quadrant (since 3pi/8 is in the first quadrant) simply subtract it from pi pi - 3pi/8 = 5pi/8

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