1) h(t)=20(5/8) - 16(5/8)^2 + 10 = 65/4
All I need to know for this is how to calculate the fraction parts to get 65/4. I am not good with fractions.
2) A manufacturer's profit from producing x units of a product is given by P(x)=0.002x^3 - 0.01x^2 + 0.5x. At what production level(s) will the marginal profit be $9.30 per unit. Enter just an integer, no units.
the derivative would be p(x)=0.006x^2 - 0.02x + 0.50. Then would I just plug in 9.30 to x?
1) (5/8)^2 = (5/8)(5/8) = 25/64
h(t) = 100/8 - 16 (25/64) + 10 =
800/64 - 400/64 + 640/64 = 1040/64 = 65/4
2) I would just plug the value in, but I don't know which equation you want to use.
so 0.006(9.30)^2 - 0.02(9.30) + 0.50
For the first question how did you get 800/64 and 640/64?
The 20*(5/8)^2= 20*25/64
The 640/64 came from 10= 10*64/64
1) To calculate the fraction part of the expression h(t) = 20(5/8) - 16(5/8)^2 + 10 = 65/4, you can follow these steps:
Step 1: Simplify the individual fractions:
- 20(5/8) = (20 * 5)/8 = 100/8 = 25/2
- 16(5/8)^2 = 16 * (5/8)^2 = 16 * (5/8 * 5/8) = 16 * (25/64) = (16 * 25)/64 = 400/64 = 25/4
Step 2: Substitute the simplified fractions back into the expression:
h(t) = 25/2 - 25/4 + 10 = 65/4
Therefore, the fraction part of the expression is 65/4.
2) To determine the production level(s) at which the marginal profit is $9.30 per unit, you need to find the value(s) of x that satisfy the equation P'(x) = 0.006x^2 - 0.02x + 0.50 = 9.30.
Step 1: Set the derivative P'(x) equal to 9.30:
0.006x^2 - 0.02x + 0.50 = 9.30
Step 2: Rearrange the equation to form a quadratic equation:
0.006x^2 - 0.02x + 0.50 - 9.30 = 0
0.006x^2 - 0.02x - 8.80 = 0
Step 3: Solve the quadratic equation:
You can use the quadratic formula: x = (-b ± √(b^2 - 4ac))/(2a)
In this case, a = 0.006, b = -0.02, and c = -8.80.
x = (-(-0.02) ± √((-0.02)^2 - 4 * 0.006 * (-8.80)))/(2 * 0.006)
x = (0.02 ± √(0.0004 + 0.2112))/(0.012)
x = (0.02 ± √(0.2116))/(0.012)
x = (0.02 ± 0.4608)/(0.012)
Step 4: Calculate the possible values of x:
x = (0.02 + 0.4608)/(0.012) = 38.4/0.012 = 3200
x = (0.02 - 0.4608)/(0.012) = -0.4408/0.012 = -36.73 (approximately)
Therefore, the production level(s) at which the marginal profit is $9.30 per unit is 3200.