Answer:
Step-by-step explanation:
Let
Side of square base=x
Height of rectangular box=y
Area of square base=Area of top=
Area of one side face=
Cost of bottom=$9 per square ft
Cost of top=$5 square ft
Cost of sides=$4 per square ft
Total cost=$204
Volume of rectangular box=
Total cost=
Substitute the values of y
Differentiate w.r.t x
It takes positive because side length cannot be negative.
Again differentiate w.r. t x
Substitute the value
Hence, the volume of box is maximum at x=2.2 ft
Substitute the value of x
Greatest volume of box=
<span> x = 5/6 = 0.833.................</span>
This is one example of a trinomial with a leading coefficient of 3 and a constant term of -5
This is an exponential growth/decay problem. It has a formula, and it doesn't matter which you have...the formula is the same for both, except for the fact that you're rate is decreasing instead of increasing so you will use a negative rate. The formula is this: A = Pe^rt, where A is the ending amount, P is the beginning amount, e is euler's number, r is the rate at which something is growing or dying, and t is the time in years. Our particular formula will look like this: A = 2280e^(-.30*3), Notice we have a negative number in for the rate (and of course it's expressed as a decimal!). First simplify the exponents: -.30*3 = -.9. On your calculator you have a 2nd button and a LN button. When you hit 2nd-->LN you have "e^( " on your display. Enter in -.9 and hit enter. That should give you a display of .4065695. Now multiply that by 2280 to get 926.98, the value of the computer after it depreciates for 3 years at a rate of 30% per year.
We use FOIL method to multiply this out. First termsOuter termsInner termsLast terms Product = (3m3 * 3m3) + (3m3 * -1/2y) + (-1/2y * 3m3) + (-1/2y * -1/2y) Product = 9m6 - (3/2)m3y - (3/2)m3y + (1/4)y2 <span>Product = 9m6 - 3m3y + (1/4)y<span>2</span></span>
