Surface area of box=1200 cm²
<span>Volume of box=s²h </span>
<span>s = side of square base </span>
<span>h = height of box </span>
<span>S.A. = s² + 4sh </span>
<span>S.A. = surface area or 1200 cm², s²
= the square base, and 4sh = the four 'walls' of the box. </span>
<span>1200 = s² + 4sh </span>
<span>1200 - s² = 4sh </span>
<span>(1200 - s²)/(4s) = h </span>
<span>v(s) = s²((1200 - s²)/(4s)) </span>
<span>v(s) = s(1200 - s²)/4 . </span>
<span>v(s) = 300s - (1/4)s^3</span>
by derivating
<span>v'(s) = 300 - (3/4)s² </span>
<span>0 = 300 - (3/4)s² </span>
<span>-300 = (-3/4)s² </span>
<span>400 = s² </span>
<span>s = -20 and 20. </span>
again derivating
<span>v"(s) = -(3/2)s </span>
<span>v"(-20) = -(3/2)(-20) </span>
<span>v"(-20) = 30 </span>
<span>v"(20) = -(3/2)(20) </span>
<span>v"(20) = -30 </span>
<span>v(s) = 300s - (1/4)s^3 </span>
<span>v(s) = 300(20) - (1/4)(20)^3 </span>
<span>v(s) = 6000 - (1/4)(8000) </span>
<span>v = 6000 - 2000
v=4000</span>
Answer:
16 years
Step-by-step explanation:
Let x represent the number of years. The suburb population is growing at a rate of 5000 per year after x years, it can be represented by the equation:
320000 + 5000x
The city population is declining at a rate of 14000 per year after x years, it can be represented by the equation:
624000 - 14000x
The number of years for the city and suburb population to be equal can be gotten from:
320000 + 5000x = 624000 - 14000x
14000x + 5000x = 624000 - 320000
19000x = 304000
x = 304000 / 19000
x = 16
In 16 years the populations of the suburb and the city be equal
Answer:
Copy the second line segment with one endpoint at the same endpoint of the first line segment.
c is correct a is wrong
So the problem ask to simplify the trigonometric function in your problem and base on the expression and using the theory in simplifying trigonometric function, the answer would be letter B. 2 sec^2 theta. I hope you are satisfied with my answer and feel free to ask for more
