Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Represent the length of one side of the base be s and the height by h. Then the volume of the box is V = s^2*h; this is to be maximized.
The constraints are as follows: 2s + h = 114 in. Solving for h, we get 114 - 2s = h.
Substituting 114 - 2s for h in the volume formula, we obtain:
V = s^2*(114 - 2s), or V = 114s^2 - 2s^3, or V = 2*(s^2)(57 - s)
This is to be maximized. To accomplish this, find the first derivative of this formula for V, set the result equal to 0 and solve for s:
dV
----- = 2[(s^2)(-1) + (57 - s)(2s)] = 0 = 2s^2(-1) + 114s - 2s^2
ds
Simplifying this, we get dV/ds = -4s^2 + 114s = 0. Then either s = 28.5 or s = 0.
Then the area of the base is 28.5^2 in^2 and the height is 114 - 2(28.5) = 57 in
and the volume is V = s^2(h) = 46,298.25 in^3
When Peter does this, he is creating two sides of a right-angle triangle. The distance from his house to that point will be the hypotenuse of the triangle thus, to work out the length of the hypotenuse, we have to use Pythagoras Theorem! So:
a² + b² = c²
15² + 15² = c²
225 + 225 = c²
450 = c²
15√2 = c
21.21320344 = c
So, this rounded to the nearest tenth would be:
21.2 meters !
Answer:
1=n
Step-by-step explanation:
Step 1- Distribute into the parenthesis.
7(3)+5(3)n= 6n+1(6)+4(6)n
Step 2- Multiply
21+15n= 6n+6+24n
Step 3- Add common variables to simplify.
21+15n= (24n+6n)+6
21+15n= 30n+6
Step 4- Subtract the smallest variable to both sides.
21+15n= 30n+6
-15n -15n
21= 15n+6
Step 5- Subtract 6 to both sides.
21= 15n+6
-6 -6
15= 15n
Step 6- Divide both sides by 15.
<u>15</u>= <u>15n</u>
15 15
1=n
