Answer:
The dimensions that minimize the surface are:
Wide: 1.65 yd
Long: 3.30 yd
Height: 2.20 yd
Step-by-step explanation:
We have a rectangular base, that its twice as long as it is wide.
It must hold 12 yd^3 of debris.
We have to minimize the surface area, subjet to the restriction of volume (12 yd^3).
The surface is equal to:
The volume restriction is:
If we replace h in the surface equation, we have:
To optimize, we derive and equal to zero:
![dS/dw=36(-1)w^{-2} + 8w=0\\\\36w^{-2}=8w\\\\w^3=36/8=4.5\\\\w=\sqrt[3]{4.5} =1.65](https://tex.z-dn.net/?f=dS%2Fdw%3D36%28-1%29w%5E%7B-2%7D%20%2B%208w%3D0%5C%5C%5C%5C36w%5E%7B-2%7D%3D8w%5C%5C%5C%5Cw%5E3%3D36%2F8%3D4.5%5C%5C%5C%5Cw%3D%5Csqrt%5B3%5D%7B4.5%7D%20%3D1.65)
Then, the height h is:
The dimensions that minimize the surface are:
Wide: 1.65 yd
Long: 3.30 yd
Height: 2.20 yd
Answer:
s + 3w = 64
Step-by-step explanation:
s represents the amount of strawberry juice
w represents the amount of water
then,
s + 3w = 64
Answer:
12 is the answer.
Step-by-step explanation:
The best way to get the roots of the equation is to factorize the equation but when the factors are not possible then we should apply the quadratic equations formula to get the value of x.
Now we will try to factorize
x² - 8x -48 = 0
Now we multiply coefficient of highest degree term and constant term
48×1 = 48 which may be factored in 12×4. 8×6, 24×2.
Now we will choose 12×4 out of three because the 12-4 = 8 which is the coefficient of x.
Now its simple.
x²-12x + 4x -48 = 0
x(x -12) + 4(x-12) = 0
(x +4)(x-12) = 0
Therefore roots are x + 4 = 0
x = -4
and x - 12 = 0
x = 12
So the answer is 12.
Answer:
the seventh grader because the eighth graders got 58 which is more than 50 so the 7th grader would get the pts
Step-by-step explanation:
Answer:
BD = 4.99 units
Step-by-step explanation:
Consider the triangle ABD only.
The angle formed is 31 degrees which occurs between two sides that are AD and BC.
We know that for a right angled triangle, the angle can always be taken as an angle between hypotenuse and base.
Thus, The perpendicular sides is then 3 units, where base is BD and Hypotenuse is AD
Using formula for tanθ
tanθ = Perpendicular/Base
tan31 = 3/BD
0.601 = 3/BD
BD = 3/0.601
BD = 4.99 units
