Answer:
Step-by-step explanation:
We have the equations
4x + 3y = 18 where x = the side of the square and y = the side of the triangle
For the areas:
A = x^2 + √3y/2* y/2
A = x^2 + √3y^2/4
From the first equation x = (18 - 3y)/4
So substituting in the area equation:
A = [ (18 - 3y)/4]^2 + √3y^2/4
A = (18 - 3y)^2 / 16 + √3y^2/4
Now for maximum / minimum area the derivative = 0 so we have
A' = 1/16 * 2(18 - 3y) * -3 + 1/4 * 2√3 y = 0
-3/8 (18 - 3y) + √3 y /2 = 0
-27/4 + 9y/8 + √3y /2 = 0
-54 + 9y + 4√3y = 0
y = 54 / 15.93
= 3.39 metres
So x = (18-3(3.39) / 4 = 1.96.
This is a minimum value for x.
So the total length of wire the square for minimum total area is 4 * 1.96
= 7.84 m
There is no maximum area as the equation for the total area is a quadratic with a positive leading coefficient.
Answer:5
Step-by-step explanation:there are 6 boxes between the top of the 3rd box and the bottom of the 10th box.
Since each box is 10 inches tall, the length of the 6 boxes sum up to 60 inches.
and since 12 inches =1 feet,
Then 60 inches = 5 feet
How to solve
Let "y" = the unknown number of feet's
12 inches = 1 feet
60 inches = y
Cross multiply
> 12×y =60×1
> 12y =60
Divide both sides by 12 since you want the value of "y".
> 12y÷12=60÷12
So 12 cancels out leaving the final answer to be:
> y=5
Answer:
5+√97/4
Also 5-√97/4
Step-by-step explanation:
The Quadratic formula is x=-b+-√b^2-4ac/2a
This means that we should plug the values for A B AND C into the formula
We can work out that
<u><em>A = 2</em></u>
<u><em>B=-5</em></u>
<u><em>C=-9</em></u>
Once we have put these into the formula we get
5+√97/4 (all over 4) aka 3.71
Also 5-√97/4 (all over 4) aka -1.21
what's up? the answer to this is 339+340+341
best of luck with your studies
