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.
We know that : Sum of Angles in a Triangle is equal to : 180°
⇒ In ΔRST, The Sum of Angles ∠R , ∠S , ∠T should be equal to 180°
⇒ m∠R + m∠S + m∠T = 180°
⇒ (2x + 10)° + (2x + 25)° + (x - 5)° = 180°
⇒ (2x + 2x + x) + (10° + 25° - 5°) = 180°
⇒ 5x + 30° = 180°
⇒ 5x = 180° - 30°
⇒ 5x = 150°
⇒ x = 30°
Answer:
#3) 2/5×2= 4/5 full bucket per one hour.
BD is right but PA is wrong, would be BD and MK.
Answer:
Divide both sides by 9.
Step-by-step explanation:
To find the second step of the equation, we actually have to solve parts of the equation until we get to step 2.
Step 1: Add 23 to both sides.
Step 2: Divide both sides by 9.
Therefore, the second step is divide both sides by 9.
Have a lovely rest of your day/night, and good luck with your assignments! ♡
