Answer:
x = 2 cm
y = 2 cm
A(max) = 4 cm²
Step-by-step explanation: See Annex
The right isosceles triangle has two 45° angles and the right angle.
tan 45° = 1 = x / 4 - y or x = 4 - y y = 4 - x
A(r) = x* y
Area of the rectangle as a function of x
A(x) = x * ( 4 - x ) A(x) = 4*x - x²
Tacking derivatives on both sides of the equation:
A´(x) = 4 - 2*x A´(x) = 0 4 - 2*x = 0
2*x = 4
x = 2 cm
And y = 4 - 2 = 2 cm
The rectangle of maximum area result to be a square of side 2 cm
A(max) = 2*2 = 4 cm²
To find out if A(x) has a maximum in the point x = 2
We get the second derivative
A´´(x) = -2 A´´(x) < 0 then A(x) has a maximum at x = 2
Answer:
162 mL
Step-by-step explanation:
1.Convert all volumes to millilitres
(a) Chlorpheniramine
V = 100 mL
(b) Lidocaine
(c) Banana flavouring
2.Calculate the total volume
Chlorpheniramine = 100 mL
Lidocaine = 59
Banana flavouring = <u> 2.5 </u>
TOTAL = 162 mL
Answer:
Height: 6 feet, Length: 14 feet, Width: 35 feet.
Step-by-step explanation:
The volume of a rectangular prism is length * width * height.
We know that the height of the pool is 6 feet and that one side is 2.5 times longer than the other. It doesn't matter which side, as long it's not the height. So let's just say the width is 2.5 times bigger than the length.
That means our equation can be rewritten as V = height * length* 2.5 * length.
Plugging in what we know, we get:
Now we need to find the width.
<em>x = - 9</em>
- Step-by-step explanation:
<em>6x + 10 = 4x - 8</em>
<em>6x - 4x = - 10 - 8</em>
<em>2x = - 18</em>
<em>x = - 18 : 2</em>
<em>x = - 9</em>
Answer:
B. 1 and -2
Explanation:
First, add up the equations:
x-x+3y+y=4
4y=4
y=1
Now, plug y into any of the original equations above and solve for x:
-x+1=3
-x=2
x=-2
Therefore, the answer is B. 1 and -2
