√(4×18)= √72 or √36√2= 6√2 simplified
Answer: He will need 1 1/4 cups of butter
Step-by-step explanation:
1. We can do 28/8 to find how much we need to multiply our 1/2 cup of butter to keep the ratio of people to cups of butter the same. 28/8= 3 1/2
2. Then we can multiply 3 1/2 and 1/2 to get 1 1/4 cups of butter.
1. We assume, that the number 432 is 100% - because it's the output value of the task.
<span>2. We assume, that x is the value we are looking for. </span>
<span>3. If 432 is 100%, so we can write it down as 432=100%. </span>
<span>4. We know, that x is 45% of the output value, so we can write it down as x=45%. </span>
5. Now we have two simple equations:
1) 432=100%
2) x=45%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
432/x=100%/45%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for what is 45% of 432
432/x=100/45
<span>(432/x)*x=(100/45)*x - </span>we multiply both sides of the equation by x
<span>432=2.22222222222*x - </span>we divide both sides of the equation by (2.22222222222) to get x
<span>432/2.22222222222=x </span>
<span>194.4=x </span>
x=194.4
<span>now we have: </span>
<span>45% of 432=194.4</span>
Answer:
Length = 225 ft
Width = 150 ft
Step-by-step explanation:
If L is the length and W is the width, then:
900 = 2L + 3W
A = LW
Solve for W in the first equation:
3W = 900 − 2L
W = 300 − ⅔ L
Substitute into the area equation:
A = L (300 − ⅔ L)
A = 300L − ⅔ L²
Use calculus to find dA/dL and set to 0, or use the formula for vertex of a parabola.
Using calculus:
dA/dL = 300 − 4/3 L
0 = 300 − 4/3 L
L = 225
Using vertex formula:
L = -b / (2a)
L = -300 / (-4/3)
L = 225
Find the width:
W = 300 − ⅔ L
W = 150
You got the right answers, but the problem says to assume that the length is greater than the width.
