Answer:
Dimensions are;
2.5 inches height
Base: 10 inches by 10 inches
Max volume; 250 Sq.in
Step-by-step explanation:
Let each side of the square that's cut-off from each corner be represented by x.
This means that the base of the box will be of dimension of the side 15−2x while the height of the box will be x.
Thus;
Volume of box is:
V = (15 − 2x)(15 − 2x)x
V = (15 − 2x)²x
V = (4x² - 60x + 225)x
V = 4x³ - 60x² + 225x
Let's differentiate with respect to x to get;
dV/dx = 12x² - 120x + 225
Maximum value of x is at dV/dx = 0
12x² - 120x + 225 = 0
Using quadratic formula, we arrive at;
x = 2.5 or 7.5
Now, let's find the second derivative of the volume;
d²V/dx² = 24x - 120
Putting x = 2.5 gives;
d²V/dx² = 24(2.5) - 120
d²V/dx² = -60
Thus, V is maximum at x = 2.5, since d²V/dx² is negative
At x = 7.5;
d²V/dx² = 24(7.5) - 120
d²V/dx² = 60
Thus, V is minimum at x = 7.5, since d²V/dx² is negative
Thus,we will use x = 2.5
Maximum volume; V = (15 − 2(2.5))(15 − 2(2.5))(2.5)
V = 10 × 10 × 2.5
V = 250 Sq.inches
Dimensions are;
(15 − 2x) = 15 - 2(2.5) = 10 inches
(15 − 2x) = 15 - 2(2.5) = 10 inches
x = 2.5 inches
Answer:
The mean score in the math test for class B=28.47
Step-by-step explanation:
<em>Step 1: Determine the total number of students in both Classes</em>
Total number of students=number in class A+number in class B
where;
number in class A=11 pupils
number in class B=15 pupils
replacing;
Total number of students=11+15=26 students
<em>Step 2: Determine total score for both classes</em>
Total score for both classes=total score for class A+total score for class B
total score for both classes=mean score for both classes×total number of students
total score for both classes=(49×26)=1,274
total score for class A=mean score for class A×total number of class A students
total score for class A=(77×11)=847
total score for class B=mean score for class B×total number of class B students
total score for class B=m×15=15 m
replacing;
1,274=847+15 m
15 m=1,274-847
15 m=427
m=427/15=28.47
The mean score in the math test for class B=28.47
The average was 34 yards because 35+30+37= 102 then you do 102/3
Least common denominator is (x-1)(x-2) = x²-3x+2.
2x(x-2)/((x-1)(x-2)) - (2x-5)/((x-1)(x-2)) = -3(x-1)/((x-1)(x-2))
2x(x-2) - (2x-5) = -3(x-1)
(2x²-4)-(2x-5) = -3x+1
2x²-2x+1 = -3x+1
2x²+x = 0
x(2x+1) = 0
x = 0,-½