Please help me, 30 points and brainliest
1 answer:
You might be interested in
Given:
l = length of the rectangle
w = width of the rectangle
P = 4 ft, constant perimeter
Because the given perimeter is constant,
2(w + l) = 4
w + l = 2
w = 2 - l (1)
Part A.
The area is
A = w*l
= (2 - l)*l
A = 2l - l²
This is a quadratic function or a parabola.
Part B.
Write the parabola in standard form.
A = -[l² - 2l]
= -[ (l -1)² - 1]
= -(l -1)² + 1
This is a parabola with vertex at (1, 1). Because the leading coefficient is negative the curve is downward, as shown below.
The maximum value occurs at the vertex, so the maximum value of A = 1.
From equation (1), obtain
w = 2 - l = 2 - 1 = 1.
The maximum value of the area occurs when w=1 and l=1 (a square).
Answer:
The area is maximum when l=1 and w=1.
The geometric argument is based on the vertex of the parabola denoting maximum area.
l = length of the rectangle
w = width of the rectangle
P = 4 ft, constant perimeter
Because the given perimeter is constant,
2(w + l) = 4
w + l = 2
w = 2 - l (1)
Part A.
The area is
A = w*l
= (2 - l)*l
A = 2l - l²
This is a quadratic function or a parabola.
Part B.
Write the parabola in standard form.
A = -[l² - 2l]
= -[ (l -1)² - 1]
= -(l -1)² + 1
This is a parabola with vertex at (1, 1). Because the leading coefficient is negative the curve is downward, as shown below.
The maximum value occurs at the vertex, so the maximum value of A = 1.
From equation (1), obtain
w = 2 - l = 2 - 1 = 1.
The maximum value of the area occurs when w=1 and l=1 (a square).
Answer:
The area is maximum when l=1 and w=1.
The geometric argument is based on the vertex of the parabola denoting maximum area.
QUESTION 1.
The factors of 54 are all natural numbers that can divide 54 exactly.
The factors of 54 are: {1,2,3,6,9,18,27,54}
QUESTION 2
The prime factors of 54 are factors of 54 that are prime numbers.
The prime factors of 54 are {2,3}.
Product of prime factors of 54 is
QUESTION 3
All the factors of 60 are all positive integers that divide exactly into 60.
The factors of 60 are {1,2,3,4,5,6,10,12,15,20,30,60}
QUESTION 4
The prime factors of 60 are factors of 60 that are prime numbers.
The prime factors of 60 are {2,3,5}
The prime factorization of 60 is .
QUESTION 5
The factors of 30 are {1,2,3,5,6,10,15,30}
The different ways she can put the beads into the boxes are
,
All 30 beads into one box or 1 bead in 30 boxes.
,
2 beads each into 15 boxes or 15 beads each into 2 boxes
,
3 beads each into 10 boxes or 10 beads each into 3 boxes
,
6 beads each into 5 boxes or 5 beads each into 6 boxes